As datasets continue to grow in size and complexity, finding succinct yet accurate data summaries poses a key challenge. Centroid-based clustering, a widely adopted approach to address this challenge, finds informative summaries of datasets in terms of few prototypes, each representing a cluster in the data. Despite their wide adoption, the resulting data summaries often contain redundancies, limiting their effectiveness particularly in datasets characterized by a large number of underlying clusters. To overcome this limitation, we introduce the Khatri-Rao clustering paradigm that extends traditional centroid-based clustering to produce more succinct but equally accurate data summaries by postulating that centroids arise from the interaction of two or more succinct sets of protocentroids. We study two approaches to centroid-based clustering, the well-established -Means algorithm and the increasingly popular deep clustering, under the lens of the Khatri-Rao paradigm. To this end, we introduce the Khatri-Rao--Means algorithm and the Khatri-Rao deep clustering framework. Extensive experiments show that Khatri-Rao--Means can strike a more favorable trade-off between succinctness and accuracy in data summarization than standard -Means. Leveraging representation learning, the Khatri-Rao deep clustering framework offerseven greater benefits, reducing even more the size of data summaries given by deep clustering while preserving their accuracy

Social and information networks may become polarized, leading to echo chambers and political gridlock. Accurately measuring this phenomenon is a critical challenge. Existing measures often conflate genuine structural division with random topological features, yielding misleadingly high polarization scores on random networks, and failing to distinguish real-world networks from randomized null models. We introduce DSP, a Diffusion-based Structural Polarization measure designed from first principles to correct for such biases. DSP removes the arbitrary concept of 'influencers' used by the popular Random Walk Controversy (RWC) score, instead treating every node as a potential origin for a random walk. To validate our approach, we introduce a set of desirable properties for polarization measures, expressed through reference topologies with known structural properties. We show that DSP satisfies these desiderata, being near-zero for non-polarized structures such as cliques and random networks, while correctly capturing the expected polarization of reference topologies such as monochromatic-splittable networks. Our method applied to U.S. Congress datasets uncovers trends of increasing polarization in recent years. By integrating a null model into its core definition, DSP provides a reliable and interpretable diagnostic tool, highlighting the necessity of statistically-grounded metrics to analyze societal fragmentation.

Link-analysis algorithms, such as PageRank, are instrumental in understanding the structural dynamics of networks by evaluating the importance of individual vertices based on their connectivity. Recently, with the rising importance of responsible AI, the question of fairness in link-analysis algorithms has gained traction.

The directed Steiner tree problem is fundamental in computer science with numerous applications. However, to date, there are no efficient algorithms with quality guarantees. In this paper, we take on this challenge and offer a fast algorithm with provable approximation guarantees. We introduce SpeedSteiner, a O(k1/2)-approximation algorithm, where k is the number of terminal nodes. In practice, SpeedSteiner can be several orders of magnitude faster than other methods with a similar approximation ratio. The speedup is achieved by combining several optimization techniques that exploit the inner structure of recursive-greedy algorithms. We systematically evaluate the proposed algorithm and verify its scalability and strong empirical performance.

Diversification is a useful tool for exploring large collections of information items. It has been used to reduce redundancy and cover multiple perspectives in information-search settings. Diversification finds applications in many different domains, including presenting search results of information-retrieval systems and selecting suggestions for recommender systems.

Content feeds provided by platforms such as X (formerly Twitter) and TikTok are consumed by users on a daily basis. In this paper, we revisit the native advertising problem in content feeds, initiated by Ieong et al. Given a sequence of organic items (e.g., videos or posts) relevant to a user's interests or to an information search, the goal is to place ads within the organic content so as to maximize a reward function (e.g., number of clicks), while accounting for two considerations: (1) an ad can only be inserted after a relevant content item; (2) the users' attention decays after consuming content or ads. These considerations provide a natural model for capturing both the advertisement effectiveness and the user experience. In this paper, we design fast and practical 2-approximation greedy algorithms for the associated optimization problem, improving over the best-known practical algorithm that only achieves an approximation factor of 4. Our algorithms exploit a counter-intuitive observation, namely, while top items are seemingly more important due to the decaying attention of the user, taking good care of the bottom items is key for obtaining improved approximation guarantees. We then provide the first comprehensive empirical evaluation on the problem, showing the strong empirical performance of our~methods.

Data summarization tasks are often modeled as k-clustering problems, where the goal is to choose k data points, called cluster centers, that best represent the dataset by minimizing a clustering objective. A popular objective is to minimize the maximum distance between any data point and its nearest center, which is formalized as the k-center problem. While in some applications all data points can be chosen as centers, in the general setting, centers must be chosen from a predefined subset of points, referred as facilities or suppliers; this is known as the k-supplier problem. In this work, we focus on fair data summarization modeled as the fair k-supplier problem, where data consists of several groups, and a minimum number of centers must be selected from each group while minimizing the k-supplier objective. The groups can be disjoint or overlapping, leading to two distinct problem variants each with different computational complexity.

Abstract Data-analysis tasks often involve an iterative process, which requires refining previous solutions. For instance, when analyzing social networks, we may obtain initial communities based on noisy metadata, and we want to improve them by adding influential nodes and removing non-important ones, without making too many changes. However, classic optimization algorithms, which typically find solutions from scratch, potentially return communities that are very dissimilar to the initial one. To mitigate these issues, we introduce the OptiRefine framework . The framework optimizes initial solutions by making a small number of refinements , thereby ensuring that the new solution remains close to the initial solution and simultaneously achieving a near-optimal solution for the optimization problem. We apply the OptiRefine framework to two classic graph-optimization problems: densest subgraph and maximum cut . For the densest-subgraph problem , we optimize a given subgraph’s density by adding or removing k nodes. We show that this novel problem is a generalization of k -densest subgraph, and provide constant-factor approximation algorithms for $$k=\Omega (n)$$ refinements. We also study a version of maximum cut in which the goal is to improve a given cut. We provide connections to the maximum cut with cardinality constraints and provide an optimal approximation algorithm in most parameter regimes under the Unique Games Conjecture for $$k=\Omega (n)$$ refinements. We evaluate our theoretical methods and scalable heuristics on synthetic and real-world data and show that they are highly effective in practice.

Abstract We study a family of reachability problems under waiting-time restrictions in temporal and vertex-colored temporal graphs. Given a temporal graph and a set of source vertices, we find the set of vertices that are reachable from a source via a time-respecting path, where the difference in timestamps between consecutive edges is at most a resting time. Given a vertex-colored temporal graph and a multiset query of colors, we find the set of vertices reachable from a source via a time-respecting path such that the vertex colors of the path agree with the multiset query and the difference in timestamps between consecutive edges is at most a resting time. These kinds of problems have applications in understanding the spread of a disease in a network, tracing contacts in epidemic outbreaks, finding signaling pathways in the brain network, and recommending tours for tourists, among others. We present an algebraic algorithmic framework based on constrained multilinear sieving for solving the restless reachability problems we propose. In particular, parameterized by the length k of a path sought, we show that the proposed problems can be solved in $$O(2^k k m \Delta )$$ O ( 2 k k m Δ ) time and $$O(n \Delta )$$ O ( n Δ ) space, where n is the number of vertices, m the number of edges, and $$\Delta $$ Δ the maximum resting time of an input temporal graph. The approach can be extended to extract paths and connected subgraphs in both static and temporal graphs, thus improving the work of Björklund et al. (in Proceedings of the European symposium on algorithms, 2014) and Thejaswi et al. (Big Data 8:335–362, 2020). In addition, we prove that our algorithms for the restless reachability problems in vertex-colored temporal graphs are optimal under plausible complexity-theoretic assumptions. Finally, with an open-source implementation, we demonstrate that our algorithm scales to large graphs with up to one billion temporal edges, despite the problems being NP-hard. Specifically, we present extensive experiments to evaluate our scalability claims both on synthetic and on real-world graphs. Our implementation is efficiently engineered and highly optimized. For instance, we can solve the restless reachability problem by restricting the path length to 9 in a real-world graph dataset with over 36 million directed edges in less than one hour on a commodity desktop with a 4-core Haswell CPU.

Characterizing graph properties is fundamental to the analysis and to our understanding of real-world networked systems. The local clustering coefficient , and the more-recent, local closure coefficient , capture powerful properties that are essential in a large number of applications, ranging from graph embeddings to graph partitioning. Such coefficients capture the local density of the neighborhood of each node, considering incident triangle structures and paths of size 2. For this reason, we refer to these coefficients collectively as local triadic coefficients. In this work, we consider the novel and fundamental problem of efficiently computing the average of local triadic coefficients, over a given partition of the nodes of the input graph into a set of disjoint buckets. The average local triadic coefficients of the nodes in each bucket provide a better insight into the interplay of graph structure and the properties of the nodes associated to each bucket. Unfortunately, exact computation, which requires listing all triangles in a graph, is infeasible for large networks. Hence, we focus on obtaining highly-accurate probabilistic estimates. We develop Triad, an adaptive algorithm based on sampling, which can be used to estimate the average local triadic coefficients for a partition of the nodes into buckets. Triad is based on a new class of unbiased estimators, and non-trivial bounds on its sample complexity, enabling the efficient computation of highly accurate estimates. Finally, we show how Triad can be efficiently used in practice on large networks, and we present a case study showing that average local triadic coefficients can capture highorder patterns over collaboration networks.

Today, as increasingly complex predictive models are developed, simple rule sets remain a crucial tool to obtain interpretable predictions and drive high-stakes decision making. However, a single rule set provides a partial representation of a learning task. An emerging paradigm in interpretable machine learning aims at exploring the Rashomon set of all models exhibiting near-optimal performance. Existing work on Rashomon-set exploration focuses on exhaustive search of the Rashomon set for particular classes of models, which can be a computationally challenging task. On the other hand, exhaustive enumeration leads to redundancy that often is not necessary, and a representative sample or an estimate of the size of the Rashomon set is sufficient for many applications. In this work, we propose, for the first time, efficient methods to explore the Rashomon set of rule-set models with or without exhaustive search. Extensive experiments demonstrate the effectiveness of the proposed methods in a variety of scenarios.

Providing recommendations that are both relevant and diverse is a key consideration of modern recommender systems. Optimizing both of these measures presents a fundamental trade-off, as higher diversity typically comes at the cost of relevance, resulting in lower user engagement. Existing recommendation algorithms try to resolve this trade-off by combining the two measures, relevance and diversity, into one aim and then seeking recommendations that optimize the combined objective, for a given number of items to recommend. Traditional approaches, however, do not consider the user interaction with the recommended items. In this paper, we put the user at the central stage, and build on the interplay between relevance, diversity, and user behavior. In contrast to applications where the goal is solely to maximize engagement, we focus on scenarios aiming at maximizing the total amount of knowledge encountered by the user. We use diversity as a surrogate of the amount of knowledge obtained by the user while interacting with the system, and we seek to maximize diversity. We propose a probabilistic user-behavior model in which users keep interacting with the recommender system as long as they receive relevant recommendations, but they may stop if the relevance of the recommended items drops. Thus, for a recommender system to achieve a high-diversity measure, it will need to produce recommendations that are both relevant and diverse. Finally, we propose a novel recommendation strategy that combines relevance and diversity by a copula function. We conduct an extensive evaluation of the proposed methodology over multiple datasets, and we show that our strategy outperforms several state-of-the-art competitors. Our implementation is publicly available at https://github.com/EricaCoppolillo/EXPLORE.

Finding dense subnetworks, with density based on edges or more complex structures, such as subgraphs or k-cliques, is a fundamental algorithmic problem with many applications. While the problem has been studied extensively in static networks, much remains to be explored for temporal networks.

Integrity 2024 is the fifth edition of the Workshop on Integrity in Social Networks and Media, held in conjunction with the ACM Conference on Web Search and Data Mining (WSDM) since the 2020 edition [1-4]. The goal of the workshop is to bring together academic and industry researchers working on integrity, fairness, trust and safety in social networks to discuss the most pressing risks and cutting-edge technologies to reliably measure and mitigate them. The event consists of invited talks from academic experts and industry leaders as well as peer-reviewed papers and posters through an open call-for-papers.

We consider a variant of the densest subgraph problem in networks with single or multiple edge attributes. For example, in a social network, the edge attributes may describe the type of relationship between users, such as friends, family, or acquaintances, or different types of communication. For conceptual simplicity, we view the attributes as edge colors. The new problem we address is to find a diverse densest subgraph that fulfills given requirements on the numbers of edges of specific colors. When searching for a dense social network community, our problem will enforce the requirement that the community is diverse according to criteria specified by the edge attributes. We show that the decision versions for finding exactly, at most, and at least h colored edges densest subgraph, where h is a vector of color requirements, are NP-complete, for already two colors. For the problem of finding a densest subgraph with at least h colored edges, we provide a linear-time constant-factor approximation algorithm when the input graph is sparse. On the way, we introduce the related at least h (non-colored) edges densest subgraph problem, show its hardness, and also provide a linear-time constant-factor approximation. In our experiments, we demonstrate the efficacy and efficiency of our new algorithms.

Timeline algorithms are key parts of online social networks, but during recent years they have been blamed for increasing polarization and disagreement in our society. Opinion-dynamics models have been used to study a variety of phenomena in online social networks, but an open question remains on how thesemodels can be augmented to take into account the fine-grained impact of user-level timeline algorithms. We make progress on this question by providing a way to model the impact of timeline algorithms on opinion dynamics. Specifically, we show how the popular Friedkin--Johnsen opinion-formation model can be augmented based on aggregate information, extracted from timeline data. We use our model to study the problem of minimizing the polarization and disagreement; we assume that we are allowed to make small changes to the users' timeline compositions by strengthening some topics of discussion and penalizing some others. We present a gradient descent-based algorithm for this problem, and show that under realistic parameter settings, our algorithm computes a (1+\varepsilon)-approximate solution in time~\tO(m\sqrtn łg(1/\varepsilon)), where m~is the number of edges in the graph and n~is the number of vertices. We also present an algorithm that provably computes an \varepsilon-approximation of our model in near-linear time. We evaluate our method on real-world data and show that it effectively reduces the polarization and disagreement in the network. Finally, we release an anonymized graph dataset with ground-truth opinions and more than 27\,000~nodes (the previously largest publicly available dataset contains less than 550~nodes).

Abstract We introduce the Hadamard decomposition problem in the context of data analysis. The problem is to represent exactly or approximately a given matrix as the Hadamard (or element-wise) product of two or more low-rank matrices. The motivation for this problem comes from situations where the input matrix has a multiplicative structure. The Hadamard decomposition has potential for giving more succint but equally accurate representations of matrices when compared with the gold-standard of singular value decomposition (svd). Namely, the Hadamard product of two rank- $$h$$ h matrices can have rank as high as $${h}^2$$ h 2 . We study the computational properties of the Hadamard decomposition problem and give gradient-based algorithms for solving it approximately. We also introduce a mixed model that combines svd and Hadamard decomposition. We present extensive empirical results comparing the approximation accuracy of the Hadamard decomposition with that of the svd using the same number of basis vectors. The results demonstrate that the Hadamard decomposition is competitive with the svd and, for some datasets, it yields a clearly higher approximation accuracy, indicating the presence of multiplicative structure in the data.

Social media have great potential for enabling public discourse on important societal issues. However, adverse effects, such as polarization and echo chambers, greatly impact the benefits of social media and call for algorithms that mitigate these effects. In this paper, we propose a novel problem formulation aimed at slightly nudging users' social feeds in order to strike a balance between relevance and diversity, thus mitigating the emergence of polarization, without lowering the quality of the feed. Our approach is based on re-weighting the relative importance of the accounts that a user follows, so as to calibrate the frequency with which the content produced by various accounts is shown to the user.

One of the most fundamental tasks in data science is to assist a user with unknown preferences in finding high-utility tuples within a large database. To accurately elicit the unknown user preferences, a widely-adopted way is by asking the user to compare pairs of tuples. In this paper, we study the problem of identifying one or more high-utility tuples by adaptively receiving user input on a minimum number of pairwise comparisons. We devise a single-pass streaming algorithm, which processes each tuple in the stream at most once, while ensuring that the memory size and the number of requested comparisons are in the worst case logarithmic in n, where n is the number of all tuples. An important variant of the problem, which can help to reduce human error in comparisons, is to allow users to declare ties when confronted with pairs of tuples of nearly equal utility. We show that the theoretical guarantees of our method can be maintained for this important problem variant. In addition, we show how to enhance existing pruning techniques in the literature by leveraging powerful tools from mathematical programming. Finally, we systematically evaluate all proposed algorithms over both synthetic and real-life datasets, examine their scalability, and demonstrate their superior performance over existing methods.

Structural bias or segregation of networks refers to situations where two or more disparate groups are present in the network, so that the groups are highly connected internally, but loosely connected to each other. Examples include polarized communities in social networks, antagonistic content in video-sharing or news-feed platforms, etc. In many cases it is of interest to increase the connectivity of disparate groups so as to, e.g., minimize social friction, or expose individuals to diverse viewpoints. A commonly-used mechanism for increasing the network connectivity is to add edge shortcuts between pairs of nodes. In many applications of interest, edge shortcuts typically translate to recommendations, e.g., what video to watch, or what news article to read next. The problem of reducing structural bias or segregation via edge shortcuts has recently been studied in the literature, and random walks have been an essential tool for modeling navigation and connectivity in the underlying networks. Existing methods, however, either do not offer approximation guarantees, or engineer the objective so that it satisfies certain desirable properties that simplify the optimization task.

Most media content consumed today is provided by digital platforms that aggregate input from diverse sources, where access to information is mediated by recommendation algorithms. One principal challenge in this context is dealing with content that is considered harmful. Striking a balance between competing stakeholder interests, rather than block harmful content altogether, one approach is to minimize the exposure to such content that is induced specifically by algorithmic recommendations. Hence, modeling media items and recommendations as a directed graph, we study the problem of reducing the exposure to harmful content via edge rewiring. We formalize this problem using absorbing random walks, and prove that it is NP-hard and NP-hard to approximate to within an additive error, while under realistic assumptions, the greedy method yields a (1-1/e)-approximation. Thus, we introduce Gamine, a fast greedy algorithm that can reduce the exposure to harmful content with or without quality constraints on recommendations. By performing just 100 rewirings on YouTube graphs with several hundred thousand edges, Gamine reduces the initial exposure by 50%, while ensuring that its recommendations are at most 5% less relevant than the original recommendations. Through extensive experiments on synthetic data and real-world data from video recommendation and news feed applications, we confirm the effectiveness, robustness, and efficiency of Gamine in practice.

In recent years, online social networks have been the target of adversaries who seek to introduce discord into societies, to undermine democracies and to destabilize communities. Often the goal is not to favor a certain side of a conflict but to increase disagreement and polarization. To get a mathematical understanding of such attacks, researchers use opinion-formation models from sociology, such as the Friedkin--Johnsen model, and formally study how much discord the adversary can produce when altering the opinions for only a small set of users. In this line of work, it is commonly assumed that the adversary has full knowledge about the network topology and the opinions of all users. However, the latter assumption is often unrealistic in practice, where user opinions are not available or simply difficult to estimate accurately.

Maximizing submodular functions have been studied extensively for a wide range of subset-selection problems. However, much less attention has been given to the role of submodularity in sequence-selection and ranking problems. A recently- introduced framework, named maximum submodular ranking (MSR), tackles a family of ranking problems that arise naturally when resources are shared among multiple demands with different budgets. For example, the MSR framework can be used to rank web pages for multiple user intents. In this paper, we extend the MSR framework in the streaming setting. In particular, we consider two different streaming models and we propose practical approximation algorithms. In the first streaming model, called function arriving, we assume that submodular functions (demands) arrive continuously in a stream, while in the second model, called item arriving, we assume that items (resources) arrive continuously. Furthermore, we study the MSR problem with additional constraints on the output sequence, such as a matroid constraint that can ensure fair exposure among items from different groups. These extensions significantly broaden the range of problems that can be captured by the MSR framework. On the practical side, we develop several novel applications based on the MSR formulation, and empirically evaluate the performance of the proposed methods.

Decision trees are popular classification models, providing high accuracy and intuitive explanations. However, as the tree size grows the model interpretability deteriorates. Traditional tree-induction algorithms, such as C4.5 and CART, rely on impurity-reduction functions that promote the discriminative power of each split. Thus, although these traditional methods are accurate in practice, there has been no theoretical guarantee that they will produce small trees. In this paper, we justify the use of a general family of impurity functions, including the popular functions of entropy and Gini-index, in scenarios where small trees are desirable, by showing that a simple enhancement can equip them with complexity guarantees. We consider a general setting, where objects to be classified are drawn from an arbitrary probability distribution, classification can be binary or multi-class, and splitting tests are associated with non-uniform costs. As a measure of tree complexity, we adopt the expected cost to classify an object drawn from the input distribution, which, in the uniform-cost case, is the expected number of tests. We propose a tree-induction algorithm that gives a logarithmic approximation guarantee on the tree complexity. This approximation factor is tight up to a constant factor under mild assumptions. The algorithm recursively selects a test that maximizes a greedy criterion defined as a weighted sum of three components. The first two components encourage the selection of tests that improve the balance and the cost-efficiency of the tree, respectively, while the third impurity-reduction component encourages the selection of more discriminative tests. As shown in our empirical evaluation, compared to the original heuristics, the enhanced algorithms strike an excellent balance between predictive accuracy and tree complexity.

Abstract Multi-label classification is becoming increasingly ubiquitous, but not much attention has been paid to interpretability. In this paper, we develop a multi-label classifier that can be represented as a concise set of simple “if-then” rules, and thus, it offers better interpretability compared to black-box models. Notably, our method is able to find a small set of relevant patterns that lead to accurate multi-label classification, while existing rule-based classifiers are myopic and wasteful in searching rules, requiring a large number of rules to achieve high accuracy. In particular, we formulate the problem of choosing multi-label rules to maximize a target function, which considers not only discrimination ability with respect to labels, but also diversity. Accounting for diversity helps to avoid redundancy, and thus, to control the number of rules in the solution set. To tackle the said maximization problem, we propose a 2-approximation algorithm, which circumvents the exponential-size search space of rules using a novel technique to sample highly discriminative and diverse rules. In addition to our theoretical analysis, we provide a thorough experimental evaluation and a case study, which indicate that our approach offers a trade-off between predictive performance and interpretability that is unmatched in previous work.

Bayesian networks are popular probabilistic models that capture the conditional dependencies among a set of variables. Inference in Bayesian networks is a fundamental task for answering probabilistic queries over a subset of variables in the data. However, exact inference in Bayesian networks is NP-hard, which has prompted the development of many practical inference methods. In this paper, we focus on improving the performance of the junction-tree algorithm, a well-known method for exact inference in Bayesian networks. In particular, we seek to leverage information in the workload of probabilistic queries to obtain an optimal workload-aware materialization of junction trees, with the aim to accelerate the processing of inference queries. We devise an optimal pseudo-polynomial algorithm to tackle this problem and discuss approximation schemes. Compared to state-of-the-art approaches for efficient processing of inference queries via junction trees, our methods are the first to exploit the information provided in query workloads. Our experimentation on several real-world Bayesian networks confirms the effectiveness of our techniques in speeding-up query processing.

In recent years we have witnessed an increase on the development of methods for submodular optimization, which have been motivated by the wide applicability of submodular functions in real-world data-science problems. In this paper, we contribute to this line of work by considering the problem of robust submodular maximization against unexpected deletions, which may occur due to privacy issues or user preferences. Specifically, we consider the minimum number of items an algorithm has to remember, in order to achieve a non-trivial approximation guarantee against adversarial deletion of up to d items. We refer to the set of items that an algorithm has to keep before adversarial deletions as a deletion-robust coreset.Our theoretical contributions are two-fold. First, we propose a single- pass streaming algorithm that yields a(1-2$\epsilon$)/(4 p)-approximation for maximizing a non-decreasing submodular function under a general p-matroid constraint and requires a coreset of size k+ d/$\epsilon$, where k is the maximum size of a feasible solution. To the best of our knowledge, this is the first work to achieve an (asymptotically) optimal coreset, as no constant-factor approximation is possible with a coreset of size sublinear in $d.$ Second, we devise an effective offline algorithm that guarantees stronger approximation ratios with a coreset of size $O(d\log(k)/\epsilon)$. We also demonstrate the superior empirical performance of the proposed algorithms in real-life applications.

We consider the problem of adding a fixed number of new edges to an undirected graph in order to minimize the diameter of the augmented graph, and under the constraint that the number of edges added for each vertex is bounded by an integer. The problem is motivated by network-design applications, where we want to minimize the worst case communication in the network without excessively increasing the degree of any single vertex, so as to avoid additional overload. We present three algorithms for this task, each with their own merits. The special case of a matching augmentation -when every vertex can be incident to at most one new edge-is of particular interest, for which we show an inapproximability result, and provide bounds on the smallest achievable diameter when these edges are added to a path. Finally, we empirically evaluate and compare our algorithms on several real-life networks of varying types.

Multi-label classification is becoming increasingly ubiquitous, but not much attention has been paid to interpretability. In this paper, we develop a multi-label classifier that can be represented as a concise set of simple “if-then” rules, and thus, it offers better interpretability compared to black-box models. Notably, our method is able to find a small set of relevant patterns that lead to accurate multi-label classification, while existing rule-based classifiers are myopic and wasteful in searching rules, requiring a large number of rules to achieve high accuracy. In particular, we formulate the problem of choosing multi-label rules to maximize a target function, which considers not only discrimination ability with respect to labels, but also diversity. Accounting for diversity helps to avoid redundancy, and thus, to control the number of rules in the solution set. To tackle the said maximization problem we propose a 2-approximation algorithm, which relies on a novel technique to sample high-quality rules. In addition to our theoretical analysis, we provide a thorough experimental evaluation, which indicates that our approach offers a trade-off between predictive performance and interpretability that is unmatched in previous work.

Can we get speech recognition tools to work on limited-memory devices? The Viterbi algorithm is a classic dynamic programming (DP) solution used to find the most likely sequence of hidden states in a Hidden Markov Model (HMM). While the algorithm finds universal application ranging from communication systems to speech recognition to bioinformatics, its scalability has been scarcely addressed, stranding it to a space complexity that grows with the number of observations.

Abstract Online social networks provide a forum where people make new connections, learn more about the world, get exposed to different points of view, and access information that were previously inaccessible. It is natural to assume that content-delivery algorithms in social networks should not only aim to maximize user engagement but also to offer opportunities for increasing connectivity and enabling social networks to achieve their full potential. Our motivation and aim is to develop methods that foster the creation of new connections, and subsequently, improve the flow of information in the network. To achieve our goal, we propose to leverage the strong triadic closure principle, and consider violations to this principle as opportunities for creating more social links. We formalize this idea as an algorithmic problem related to the densest k-subgraph problem. For this new problem, we establish hardness results and propose approximation algorithms. We identify two special cases of the problem that admit a constant-factor approximation. Finally, we experimentally evaluate our proposed algorithm on real-world social networks, and we additionally evaluate some simpler but more scalable algorithms.

When searching for information in a data collection, we are often interested not only in finding relevant items, but also in assembling a diverse set, so as to explore different concepts that are present in the data. This problem has been researched extensively. However, finding a set of items with minimal pairwise similarities can be computationally challenging, and most existing works striving for quality guarantees assume that item relatedness is measured by a distance function. Given the widespread use of similarity functions in many domains, we believe this to be an important gap in the literature. In this paper we study the problem of finding a diverse set of items, when item relatedness is measured by a similarity function. We formulate the diversification task using a flexible, broadly applicable minimization objective, consisting of the sum of pairwise similarities of the selected items and a relevance penalty term. To find good solutions we adopt a randomized rounding strategy, which is challenging to analyze because of the cardinality constraint present in our formulation. Even though this obstacle can be overcome using dependent rounding, we show that it is possible to obtain provably good solutions using an independent approach, which is faster, simpler to implement and completely parallelizable. Our analysis relies on a novel bound for the ratio of Poisson-Binomial densities, which is of independent interest and has potential implications for other combinatorial-optimization problems. We leverage this result to design an efficient randomized algorithm that provides a lower-order additive approximation guarantee. We validate our method using several benchmark datasets, and show that it consistently outperforms the greedy approaches that are commonly used in the literature.

Abstract Submodular maximization has been the backbone of many important machine-learning problems, and has applications to viral marketing, diversification, sensor placement, and more. However, the study of maximizing submodular functions has mainly been restricted in the context of selecting a set of items. On the other hand, many real-world applications require a solution that is a ranking over a set of items. The problem of ranking in the context of submodular function maximization has been considered before, but to a much lesser extent than item-selection formulations. In this paper, we explore a novel formulation for ranking items with submodular valuations and budget constraints. We refer to this problem asmax-submodular ranking( $$\text {MSR}$$ MSR ). In more detail, given a set of items and a set of non-decreasing submodular functions, where each function is associated with a budget, we aim to find a ranking of the set of items that maximizes the sum of values achieved by all functions under the budget constraints. For the $$\text {MSR}$$ MSR problem with cardinality- and knapsack-type budget constraints we propose practical algorithms with approximation guarantees. In addition, we perform an empirical evaluation, which demonstrates the superior performance of the proposed algorithms against strong baselines.

Distance oracles answer shortest-path queries between any pair of nodes in a graph. They are often built using succinct graph representations such as spanners, sketches, and compressors to minimize oracle size and query answering latency. Node embeddings, in particular, offer graph representations that place adjacent nodes nearby each other in a low-rank space. However, their use in the design of distance oracles has not been sufficiently studied. In this paper, we empirically compare exact distance oracles constructed based on a variety of node embeddings and other succinct representations. We evaluate twelve such oracles along three measures of efficiency: construction time, memory requirements, and query-processing time over fourteen real datasets and four synthetic graphs. We show that distances between embedding vectors are excellent estimators of graph distances when graphs are well-structured, but less so for more unstructured graphs. Overall, our findings suggest that exact oracles based on embeddings can be constructed faster than multi-dimensional scaling (MDS) but slower than compressed adjacency indexes, require less memory than landmark oracles but more than sparsifiers or indexes, can answer queries faster than indexes but slower than MDS, and are exact more often with a smaller additive error than spanners (that have multiplicative error) while not being lossless like adjacency lists. Finally, while the exactness of such oracles is infeasible to maintain for huge graphs even under large amounts of resources, we empirically demonstrate that approximate oracles based on GOSH embeddings can efficiently scale to graphs of 100M+ nodes with only small additive errors in distance estimations.

Social-media platforms have created new ways for citizens to stay informed and participate in public debates. However, to enable a healthy environment for information sharing, social deliberation, and opinion formation, citizens need to be exposed to sufficiently diverse viewpoints that challenge their assumptions, instead of being trapped inside filter bubbles. In this paper, we take a step in this direction and propose a novel approach to maximize the diversity of exposure in a social network. We formulate the problem in the context of information propagation, as a task of recommending a small number of news articles to selected users. In the proposed setting, we take into account content and user leanings, and the probability of further sharing an article. Our model allows to capture the balance between maximizing the spread of information and ensuring the exposure of users to diverse viewpoints. The resulting problem can be cast as maximizing a monotone and submodular function, subject to a matroid constraint on the allocation of articles to users. It is a challenging generalization of the influence-maximization problem. Yet, we are able to devise scalable approximation algorithms by introducing a novel extension to the notion of random reverse-reachable sets. We experimentally demonstrate the efficiency and scalability of our algorithm on several real-world datasets.

Bayesian networks are general, well-studied probabilistic models that capture dependencies among a set of variables. Variable Elimination is a fundamental algorithm for probabilistic inference over Bayesian networks. In this paper, we propose a novel materialization method, which can lead to significant efficiency gains when processing inference queries using the Variable Elimination algorithm. In particular, we address the problem of choosing a set of intermediate results to precompute and materialize, so as to maximize the expected efficiency gain over a given query workload. For the problem we consider, we provide an optimal polynomial-time algorithm and discuss alternative methods. We validate our technique using real-world Bayesian networks. Our experimental results confirm that a modest amount of materialization can lead to significant improvements in the running time of queries, with an average gain of 70%, and reaching up to a gain of 99%, for a uniform workload of queries. Moreover, in comparison with existing junction tree methods that also rely on materialization, our approach achieves competitive efficiency during inference using significantly lighter materialization.

Mining human-brain networks to discover patterns that can be used to discriminate between healthy individuals and patients affected by some neurological disorder, is a fundamental task in neuro-science. Learning simple and interpretable models is as important as mere classification accuracy. In this paper we introduce a novel approach for classifying brain networks based on extracting contrast subgraphs, i.e., a set of vertices whose induced subgraphs are dense in one class of graphs and sparse in the other. We formally define the problem and present an algorithmic solution for extracting contrast subgraphs. We then apply our method to a brain-network dataset consisting of children affected by Autism Spectrum Disorder and children Typically Developed. Our analysis confirms the interestingness of the discovered patterns, which match background knowledge in the neuro-science literature. Further analysis on other classification tasks confirm the simplicity, soundness, and high explainability of our proposal, which also exhibits superior classification accuracy, to more complex state-of-the-art methods.

While machine-learning models are flourishing and transforming many aspects of everyday life, the inability of humans to understand complex models poses difficulties for these models to be fully trusted and embraced. Thus, interpretability of models has been recognized as an equally important quality as their predictive power. In particular, rule-based systems are experiencing a renaissance owing to their intuitive if-then representation.

Understanding the local structure of a graph provides valuable insights about the underlying phenomena from which the graph has originated. Sampling and examining k-subgraphs is a widely used approach to understand the local structure of a graph. In this paper, we study the problem of sampling uniformly k-subgraphs from a given graph. We analyse a few different Markov chain Monte Carlo (MCMC) approaches, and obtain analytical results on their mixing times, which improve significantly the state of the art. In particular, we improve the bound on the mixing times of the standard MCMC approach, and the state-of-the-art MCMC sampling method PSRW, using the canonical-paths argument. In addition, we propose a novel sampling method, which we call recursive subgraph sampling RSS, and its optimized variant RSS'. The proposed methods, RSS and RSS', are provably faster than the existing approaches. We conduct experiments and verify the uniformity of samples and the efficiency of RSS and RSS'.

In this paper, we study a family of pattern-detection problems in vertex-colored temporal graphs. In particular, given a vertex-colored temporal graph and a multi-set of colors as a query, we search for temporal paths in the graph that contain the colors specified in the query. These types of problems have several interesting applications, for example, recommending tours for tourists, or searching for abnormal behavior in a network of financial transactions. For the family of pattern-detection problems we define, we establish complexity results and design an algebraic-algorithmic framework based on constrained multilinear sieving. We demonstrate that our solution can scale to massive graphs with up to hundred million edges, despite the problems being NP-hard. Our implementation, which is publicly available, exhibits practical edge-linear scalability and highly optimized. For example, in a real-world graph dataset with more than six million edges and a multi-set query with ten colors, we can extract an optimal solution in less than eight minutes on a haswell desktop with four cores.

Maximum diversity aims at selecting a diverse set of high-quality objects from a collection, which is a fundamental problem and has a wide range of applications, e.g., in Web search. Diversity under a uniform or partition matroid constraint naturally describes useful cardinality or budget requirements, and admits simple approximation algorithms [5]. When applied to clustered data, however, popular algorithms such as picking objects iteratively and performing local search lose their approximation guarantees towards maximum intra-cluster diversity because they fail to optimize the objective in a global manner. We propose an algorithm that greedily adds a pair of objects instead of a singleton, and which attains a constant approximation factor over clustered data. We further extend the algorithm to the case of monotone and submodular quality function, and under a partition matroid constraint. We also devise a technique to make our algorithm scalable, and on the way we obtain a modification that gives better solutions in practice while maintaining the approximation guarantee in theory. Our algorithm achieves excellent performance, compared to strong baselines in a mix of synthetic and real-world datasets.

The first Workshop on Integrity in Social Networks and Media is held in conjunction with the 13th ACM Conference on Web Search and Data Mining (WSDM) in Houston, Texas, USA. The goal of the workshop is to bring together researchers and practitioners to discuss content and interaction integrity challenges in social networks and social media platforms.

Signed networks are graphs whose edges are labelled with either a positive or a negative sign, and can be used to capture nuances in interactions that are missed by their unsigned counterparts. The concept of balance in signed graph theory determines whether a network can be partitioned into two perfectly opposing subsets, and is therefore useful for modelling phenomena such as the existence of polarized communities in social networks. While determining whether a graph is balanced is easy, finding a large balanced subgraph is hard. The few heuristics available in the literature for this purpose are either ineffective or non-scalable. In this paper we propose an efficient algorithm for finding large balanced subgraphs in signed networks. The algorithm relies on signed spectral theory and a novel bound for perturbations of the graph Laplacian. In a wide variety of experiments on real-world data we show that our algorithm can find balanced subgraphs much larger than those detected by existing methods, and in addition, it is faster. We test its scalability on graphs of up to 34 million edges.

Signed graphs have been used to model interactions in social networks, which can be either positive (friendly) or negative (antagonistic). The model has been used to study polarization and other related phenomena in social networks, which can be harmful to the process of democratic deliberation in our society. An interesting and challenging task in this application domain is to detect polarized communities in signed graphs. A number of different methods have been proposed for this task. However, existing approaches aim at finding globally optimal solutions. Instead, in this paper we are interested in finding polarized communities that are related to a small set of seed nodes provided as input. Seed nodes may consist of two sets, which constitute the two sides of a polarized structure.

Abstract Social networks often provide only a binary perspective on social ties: two individuals are either connected or not. While sometimes external information can be used to infer thestrengthof social ties, access to such information may be restricted or impractical to obtain. Sintos and Tsaparas (KDD 2014) first suggested to infer the strength of social ties from the topology of the network alone, by leveraging theStrong Triadic Closure(STC) property. The STC property states that if personAhas strong social ties with personsBandC,BandCmust be connected to each other as well (whether with a weak or strong tie). They exploited this property to formulate the inference of the strength of social ties as a NP-hard maximization problem, and proposed two approximation algorithms. We refine and improve this line of work, by developing a sequence of linear relaxations of the problem, which can be solved exactly in polynomial time. Usefully, these relaxations infer more fine-grained levels of tie strength (beyond strong and weak), which also allows one to avoid making arbitrary strong/weak strength assignments when the network topology provides inconclusive evidence. Moreover, these relaxations allow us to easily change the objective function to more sensible alternatives, instead of simply maximizing the number of strong edges. An extensive theoretical analysis leads to two efficient algorithmic approaches. Finally, our experimental results elucidate the strengths of the proposed approach, while at the same time questioning the validity of leveraging the STC property for edge strength inference in practice.

Time series classification has received great attention over the past decade with a wide range of methods focusing on predictive performance by exploiting various types of temporal features. Nonetheless, little emphasis has been placed on interpretability and explainability. In this paper, we formulate the novel problem of explainable time series tweaking, where, given a time series and an opaque classifier that provides a particular classification decision for the time series, we want to find the changes to be performed to the given time series so that the classifier changes its decision to another class. We show that the problem is \({\mathbf {NP}}\) -hard, and focus on three instantiations of the problem using global and local transformations. In the former case, we investigate the k -nearest neighbor classifier and provide an algorithmic solution to the global time series tweaking problem. In the latter case, we investigate the random shapelet forest classifier and focus on two instantiations of the local time series tweaking problem, which we refer to as reversible and irreversible time series tweaking, and propose two algorithmic solutions for the two problems along with simple optimizations. An extensive experimental evaluation on a variety of real datasets demonstrates the usefulness and effectiveness of our problem formulation and solutions.

Abstract Social media have a great potential to improve information dissemination in our society, yet they have been held accountable for a number of undesirable effects, such as polarization and filter bubbles. It is thus important to understand these negative phenomena and develop methods to combat them. In this paper, we propose a novel approach to address the problem of breaking filter bubbles in social media. We do so by aiming to maximize the diversity of the information exposed to connected social-media users. We formulate the problem of maximizing the diversity of exposure as a quadratic-knapsack problem. We show that the proposed diversity-maximization problem is inapproximable, and thus, we resort to polynomial nonapproximable algorithms, inspired by solutions developed for the quadratic-knapsack problem, as well as scalable greedy heuristics. We complement our algorithms with instance-specific upper bounds, which are used to provide empirical approximation guarantees for the given problem instances. Our experimental evaluation shows that a proposed greedy algorithm followed by randomized local search is the algorithm of choice given its quality-vs.-efficiency trade-off.

Abstract In this paper, we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity. We formulate the event discovery task as an optimization problem, where we search for a partition of the network timeline into k non-overlapping intervals, such that the intervals span subgraphs with maximum total density. The output is a sequence of dense subgraphs along with corresponding time intervals, capturing the most interesting events during the network lifetime. A naïve solution to our optimization problem has polynomial but prohibitively high running time. We adapt existing recent work on dynamic densest subgraph discovery and approximate dynamic programming to design a fast approximation algorithm. Next, to ensure richer structure, we adjust the problem formulation to encourage coverage of a larger set of nodes. This problem is NP-hard; however, we show that on static graphs a simple greedy algorithm leads to approximate solution due to submodularity. We extend this greedy approach for temporal networks, but we lose the approximation guarantee in the process. Finally, we demonstrate empirically that our algorithms recover solutions with good quality.

Cycles in graphs often signify interesting processes. For example, cyclic trading patterns can indicate inefficiencies or economic dependencies in trade networks, cycles in food webs can identify fragile dependencies in ecosystems, and cycles in financial transaction networks can be an indication of money laundering. Identifying such interesting cycles, which can also be constrained to contain a given set of query nodes, although not extensively studied, is thus a problem of considerable importance. In this paper, we introduce the problem of discovering interesting cycles in graphs. We first address the problem of quantifying the extent to which a given cycle is interesting for a particular analyst. We then show that finding cycles according to this interestingness measure is related to the longest cycle and maximum mean-weight cycle problems (in the unconstrained setting) and to the maximum Steiner cycle and maximum mean Steiner cycle problems (in the constrained setting). A complexity analysis shows that finding interesting cycles is NP-hard, and is NP-hard to approximate within a constant factor in the unconstrained setting, and within a factor polynomial in the input size for the constrained setting. The latter inapproximability result implies a similar result for the maximum Steiner cycle and maximum mean Steiner cycle problems. Motivated by these hardness results, we propose a number of efficient heuristic algorithms. We verify the effectiveness of the proposed methods and demonstrate their practical utility on two real-world use cases: a food web and an international trade-network dataset.

Signed networks contain edge annotations to indicate whether each interaction is friendly (positive edge) or antagonistic (negative edge). The model is simple but powerful and it can capture novel and interesting structural properties of real-world phenomena. The analysis of signed networks has many applications from modeling discussions in social media, to mining user reviews, and to recommending products in e-commerce sites. In this paper we consider the problem of discovering polarized communities in signed networks. In particular, we search for two communities (subsets of the network vertices) where within communities there are mostly positive edges while across communities there are mostly negative edges. We formulate this novel problem as a "discrete eigenvector'' problem, which we show to be NP-hard. We then develop two intuitive spectral algorithms: one deterministic, and one randomized with quality guarantee $\sqrtn $ (where n is the number of vertices in the graph), tight up to constant factors. We validate our algorithms against non-trivial baselines on real-world signed networks. Our experiments confirm that our algorithms produce higher quality solutions, are much faster and can scale to much larger networks than the baselines, and are able to detect ground-truth polarized communities.

Networks (or graphs) are used to represent and analyze large datasets of objects and their relations. Naturally, real-world networks have a temporal component: for instance, interactions between objects have a timestamp and a duration. In this tutorial we present models and algorithms for mining temporal networks, i.e., network data with temporal information. We overview different models used to represent temporal networks. We highlight the main differences between static and temporal networks, and discuss the challenges arising from introducing the temporal dimension in the network representation. We present recent papers addressing the most well-studied problems in the setting of temporal networks, including computation of centrality measures, motif detection and counting, community detection and monitoring, event and anomaly detection, analysis of epidemic processes and influence spreading, network summarization, and structure prediction.

We propose a new variant of the k-median problem, where the objective function models not only the cost of assigning data points to cluster representatives, but also a penalty term for disagreement among the representatives. We motivate this novel problem by applications where we are interested in clustering data while avoiding selecting representatives that are too far from each other. For example, we may want to summarize a set of news sources, but avoid selecting ideologically-extreme articles in order to reduce polarization.

Given a labeled graph, the frequent-subgraph mining (FSM) problem asks to find all the k-vertex subgraphs that appear with frequency greater than a given threshold. FSM has numerous applications ranging from biology to network science, as it provides a compact summary of the characteristics of the graph. However, the task is challenging, even more so for evolving graphs due to the streaming nature of the input and the exponential time complexity of the problem.

Social-media platforms have created new ways for citizens to stay informed and participate in public debates. However, to enable a healthy environment for information sharing, social deliberation, and opinion formation, citizens need to be exposed to sufficiently diverse viewpoints that challenge their assumptions, instead of being trapped inside filter bubbles. In this paper, we take a step in this direction and propose a novel approach to maximize the diversity of exposure in a social network. We formulate the problem in the context of information propagation, as a task of recommending a small number of news articles to selected users. We propose a realistic setting where we take into account content and user leanings, and the probability of further sharing an article. This setting allows us to capture the balance between maximizing the spread of information and ensuring the exposure of users to diverse viewpoints. The resulting problem can be cast as maximizing a monotone and submodular function subject to a matroid constraint on the allocation of articles to users. It is a challenging generalization of the influence maximization problem. Yet, we are able to devise scalable approximation algorithms by introducing a novel extension to the notion of random reverse-reachable sets. We experimentally demonstrate the efficiency and scalability of our algorithm on several real-world datasets.

Time series classification has received great attention over the past decade with a wide range of methods focusing on predictive performance by exploiting various types of temporal features. Nonetheless, little emphasis has been placed on interpretability and explainability. In this paper, we formulate the novel problem of explainable time series tweaking, where, given a time series and an opaque classifier that provides a particular classification decision for the time series, we want to find the minimum number of changes to be performed to the given time series so that the classifier changes its decision to another class. We show that the problem is NP-hard, and focus on two instantiations of the problem, which we refer to as reversible and irreversible time series tweaking. The classifier under investigation is the random shapelet forest classifier. Moreover, we propose two algorithmic solutions for the two problems along with simple optimizations, as well as a baseline solution using the nearest neighbor classifier. An extensive experimental evaluation on a variety of real datasets demonstrates the usefulness and effectiveness of our problem formulation and solutions.

In this paper we study the problem of discovering a timeline of events in a temporal network. We model events as dense subgraphs that occur within intervals of network activity. We formulate the event-discovery task as an optimization problem, where we search for a partition of the network timeline into k non-overlapping intervals, such that the intervals span subgraphs with maximum total density. The output is a sequence of dense subgraphs along with corresponding time intervals, capturing the most interesting events during the network lifetime. A naive solution to our optimization problem has polynomial but prohibitively high running time complexity. We adapt existing recent work on dynamic densest-subgraph discovery and approximate dynamic programming to design a fast approximation algorithm. Next, to ensure richer structure, we adjust the problem formulation to encourage coverage of a larger set of nodes. This problem is NP-hard even for static graphs. However, on static graphs a simple greedy algorithm leads to approximate solution due to submodularity. We extended this greedy approach for the case of temporal networks. However, the approximation guarantee does not hold. Nevertheless, according to the experiments, the algorithm finds good quality solutions.

We consider a network where an infection has taken place and a subset of infected nodes has been partially observed. Our goal is to reconstruct the underlying cascade that is likely to have generated these observations. We reduce this cascade-reconstruction problem to computing the marginal probability that a node is infected given the partial observations, which is a #P-hard problem. To circumvent this issue, we resort to estimating infection probabilities by generating a sample of probable cascades, which span the nodes that have already been observed to be infected, and avoid the nodes that have been observed to be uninfected. The sampling problem corresponds to sampling directed Steiner trees with a given set of terminals, which is a problem of independent interest and has received limited attention in the literature. For the latter problem we propose two novel algorithms with provable guarantees on the sampling distribution of the returned Steiner trees. The resulting method improves over state-of-the-art approaches that often make explicit assumptions about the infection-propagation model, or require additional parameters. Our method provides a more robust approach to the cascade-reconstruction problem, which makes weaker assumptions about the infection model, requires fewer additional parameters, and can be used to estimate node infection probabilities. We experimentally validate the proposed reconstruction algorithm on real-world graphs with both synthetic and real cascades. We show that our method outperforms all other baseline strategies in most cases.

Given a subset of active nodes in a network can we reconstruct the cascade that has generated these observations? This is a problem that has been studied in the literature, but here we focus in the case that temporal information is available about the active nodes. In particular, we assume that in addition to the subset of active nodes we also know their activation time. We formulate this cascade-reconstruction problem as a variant of a Steiner-tree problem: we ask to find a tree that spans all reported active nodes while satisfying temporal-consistency constraints. We present three approximation algorithms. The best algorithm in terms of quality achieves a -approximation guarantee, where k is the number of active nodes, while the most efficient algorithm has linearithmic running time, making it scalable to very large graphs. We evaluate our algorithms on real-world networks with both simulated and real cascades. Our results indicate that utilizing the available temporal information allows for more accurate cascade reconstruction. Furthermore, our objective leads to finding the “backbone” of the cascade and it gives solutions of high precision.

People are shifting from traditional news sources to online news at an incredibly fast rate. However, the technology behind online news consumption promotes content that confirms the users» existing point of view. This phenomenon has led to polarization of opinions and intolerance towards opposing views. Thus, a key problem is to model information filter bubbles on social media and design methods to eliminate them. In this paper, we use a machine-learning approach to learn a liberal-conservative ideology space on Twitter, and show how we can use the learned latent space to tackle the filter bubble problem.

Echo chambers, i.e., situations where one is exposed only to opinions that agree with their own, are an increasing concern for the political discourse in many democratic countries. This paper studies the phenomenon of political echo chambers on social media. We identify the two components in the phenomenon: the opinion that is shared, and the »chamber» (i.e., the social network) that allows the opinion to »echo» (i.e., be re-shared in the network) -- and examine closely at how these two components interact. We define a production and consumption measure for social-media users, which captures the political leaning of the content shared and received by them. By comparing the two, we find that Twitter users are, to a large degree, exposed to political opinions that agree with their own. We also find that users who try to bridge the echo chambers, by sharing content with diverse leaning, have to pay a »price of bipartisanship» in terms of their network centrality and content appreciation. In addition, we study the role of »gatekeepers,» users who consume content with diverse leaning but produce partisan content (with a single-sided leaning), in the formation of echo chambers. Finally, we apply these findings to the task of predicting partisans and gatekeepers from social and content features. While partisan users turn out relatively easy to identify, gatekeepers prove to be more challenging.

Genealogical networks, also known as family trees or population pedigrees, are commonly studied by genealogists wanting to know about their ancestry, but they also provide a valuable resource for disciplines such as digital demography, genetics, and computational social science. These networks are typically constructed by hand through a very time-consuming process, which requires comparing large numbers of historical records manually. We develop computational methods for automatically inferring large-scale genealogical networks. A comparison with human-constructed networks attests to the accuracy of the proposed methods. To demonstrate the applicability of the inferred large-scale genealogical networks, we present a longitudinal analysis on the mating patterns observed in a network. This analysis shows a consistent tendency of people choosing a spouse with a similar socioeconomic status, a phenomenon known as assortative mating. Interestingly, we do not observe this tendency to consistently decrease (nor increase) over our study period of 150 years.

Finding topical experts on micro-blogging sites, such as Twitter, is an essential information-seeking task. In this paper, we introduce an expert-finding algorithm for Twitter, which can be generalized to find topical experts in any social network with endorsement features.

Network alignment is the problem of matching the nodes of two graphs, maximizing the similarity of the matched nodes and the edges between them. This problem is encountered in a wide array of applications---from biological networks to social networks to ontologies---where multiple networked data sources need to be integrated. Due to the difficulty of the task, an accurate alignment can rarely be found without human assistance. Thus, it is of great practical importance to develop network alignment algorithms that can optimally leverage experts who are able to provide the correct alignment for a small number of nodes. Yet, only a handful of existing works address this active network alignment setting.

Given a large graph,the densest-subgraph problem asks to find a subgraph with maximum average degree. When considering the top-k version of this problem, a naïve solution is to iteratively find the densest subgraph and remove it in each iteration. However, such a solution is impractical due to high processing cost. The problem is further complicated when dealing with dynamic graphs, since adding or removing an edge requires re-running the algorithm. In this paper, we study the top-k densest-subgraph problem in the sliding-window model and propose an efficient fully-dynamic algorithm. The input of our algorithm consists of an edge stream, and the goal is to find the node-disjoint subgraphs that maximize the sum of their densities. In contrast to existing state-of-the-art solutions that require iterating over the entire graph upon any update, our algorithm profits from the observation that updates only affect a limited region of the graph. Therefore, the top-k densest subgraphs are maintained by only applying local updates. We provide a theoretical analysis of the proposed algorithm and show empirically that the algorithm often generates denser subgraphs than state-of-the-art competitors. Experiments show an improvement in efficiency of up to five orders of magnitude compared to state-of-the-art solutions.

Online social networks are growing and becoming denser.The social connections of a given person may have very high variability: from close friends and relatives to acquaintances to people who hardly know. Inferring the strength of social ties is an important ingredient for modeling the interaction of users in a network and understanding their behavior. Furthermore, the problem has applications in computational social science, viral marketing, and people recommendation. In this paper we study the problem of inferring the strength of social ties in a given network. Our work is motivated by a recent approach by Sintos et. al [24], which leverages the Strong Triadic Closure} STC principle, a hypothesis rooted in social psychology. To guide our inference process, in addition to the network structure, we also consider as input a collection of tight communities. Those are sets of vertices that we expect to be connected via strong ties. Such communities appear in different situations, e.g., when being part of a community implies a strong connection to one of the existing members. We consider two related problem formalizations that reflect the assumptions of our setting: small number of STC violations and strong-tie connectivity in the input communities. We show that both problem formulations are NP-hard. We also show that one problem formulation is hard to approximate, while for the second we develop an algorithm with approximation guarantee. We validate the proposed method on real-world datasets by comparing with baselines that optimize STC violations and community connectivity separately.

Motivated by applications that arise in online social media and collaboration networks, there has been a lot of work on community-search. In this class of problems, the goal is to find a subgraph that satisfies a certain connectivity requirement and contains a given collection of seed nodes. In this paper, we extend the community-search problem by associating each individual with a profile. The profile is a numeric score that quantifies the position of an individual with respect to a topic. We adopt a model where each individual starts with a latent profile and arrives to a conformed profile through a dynamic conformation process, which takes into account the individual's social interaction and the tendency to conform with one's social environment. In this framework, social tension arises from the differences between the conformed profiles of neighboring individuals as well as from the differences between individuals' conformed and latent profiles. Given a network of individuals, their latent profiles and this conformation process, we extend the community-search problem by requiring the output subgraphs to have low social tension. From the technical point of view, we study the complexity of this problem and propose algorithms for solving it effectively. Our experimental evaluation in a number of social networks reveals the efficacy and efficiency of our methods.

Network sparsification aims to reduce the number of edges of a network while maintaining its structural properties; such properties include shortest paths, cuts, spectral measures, or network modularity. Sparsification has multiple applications, such as, speeding up graph-mining algorithms, graph visualization, as well as identifying the important network edges. In this paper we consider a novel formulation of the network-sparsification problem. In addition to the network, we also consider as input a set of communities. The goal is to sparsify the network so as to preserve the network structure with respect to the given communities. We introduce two variants of the community-aware sparsification problem, leading to sparsifiers that satisfy different connectedness community properties. From the technical point of view, we prove hardness results and devise effective approximation algorithms. Our experimental results on a large collection of datasets demonstrate the effectiveness of our algorithms.

Society is often polarized by controversial issues that split the population into groups with opposing views. When such issues emerge on social media, we often observe the creation of `echo chambers', i.e., situations where like-minded people reinforce each other's opinion, but do not get exposed to the views of the opposing side. In this paper we study algorithmic techniques for bridging these chambers, and thus reduce controversy. Specifically, we represent the discussion on a controversial issue with an endorsement graph, and cast our problem as an edge-recommendation problem on this graph. The goal of the recommendation is to reduce the controversy score of the graph, which is measured by a recently-developed metric based on random walks. At the same time, we take into account the acceptance probability of the recommended edge, which represents how likely the edge is to materialize in the endorsement graph.

Online social networks are often defined by considering interactions of entities at an aggregate level. For example, a call graph is formed among individuals who have called each other at least once; or at least k times. Similarly, in social-media platforms, we consider implicit social networks among users who have interacted in some way, e.g., have made a conversation, have commented to the content of each other, and so on. Such definitions have been used widely in the literature and they have offered significant insights regarding the structure of social networks. However, it is obvious that they suffer from a severe limitation: They neglect the precise time that interactions among the network entities occur. In this article, we consider interaction networks , where the data description contains not only information about the underlying topology of the social network, but also the exact time instances that network entities interact. In an interaction network, an edge is associated with a timestamp, and multiple edges may occur for the same pair of entities. Consequently, interaction networks offer a more fine-grained representation, which can be leveraged to reveal otherwise hidden dynamic phenomena. In the setting of interaction networks, we study the problem of discovering dynamic dense subgraphs whose edges occur in short time intervals . We view such subgraphs as fingerprints of dynamic activity occurring within network communities. Such communities represent groups of individuals who interact with each other in specific time instances, for example, a group of employees who work on a project and whose interaction intensifies before certain project milestones. We prove that the problem we define is NP -hard, and we provide efficient algorithms by adapting techniques for finding dense subgraphs. We also show how to speed-up the proposed methods by exploiting concavity properties of our objective function and by the means of fractional programming . We perform extensive evaluation of the proposed methods on synthetic and real datasets, which demonstrates the validity of our approach and shows that our algorithms can be used to obtain high-quality results.

We study the problem of discrepancy maximization on graphs: given a set of nodes Q of an underlying graph G, we aim to identify a connected subgraph of G that contains many more nodes from Q than other nodes. This variant of the discrepancy maximization problem extends the well-known notion of “bump hunting” in the Euclidean space [1]. We consider the problem under two access models. In the unrestricted-access model, the whole graph G is given as input, while in the local-access model we can only retrieve the neighbors of a given node in G using a possibly slow and costly interface. We prove that the basic problem of discrepancy maximization on graphs is NP-hard, and empirically evaluate the performance of four heuristics for solving it. For the local-access model, we consider three different algorithms that aim to recover a part of G large enough to contain an optimal solution, while using only a small number of calls to the neighbor-function interface. We perform a thorough experimental evaluation in order to understand the trade offs between the proposed methods and their dependencies on characteristics of the input graph.

People are increasingly communicating and collaborating via digital platforms, such as email and messaging applications. Data exchanged on these digital communication platforms can be a treasure trove of information on people who participate in the discussions: who they are collaborating with, what they are working on, what their expertise is, and so on. Yet, personal communication data is very rarely analyzed due to the sensitivity of the information it contains. In this paper, we mine personal communication data with the goal of generating skill endorsements of the type "person A endorses person B on skill X." To address privacy concerns, we consider that each person has access only to their own data (i.e., conversations with their peers). By using our method, they can generate endorsements for their peers, which they can inspect and opt to publish. To identify meaningful skills we use a knowledge base created from the StackExchange Q&A forum. We study two different approaches, one based on building a skill graph, and one based on information retrieval techniques. We find that the latter approach outperforms the graph-based algorithms when tested on a dataset of user profiles from StackOverflow. We also conduct a user study on email data from nine volunteers, and we find that the information retrieval-based approach achieves a [email protected] score of 0.617.

We provide a new formulation for the problem of role discovery in graphs. Our definition is structural: two vertices should be assigned to the same role if the roles of their neighbors, when viewed as multi-sets, are similar enough. An attractive characteristic of our approach is that it is based on optimizing a well-defined objective function, and thus, contrary to previous approaches, the role-discovery task can be studied with the tools of combinatorial optimization. We demonstrate that, when fixing the number of roles to be used, the proposed role-discovery problem is np-hard, while another (seemingly easier) version of the problem is np-hard to approximate. On the positive side, despite the recursive nature of our objective function, we can show that finding a perfect (zero-cost) role assignment with the minimum number of roles can be solved in polynomial time. We do this by connecting the zero-cost role assignment with the notion of equitable partition. For the more practical version of the problem with fixed number of roles we present two natural heuristic methods, and discuss how to make them scalable in large graphs.

Writing rap lyrics requires both creativity to construct a meaningful, interesting story and lyrical skills to produce complex rhyme patterns, which form the cornerstone of good flow. We present a rap lyrics generation method that captures both of these aspects. First, we develop a prediction model to identify the next line of existing lyrics from a set of candidate next lines. This model is based on two machine-learning techniques: the RankSVM algorithm and a deep neural network model with a novel structure. Results show that the prediction model can identify the true next line among 299 randomly selected lines with an accuracy of 17%, i.e., over 50 times more likely than by random. Second, we employ the prediction model to combine lines from existing songs, producing lyrics with rhyme and a meaning. An evaluation of the produced lyrics shows that in terms of quantitative rhyme density, the method outperforms the best human rappers by 21%. The rap lyrics generator has been deployed as an online tool called DeepBeat, and the performance of the tool has been assessed by analyzing its usage logs. This analysis shows that machine-learned rankings correlate with user preferences.

We consider the problem of reconstructing an epidemic over time, or, more general, reconstructing the propagation of an activity in a network. Our input consists of a temporal network, which contains information about when two nodes interacted, and a sample of nodes that have been reported as infected. The goal is to recover the flow of the spread, including discovering the starting nodes, and identifying other likely-infected nodes that are not reported. The problem we consider has multiple applications, from public health to social media and viral marketing purposes.

Which topics spark the most heated debates in social media? Identifying these topics is a first step towards creating systems which pierce echo chambers. In this paper, we perform a systematic methodological study of controversy detection using social media network structure and content.

We introduce and study the problem of computing the similarity self-join in a streaming context (SSSJ), where the input is an unbounded stream of items arriving continuously. The goal is to find all pairs of items in the stream whose similarity is greater than a given threshold. The simplest formulation of the problem requires unbounded memory, and thus, it is intractable. To make the problem feasible, we introduce the notion of time-dependent similarity: the similarity of two items decreases with the difference in their arrival time. By leveraging the properties of this time-dependent similarity function, we design two algorithmic frameworks to solve the SSSJ problem. The first one, MiniBatch (MB), uses existing index-based filtering techniques for the static version of the problem, and combines them in a pipeline. The second framework, Streaming (STR), adds time filtering to the existing indexes, and integrates new time-based bounds deeply in the working of the algorithms. We also introduce a new indexing technique (L2), which is based on an existing state-of-the-art indexing technique (L2AP), but is optimized for the streaming case. Extensive experiments show that the STR algorithm, when instantiated with the L2 index, is the most scalable option across a wide array of datasets and parameters.

We propose a new scalable algorithm for the facility-location problem. We study the graph setting, where the cost of serving a client from a facility is represented by the shortest-path distance on a graph. This setting is applicable to various problems arising in the Web and social media, and allows to leverage the inherent sparsity of such graphs.

We study the problem of discrepancy maximization on graphs: given a set of nodes Q of an underlying graph G, we aim to identify a connected subgraph of G that contains many more nodes from Q than other nodes. This variant of the discrepancy-maximization problem extends the well-known notion of “bump hunting” in the Euclidean space. We consider the problem under two access models. In the unrestricted-access model, the whole graph G is given as input, while in the local-access model we can only retrieve the neighbors of a given node in G using a possibly slow and costly interface. We prove that the basic problem of discrepancy maximization on graphs is NP-hard, and empirically evaluate the performance of four heuristics for solving it. For the local-access model we consider three different algorithms that aim to recover a part of G large enough to contain an optimal solution, while using only a small number of calls to the neighbor-function interface. We perform a thorough experimental evaluation in order to understand the trade offs between the proposed methods and their dependencies on characteristics of the input graph.

We study a new notion of graph centrality based on absorbing random walks. Given a graph G = (V, E) and a set of query nodes Q ⊆ V, we aim to identify the k most central nodes in G with respect to Q. Specifically, we consider central nodes to be absorbing for random walks that start at the query nodes Q. The goal is to find the set of k central nodes that minimizes the expected length of a random walk until absorption. The proposed measure, which we call k absorbing random-walk centrality, favors diverse sets, as it is beneficial to place the k absorbing nodes in different parts of the graph so as to “intercept” random walks that start from different query nodes. Although similar problem definitions have been considered in the literature, e.g., in information-retrieval settings where the goal is to diversify web-search results, in this paper we study the problem formally and prove some of its properties. We find that the problem is NP-hard, while the objective function is monotone and supermodular, implying that a greedy algorithm provides solutions with an approximation guarantee. On the other hand, the greedy algorithm involves expensive matrix operations that make it prohibitive to employ on large datasets. To confront this challenge, we explore the performance of efficient heuristics.

Finding dense subgraphs is a fundamental graph-theoretic problem, that lies in the heart of numerous graph-mining applications, ranging from finding communities in social networks, to detecting regulatory motifs in DNA, and to identifying real-time stories in news. The problem of finding dense subgraphs has been studied extensively in theoretical computer science, and recently, due to the relevance of the problem in real-world applications, it has attracted considerable attention in the data-mining community.

We study the problem of subsequence search in databases of event-interval sequences, or e-sequences. In contrast to sequences of instantaneous events, e-sequences contain events that have a duration. In Information Retrieval applications, e-sequences are used for American Sign Language. We show that the subsequence-search problem is NP-hard and provide an exact (worst-case exponential) algorithm. We extend our algorithm to handle different cases of subsequence matching with errors. We then propose the Relation Index, a scheme for speeding up exact retrieval, which we benchmark against several indexing schemes.

Decomposing a graph into a hierarchical structure via k-core analysis is a standard operation in any modern graph-mining toolkit. k-core decomposition is a simple and efficient method that allows to analyze a graph beyond its mere degree distribution. More specifically, it is used to identify areas in the graph of increasing centrality and connectedness, and it allows to reveal the structural organization of the graph.

We study a novel clustering problem in which the pairwise relations between objects are categorical . This problem can be viewed as clustering the vertices of a graph whose edges are of different types ( colors ). We introduce an objective function that ensures the edges within each cluster have, as much as possible, the same color. We show that the problem is NP -hard and propose a randomized algorithm with approximation guarantee proportional to the maximum degree of the input graph. The algorithm iteratively picks a random edge as a pivot, builds a cluster around it, and removes the cluster from the graph. Although being fast, easy to implement, and parameter-free, this algorithm tends to produce a relatively large number of clusters. To overcome this issue we introduce a variant algorithm, which modifies how the pivot is chosen and how the cluster is built around the pivot. Finally, to address the case where a fixed number of output clusters is required, we devise a third algorithm that directly optimizes the objective function based on the alternating-minimization paradigm. We also extend our objective function to handle cases where object’s relations are described by multiple labels. We modify our randomized approximation algorithm to optimize such an extended objective function and show that its approximation guarantee remains proportional to the maximum degree of the graph. We test our algorithms on synthetic and real data from the domains of social media, protein-interaction networks, and bibliometrics. Results reveal that our algorithms outperform a baseline algorithm both in the task of reconstructing a ground-truth clustering and in terms of objective-function value.

No abstract available.

A fundamental operation over edge-labeled graphs is the compu-tation of shortest-path distances subject to a constraint on the set of permissible edge labels. Applying exact algorithms for such an operation is not a viable option, especially for massive graphs, or in scenarios where the distance computation is used as a primitive for more complex computations. In this paper we study the problem of efficient approximation of shortest-path queries with edge-label constraints, for which we de-vise two indexes based on the idea of landmarks: distances from all vertices of the graph to a selected subset of landmark vertices are pre-computed and then used at query time to efficiently ap-proximate distance queries. The major challenge to face is that, in principle, an exponential number of constraint label sets needs to be stored for each vertex-landmark pair, which makes the index pre-computation and storage far from trivial. We tackle this chal-lenge from two different perspectives, which lead to indexes with different characteristics: one index is faster and more accurate, but it requires more space than the other. We extensively evaluate our techniques on real and synthetic datasets, showing that our indexes can efficiently and accurately estimate label-constrained distance queries. 1.

Uncertain, or probabilistic, graphs have been increasingl y used to represent noisy linked data in many emerging application scenarios, and have recently attracted the attention of the databa se research community. A fundamental problem on uncertain graphs is reliability, which deals with the probability of nodes being reachable one from another. Existing literature has exclusively focused on reliability detection, which asks to compute the probability that two given nodes are connected. In this paper we study reliability search on uncertain graphs, which we define as the problem of computing all nodes reachable from a set of query nodes with probability no less than a given threshold. Existing reliability-detection approac hes are not well-suited to efficiently handle the reliability-search p roblem. We propose RQ-tree, a novel index which is based on a hierarchical clustering of the nodes in the graph, and further optimized using a balanced-minimum-cut criterion. Based on RQ-tree, we define a fast filtering-and-verification online query-evaluation s trategy that relies on a maximum-flow-based candidate-generation phase , followed by a verification phase consisting of either a lower-bo unding method or a sampling technique. The first verification method returns no incorrect nodes, thus guaranteeing perfect precis ion, completely avoids sampling, and is more efficient. The second ve rification method ensures instead better recall. Extensive experiments on real-world uncertain graphs show that our methods are very efficient—over state-of-the-art relia bilitydetection methods, we obtain a speed-up up to five orders of ma gnitude; as well as accurate—our techniques achieve precision > 0.95 and recall usually higher than 0.75.

With the fast growth of smart devices and social networks, a lot of computing systems collect data that record different types of activities. An important computational challenge is to analyze these data, extract patterns, and understand activity trends. We consider the problem of mining activity networks to identify interesting events, such as a big concert or a demonstration in a city, or a trending keyword in a user community in a social network.

The ever-increasing urbanization coupled with the unprecedented capacity to collect and process large amounts of data have helped to create the vision of intelligent urban environments. One key aspect of such environments is that they allow people to effectively navigate through their city. While GPS technology and route-planning services have undoubtedly helped towards this direction, there is room for improvement in intelligent urban navigation. This vision can be fostered by the proliferation of location-based social networks, such as Foursquare or Path, which record the physical presence of users in different venues through check-ins. This information can then be used to enhance intelligent urban navigation, by generating customized path recommendations for users.

We present ShoppingAdvisor, a novel recommender system that helps users in shopping for technical products. ShoppingAdvisor leverages both user preferences and technical product attributes in order to generate its suggestions. The system elicits user preferences via a tree-shaped flowchart, where each node is a question to the user. At each node, ShoppingAdvisor suggests a ranking of products matching the preferences of the user, and that gets progressively refined along the path from the tree's root to one of its leafs.

Network science has emerged over the last years as an interdisciplinary area spanning traditional domains including mathematics, computer science, sociology, biology and economics. Since complexity in social, biological and economical systems, and more generally in complex systems, arises through pairwise interactions there exists a surging interest in understanding networks.

Influence-driven diffusion of information is a fundamental process in social networks. Learning the latent variables of such process, i.e., the influence strength along each link, is a central question towards understanding the structure and function of complex networks, modeling information cascades, and developing applications such as viral marketing.

Finding dense subgraphs is an important graph-mining task with many applications. Given that the direct optimization of edge density is not meaningful, as even a single edge achieves maximum density, research has focused on optimizing alternative density functions. A very popular among such functions is the average degree, whose maximization leads to the well-known densest-subgraph notion. Surprisingly enough, however, densest subgraphs are typically large graphs, with small edge density and large diameter.

We present a unified approach for simultaneously clustering and discovering outliers in data. Our approach is formalized as a generalization of the k-MEANS problem. We prove that the problem is NP-hard and then present a practical polynomial time algorithm, which is guaranteed to converge to a local optimum. Furthermore we extend our approach to all distance measures that can be expressed in the form of a Bregman divergence. Experiments on synthetic and real datasets demonstrate the effectiveness of our approach and the utility of carrying out both clustering and outlier detection in a concurrent manner. In particular on the famous KDD cup network-intrusion dataset, we were able to increase the precision of the outlier detection task by nearly 100% compared to the classical nearest-neighbor approach.

The process of opinion formation through synthesis and contrast of different viewpoints has been the subject of many studies in economics and social sciences. Today, this process manifests itself also in online social networks and social media. The key characteristic of successful promotion campaigns is that they take into consideration such opinion-formation dynamics in order to create a overall favorable opinion about a specific information item, such as a person, a product, or an idea. In this paper, we adopt a well-established model for social-opinion dynamics and formalize the campaigndesign problem as the problem of identifying a set of target individuals whose positive opinion about an information item will maximize the overall positive opinion for the item in the social network. We call this problem CAMPAIGN. We study the complexity of the CAMPAIGN problem, and design algorithms for solving it. Our experiments on real data demonstrate the efficiency and practical utility of our algorithms.

The popularity of social-networking sites has increased rapidly over the last decade. A basic functionalities of social-networking sites is to present users with streams of events shared by their friends. At a systems level, materialized per-user views are a common way to assemble and deliver such event streams on-line and with low latency. Access to the data stores, which keep the user views, is a major bottleneck of social-networking systems. We propose to improve the throughput of these systems by using social piggybacking, which consists of processing the requests of two friends by querying and updating the view of a third common friend. By using one such hub view, the system can serve requests of the first friend without querying or updating the view of the second. We show that, given a social graph, social piggybacking can minimize the overall number of requests, but computing the optimal set of hubs is an NP-hard problem. We propose anO(logn) approximation algorithm and a heuristic to solve the problem, and evaluate them using the full Twitter and Flickr social graphs, which have up to billions of edges. Compared to existing approaches, using social piggybacking results in similar throughput in systems with few servers, but enables substantial throughput improvements as the size of the system grows, reaching up to a 2-factor increase. We also evaluate our algorithms on a real social networking system prototype and we show that the actual increase in throughput corresponds nicely to the gain anticipated by our cost function.

In this paper we present a novel graph-based data abstraction for modeling the browsing behavior of web users. The objective is to identify users who discover interesting pages before others. We call these users early adopters. By tracking the browsing activity of early adopters we can identify new interesting pages early, and recommend these pages to similar users. We focus on news and blog pages, which are more dynamic in nature and more appropriate for recommendation.

We study a novel clustering problem in which the pairwise relations between objects are categorical. This problem can be viewed as clustering the vertices of a graph whose edges are of different types (colors). We introduce an objective function that aims at partitioning the graph such that the edges within each cluster have, as much as possible, the same color. We show that the problem is NP-hard and propose a randomized algorithm with approximation guarantee proportional to the maximum degree of the input graph. The algorithm iteratively picks a random edge as pivot, builds a cluster around it, and removes the cluster from the graph. Although being fast, easy-to-implement, and parameter free, this algorithm tends to produce a relatively large number of clusters. To overcome this issue we introduce a variant algorithm, which modifies how the pivot is chosen and and how the cluster is built around the pivot. Finally, to address the case where a fixed number of output clusters is required, we devise a third algorithm that directly optimizes the objective function via a strategy based on the alternating minimization paradigm.

The data-mining literature is rich in problems asking to assess the importance of entities in a given dataset. At a high level, existing work identifies important entities either by ranking or by selection. Ranking methods assign a score to every entity in the population, and then use the assigned scores to create a ranked list. The major shortcoming of such approaches is that they ignore the redundancy between high-ranked entities, which may in fact be very similar or even identical. Therefore, in scenarios where diversity is desirable, such methods perform poorly. Selection methods overcome this drawback by evaluating the importance of a group of entities collectively. To achieve this, they typically adopt a set-cover formulation, which identifies the entities in the minimum set cover as the important ones. However, this dichotomy of entities conceals the fact that, even though an entity may not be in the reported cover, it may still participate in many other optimal or near-optimal solutions. In this paper, we propose a framework that overcomes the above drawbacks by integrating the ranking and selection paradigms. Our approach assigns importance scores to entities based on both the number and the quality of set-cover solutions that they participate. Our algorithmic contribution lies with the design of an efficient algorithm for approximating the number of high-quality set covers that each entity participates. Our methodology applies to a wide range of applications. In a user study and an experimental evaluation on real data, we demonstrate that our framework is efficient and provides useful and intuitive results.

We propose a new methodology for recommending interesting news to users by exploiting the information in their twitter persona. We model relevance between users and news articles using a mix of signals drawn from the news stream and from twitter: the profile of the social neighborhood of the users, the content of their own tweet stream, and topic popularity in the news and in the whole twitter-land.

We study the problem of correlating micro-blogging activity with stock-market events, defined as changes in the price and traded volume of stocks. Specifically, we collect messages related to a number of companies, and we search for correlations between stock-market events for those companies and features extracted from the micro-blogging messages. The features we extract can be categorized in two groups. Features in the first group measure the overall activity in the micro-blogging platform, such as number of posts, number of re-posts, and so on. Features in the second group measure properties of an induced interaction graph, for instance, the number of connected components, statistics on the degree distribution, and other graph-based properties.

We investigate the problem of mining "tips" from Yahoo! Answers and displaying those tips in response to related web queries. Here, a "tip" is a short, concrete and self-contained bit of non-obvious advice such as "To zest a lime if you don't have a zester : use a cheese grater."

We study the problem of online team formation. We consider a setting in which people possess different skills and compatibility among potential team members is modeled by a social network. A sequence of tasks arrives in an online fashion, and each task requires a specific set of skills. The goal is to form a new team upon arrival of each task, so that (i) each team possesses all skills required by the task, (ii) each team has small communication overhead, and (iii) the workload of performing the tasks is balanced among people in the fairest possible way.

Data collected nowadays by social-networking applications create fascinating opportunities for building novel services, as well as expanding our understanding about social structures and their dynamics. Unfortunately, publishing social-network graphs is considered an ill-advised practice due to privacy concerns. To alleviate this problem, several anonymization methods have been proposed, aiming at reducing the risk of a privacy breach on the published data, while still allowing to analyze them and draw relevant conclusions. In this paper we introduce a new anonymization approach that is based on injecting uncertainty in social graphs and publishing the resulting uncertain graphs . While existing approaches obfuscate graph data by adding or removing edges entirely, we propose using a finer-grained perturbation that adds or removes edges partially : this way we can achieve the same desired level of obfuscation with smaller changes in the data, thus maintaining higher utility. Our experiments on real-world networks confirm that at the same level of identity obfuscation our method provides higher usefulness than existing randomized methods that publish standard graphs.

Small changes in the network topology can have dramatic effects on its capacity to disseminate information. In this paper, we consider the problem of adding a small number of ghost edges in the network in order to minimize the average shortest-path distance between nodes, towards a smaller-world network. We formalize the problem of suggesting ghost edges and we propose a novel method for quickly evaluating the importance of ghost edges in sparse graphs. Through experiments on real and synthetic data sets, we demonstrate that our approach performs very well, for a varying range of conditions, and it outperforms sensible baselines.

Analyzing the structure of social networks is of interest in a wide range of disciplines, but such activity is limited by the fact that these data represent sensitive information and can not be published in their raw form. One of the approaches to sanitize network data is to randomly add or remove edges from the graph. Recent studies have quantified the level of anonymity that is obtained by random perturbation by means of a-posteriori belief probabilities and, by conducting experiments on small datasets, arrived at the conclusion that random perturbation can not achieve meaningful levels of anonymity without deteriorating the graph features. We offer a new information-theoretic perspective on this issue. We make an essential distinction between image and preimage anonymity and propose a more accurate quantification, based on entropy, of the anonymity level that is provided by the perturbed network. We explain why the entropy-based quantification, which is global, is more adequate than the previously used local quantification based on a-posteriori belief. We also prove that the anonymity level quantified by means of entropy is always greater than or equal to the one based on a-posteriori belief probabilities. In addition, we introduce and explore the method of random sparsification, which randomly removes edges, without adding new ones. Extensive experimentation on several very large datasets shows that randomization techniques for identity obfuscation are back in the game, as they may achieve meaningful levels of anonymity while still preserving features of the original graph.

We introduce a new approach to the problem of overlapping clustering. The main idea is to formulate overlapping clustering as an optimization problem in which each data point is mapped to a small set of labels, representing membership to different clusters. The objective is to find a mapping so that the distances between data points agree as much as possible with distances taken over their label sets. To define distances between label sets, we consider two measures: a set-intersection indicator function and the Jaccard coefficient. To solve the main optimization problem we propose a local-search algorithm. The iterative step of our algorithm requires solving non-trivial optimization sub problems, which, for the measures of set-intersection and Jaccard, we solve using a greedy method and non-negative least squares, respectively. Since our frameworks uses pair wise similarities of objects as the input, it lends itself naturally to the task of clustering structured objects for which feature vectors can be difficult to obtain. As a proof of concept we show how easily our framework can be applied in two different complex application domains. Firstly, we develop overlapping clustering of animal trajectories, obtaining zoologically meaningful results. Secondly, we apply our framework for overlapping clustering of proteins based on pair wise similarities of amino acid sequences, outperforming the of state-of-the-art method in matching a ground truth taxonomy.

We introduce the problem of diverse dimension decomposition in transactional databases. A dimension is a set of mutually-exclusive item sets, and our problem is to find a decomposition of the item set space into dimensions, which are orthogonal to each other, and that provide high coverage of the input database. The mining framework we propose effectively represents a dimensionality-reducing transformation from the space of all items to the space of orthogonal dimensions. Our approach relies on information-theoretic concepts, and we are able to formulate the dimension-finding problem with a single objective function that simultaneously captures constraints on coverage, exclusivity and orthogonality. We describe an efficient greedy method for finding diverse dimensions from transactional databases. The experimental evaluation of the proposed approach using two real datasets, flickr and delicious, demonstrates the effectiveness of our solution. Although we are motivated by the applications in the collaborative tagging domain, we believe that the mining task we introduce in this paper is general enough to be useful in other application domains.

We present Spine, an efficient algorithm for finding the "backbone" of an influence network. Given a social graph and a log of past propagations, we build an instance of the independent-cascade model that describes the propagations. We aim at reducing the complexity of that model, while preserving most of its accuracy in describing the data.

We address the problem of recommending suitable jobs to people who are seeking a new job. We formulate this recommendation problem as a supervised machine learning problem. Our technique exploits all past job transitions as well as the data associated with employees and institutions to predict an employee's next job transition. We train a machine learning model using a large number of job transitions extracted from the publicly available employee profiles in the Web. Experiments show that job transitions can be accurately predicted, significantly improving over a baseline that always predicts the most frequent institution in the data.

The ability to aggregate huge volumes of queries over a large population of users allows search engines to build precise models for a variety of query-assistance features such as query recommendation, correction, etc. Yet, no matter how much data is aggregated, the long-tail distribution implies that a large fraction of queries are rare. As a result, most query assistance services perform poorly or are not even triggered on long-tail queries. We propose a method to extend the reach of query assistance techniques (and in particular query recommendation) to long-tail queries by reasoning about rules between query templates rather than individual query transitions, as currently done in query-flow graph models. As a simple example, if we recognize that 'Montezuma' is a city in the rare query "Montezuma surf" and if the rule 'city surf → beach has been observed, we are able to offer "Montezuma beach" as a recommendation, even if the two queries were never observed in a same session. We conducted experiments to validate our hypothesis, first via traditional small-scale editorial assessments but more interestingly via a novel automated large scale evaluation methodology. Our experiments show that general coverage can be relatively increased by 24% using templates without penalizing quality. Furthermore, for 36% of the 95M queries in our query flow graph, which have no out edges and thus could not be served recommendations, we can now offer at least one recommendation in 98% of the cases.

Matching problems are ubiquitous. They occur in economic markets, labor markets, internet advertising, and elsewhere. In this paper we focus on an application of matching for social media. Our goal is to distribute content from information suppliers to information consumers. We seek to maximize the overall relevance of the matched content from suppliers to consumers while regulating the overall activity, e.g., ensuring that no consumer is overwhelmed with data and that all suppliers have chances to deliver their content. We propose two matching algorithms, GreedyMR and StackMR, geared for the MapReduce paradigm. Both algorithms have provable approximation guarantees, and in practice they produce high-quality solutions. While both algorithms scale extremely well, we can show that Stack-MR requires only a poly-logarithmic number of MapReduce steps, making it an attractive option for applications with very large datasets. We experimentally show the trade-offs between quality and efficiency of our solutions on two large datasets coming from real-world social-media web sites.

Social network analysis has gained significant attention in recent years, largely due to the success of online social networking and media-sharing sites, and the consequent availability of a wealth of social network data. In spite of the growing interest, however, there is little understanding of the potential business applications of mining social networks. While there is a large body of research on different problems and methods for social network mining, there is a gap between the techniques developed by the research community and their deployment in real-world applications. Therefore the potential business impact of these techniques is still largely unexplored. In this article we use a business process classification framework to put the research topics in a business context and provide an overview of what we consider key problems and techniques in social network analysis and mining from the perspective of business applications. In particular, we discuss data acquisition and preparation, trust, expertise, community structure, network dynamics, and information propagation. In each case we present a brief overview of the problem, describe state-of-the art approaches, discuss business application examples, and map each of the topics to a business process classification framework. In addition, we provide insights on prospective business applications, challenges, and future research directions. The main contribution of this article is to provide a state-of-the-art overview of current techniques while providing a critical perspective on business applications of social network analysis and mining.

The internet has enabled the collaboration of groups at a scale that was unseen before. A key problem for large collaboration groups is to be able to allocate tasks effectively. An effective task assignment method should consider both how fit teams are for each job as well as how fair the assignment is to team members, in terms that no one should be overloaded or unfairly singled out. The assignment has to be done automatically or semi-automatically given that it is difficult and time-consuming to keep track of the skills and the workload of each person. Obviously the method to do this assignment must also be computationally efficient.

A lot of research in graph mining has been devoted in the discovery of communities. Most of the work has focused in the scenario where communities need to be discovered with only reference to the input graph. However, for many interesting applications one is interested in finding the community formed by a given set of nodes. In this paper we study a query-dependent variant of the community-detection problem, which we call the community-search problem: given a graph G, and a set of query nodes in the graph, we seek to find a subgraph of G that contains the query nodes and it is densely connected.

Many sorts of structured data are commonly stored in a multi-relational format of interrelated tables.Under this relational model, exploratory data analysis can be done by using relational queries.As an example, in the Internet Movie Database (IMDb) a query can be used to check whether the average rank of action movies is higher than the average rank of drama movies.We consider the problem of assessing whether the results returned by such a query are statistically significant or just a random artifact of the structure in the data.Our approach is based on randomizing the tables occurring in the queries and repeating the original query on the randomized tables.It turns out that there is no unique way of randomizing in multi-relational data.We propose several randomization techniques, study their properties, and show how to find out which queries or hypotheses about our data result in statistically significant information and which tables in the database convey most of the structure in the query.We give results on real and generated data and show how the significance of some queries vary between different randomizations.

Defining a measure of similarity between queries is an interesting and difficult problem. A reliable query-similarity measure can be used in a variety of applications such as query recommendation, query expansion, and advertising.

Query recommendation is an integral part of modern search engines. The goal of query recommendation is to facilitate users while searching for information. Query recommendation also allows users to explore concepts related to their information needs.

In this paper we study the community structure of endorsement networks, i.e., social networks in which a directed edge u → v is asserting an action of support from user u to user v. Examples include scenarios in which a user u is favoring a photo, liking a post, or following the microblog of user v.

Complex networks, such as biological, social, and communication networks, often entail uncertainty, and thus, can be modeled as probabilistic graphs . Similar to the problem of similarity search in standard graphs, a fundamental problem for probabilistic graphs is to efficiently answer k-nearest neighbor queries ( k -NN), which is the problem of computing the k closest nodes to some specific node. In this paper we introduce a framework for processing k -NN queries in probabilistic graphs. We propose novel distance functions that extend well-known graph concepts, such as shortest paths. In order to compute them in probabilistic graphs, we design algorithms based on sampling. During k -NN query processing we efficiently prune the search space using novel techniques. Our experiments indicate that our distance functions outperform previously used alternatives in identifying true neighbors in real-world biological data. We also demonstrate that our algorithms scale for graphs with tens of millions of edges.

In this article, we study the problem of approximate local triangle counting in large graphs. Namely, given a large graph G =( V,E ) we want to estimate as accurately as possible the number of triangles incident to every node v ∈ V in the graph. We consider the question both for undirected and directed graphs. The problem of computing the global number of triangles in a graph has been considered before, but to our knowledge this is the first contribution that addresses the problem of approximate local triangle counting with a focus on the efficiency issues arising in massive graphs and that also considers the directed case. The distribution of the local number of triangles and the related local clustering coefficient can be used in many interesting applications. For example, we show that the measures we compute can help detect the presence of spamming activity in large-scale Web graphs, as well as to provide useful features for content quality assessment in social networks. For computing the local number of triangles (undirected and directed), we propose two approximation algorithms, which are based on the idea of min-wise independent permutations [Broder et al. 1998]. Our algorithms operate in a semi-streaming fashion, using O (| V |) space in main memory and performing O (log | V |) sequential scans over the edges of the graph. The first algorithm we describe in this article also uses O (| E |) space of external memory during computation, while the second algorithm uses only main memory. We present the theoretical analysis as well as experimental results on large graphs, demonstrating the practical efficiency of our approach.

Web search engines are often implemented as centralized systems. Designing and implementing a Web search engine in a distributed environment is a challenging engineering task that encompasses many interesting research questions. However, distributing a search engine across multiple sites has several advantages, such as utilizing less compute resources and exploiting data locality. In this paper we investigate the cost-effectiveness of building a distributed Web search engine. We propose a model for assessing the total cost of a distributed Web search engine that includes the computational costs and the communication cost among all distributed sites. We then present a query-processing algorithm that maximizes the amount of queries answered locally, without sacrificing the quality of the results compared to a centralized search engine. We simulate the algorithm on real document collections and query workloads to measure the actual parameters needed for our cost model, and we show that a distributed search engine can be competitive compared to a centralized architecture with respect to real cost.

In this paper we study approximate landmark-based methods for point-to-point distance estimation in very large networks. These methods involve selecting a subset of nodes as landmarks and computing offline the distances from each node in the graph to those landmarks. At runtime, when the distance between a pair of nodes is needed, it can be estimated quickly by combining the precomputed distances. We prove that selecting the optimal set of landmarks is an NP-hard problem, and thus heuristic solutions need to be employed. We therefore explore theoretical insights to devise a variety of simple methods that scale well in very large networks. The efficiency of the suggested techniques is tested experimentally using five real-world graphs having millions of edges. While theoretical bounds support the claim that random landmarks work well in practice, our extensive experimentation shows that smart landmark selection can yield dramatically more accurate results: for a given target accuracy, our methods require as much as 250 times less space than selecting landmarks at random. In addition, we demonstrate that at a very small accuracy loss our techniques are several orders of magnitude faster than the state-of-the-art exact methods. Finally, we study an application of our methods to the task of social search in large graphs.

The technique ofk-anonymization allows the releasing of databases that contain personal information while ensuring some degree of individual privacy. Anonymization is usually performed by generalizing database entries. We formally study the concept of generalization, and propose three information-theoretic measures for capturing the amount of information that is lost during the anonymization process. The proposed measures are more general and more accurate than those that were proposed by Meyerson and Williams and Aggarwal et al. We study the problem of achievingk-anonymity with minimal loss of information. We prove that it is NP-hard and study polynomial approximations for the optimal solution. Our first algorithm gives an approximation guarantee of O(lnk) for two of our measures as well as for the previously studied measures. This improves the best-known O(k)-approximation in. While the previous approximation algorithms relied on the graph representation framework, our algorithm relies on a novel hypergraph representation that enables the improvement in the approximation ratio from O(k) to O(lnk). As the running time of the algorithm is O(n2k}), we also show how to adapt the algorithm in in order to obtain an O(k)-approximation algorithm that is polynomial in bothnandk.

Query logs record the queries and the actions of the users of engines, and as such they contain valuable information about the interests, the preferences, and the behavior of the users, as well as their implicit feedback to engine results. Mining the wealth of information available in the query logs has many important applications including query-log analysis, user profiling and personalization, advertising, query recommendation, and more.In this paper we introduce the query-flow graph, a graph representation of the interesting knowledge about latent querying behavior. Intuitively, in the query-flow graph a directed edge from query qi to query qj means that the two queries are likely to be part of the same search mission. Any path over the query-flow graph may be seen as a searching behavior, whose likelihood is given by the strength of the edges along the path.The query-flow graph is an outcome of query-log mining and, at the same time, a useful tool for it. We propose a methodology that builds such a graph by mining time and textual information as well as aggregating queries from different users. Using this approach we build a real-world query-flow graph from a large-scale query log and we demonstrate its utility in concrete applications, namely, finding logical sessions, and query recommendation. We believe, however, that the usefulness of the query-flow graph goes beyond these two applications.

We introduce a unified graph representation of the Web, which includes both structural and usage information. We model this graph using a simple union of the Web's hyperlink and click graphs. The hyperlink graph expresses link structure among Web pages, while the click graph is a bipartite graph of queries and documents denoting users' searching behavior extracted from a search engine's query log.

We propose a framework for searching the Wikipedia with contextual information. Our framework extends the typical keyword search, by considering queries of the type (q,p), where q is a set of terms (as in classical Web search), and p is a source Wikipedia document. The query terms q represent the information that the user is interested in finding, and the document p provides the context of the query. The task is to rank other documents in Wikipedia with respect to their relevance to the query terms q given the context document p. By associating a context to the query terms, the search results of a search initiated in a particular page can be made more relevant.

In this paper we introduce new notions of k-type anonymizations. Those notions achieve similar privacy goals as those aimed by Sweenie and Samarati when proposing the concept of k-anonymization: an adversary who knows the public data of an individual cannot link that individual to less than k records in the anonymized table. Every anonymized table that satisfies k-anonymity complies also with the anonymity constraints dictated by the new notions, but the converse is not necessarily true. Thus, those new notions allow generalized tables that may offer higher utility than k-anonymized tables, while still preserving the required privacy constraints. We discuss and compare the new anonymization concepts, which we call (1, k )-, (k, k)- and global (1, k)-anonymizations, according to several utility measures. We propose a collection of agglomerative algorithms for the problem of finding such anonymizations with high utility, and demonstrate the usefulness of our definitions and our algorithms through extensive experimental evaluation on real and synthetic datasets.

The problem of mining frequent patterns in networks has many applications, including analysis of complex networks, clustering of graphs, finding communities in social networks, and indexing of graphical and biological databases. Despite this wealth of applications, the current state of the art lacks algorithmic tools for counting the number of subgraphs contained in a large network. In this paper we develop data-stream algorithms that approximate the number of all subgraphs of three and four vertices in directed and undirected networks. We use the frequency of occurrence of all subgraphs to prove their significance in order to characterize different kinds of networks: we achieve very good precision in clustering networks with similar structure. The significance of our method is supported by the fact that such high precision cannot be achieved when performing clustering based on simpler topological properties, such as degree, assortativity, and eigenvector distributions. We have also tested our techniques using swap randomization.

In this paper we study the problem of local triangle counting in large graphs. Namely, given a large graph G = (V;E) we want to estimate as accurately as possible the number of triangles incident to every node υ ∈ V in the graph. The problem of computing the global number of triangles in a graph has been considered before, but to our knowledge this is the first paper that addresses the problem of local triangle counting with a focus on the efficiency issues arising in massive graphs. The distribution of the local number of triangles and the related local clustering coefficient can be used in many interesting applications. For example, we show that the measures we compute can help to detect the presence of spamming activity in large-scale Web graphs, as well as to provide useful features to assess content quality in social networks.

We introduce the problem of query decomposition, where we are given a query and a document retrieval system, and we want to produce a small set of queries whose union of resulting documents corresponds approximately to that of the original query. Ideally, these queries should represent coherent, conceptually well-separated topics.

The quality of user-generated content varies drastically from excellent to abuse and spam. As the availability of such content increases, the task of identifying high-quality content sites based on user contributions --social media sites -- becomes increasingly important. Social media in general exhibit a rich variety of information sources: in addition to the content itself, there is a wide array of non-content information available, such as links between items and explicit quality ratings from members of the community. In this paper we investigate methods for exploiting such community feedback to automatically identify high quality content. As a test case, we focus on Yahoo! Answers, a large community question/answering portal that is particularly rich in the amount and types of content and social interactions available in it. We introduce a general classification framework for combining the evidence from different sources of information, that can be tuned automatically for a given social media type and quality definition. In particular, for the community question/answering domain, we show that our system is able to separate high-quality items from the rest with an accuracy close to that of humans

Matrix decomposition methods represent a data matrix as a product of two factor matrices: one containing basis vectors that represent meaningful concepts in the data, and another describing how the observed data can be expressed as combinations of the basis vectors. Decomposition methods have been studied extensively, but many methods return real-valued matrices. Interpreting real-valued factor matrices is hard if the original data is Boolean. In this paper, we describe a matrix decomposition formulation for Boolean data, the Discrete Basis Problem. The problem seeks for a Boolean decomposition of a binary matrix, thus allowing the user to easily interpret the basis vectors. We also describe a variation of the problem, the Discrete Basis Partitioning Problem. We show that both problems are NP-hard. For the Discrete Basis Problem, we give a simple greedy algorithm for solving it; for the Discrete Basis Partitioning Problem we show how it can be solved using existing methods. We present experimental results for the greedy algorithm and compare it against other, well known methods. Our algorithm gives intuitive basis vectors, but its reconstruction error is usually larger than with the real-valued methods. We discuss about the reasons for this behavior.

In this article we study the trade-offs in designing efficient caching systems for Web search engines. We explore the impact of different approaches, such as static vs. dynamic caching, and caching query results vs. caching posting lists. Using a query log spanning a whole year, we explore the limitations of caching and we demonstrate that caching posting lists can achieve higher hit rates than caching query answers. We propose a new algorithm for static caching of posting lists, which outperforms previous methods. We also study the problem of finding the optimal way to split the static cache between answers and posting lists. Finally, we measure how the changes in the query log influence the effectiveness of static caching, given our observation that the distribution of the queries changes slowly over time. Our results and observations are applicable to different levels of the data-access hierarchy, for instance, for a memory/disk layer or a broker/remote server layer.

Sequence segmentation is a central problem in the analysis of sequential and time-series data. In this paper we introduce and we study a novel variation to the segmentation problem: in addition to partitioning the sequence we also seek to apply a limited amount of reordering, so that the overall representation error is minimized. Our problem formulation has applications in segmenting data collected from a sensor network where some of the sensors might be slightly out of sync, or in the analysis of newsfeed data where news reports on a few different topics are arriving in an interleaved manner. We formulate the problem of segmentation with rearrangements and we show that it is an NP-hard problem to solve or even approximate. We then proceed to devise effective algorithms for the proposed problem, combining ideas from linear programming, dynamic programming, and outlier-detection algorithms in sequences. We perform extensive experimental evaluation on synthetic and real datasets that demonstrates the efficacy of the suggested algorithms.

In this paper we study the trade-offs in designing efficient caching systems for Web search engines. We explore the impact of different approaches, such as static vs. dynamic caching, and caching query results vs.caching posting lists. Using a query log spanning a whole year we explore the limitations of caching and we demonstrate that caching posting lists can achieve higher hit rates than caching query answers. We propose a new algorithm for static caching of posting lists, which outperforms previous methods. We also study the problem of finding the optimal way to split the static cache between answers and posting lists. Finally, we measure how the changes in the query log affect the effectiveness of static caching, given our observation that the distribution of the queries changes slowly over time. Our results and observations are applicable to different levels of the data-access hierarchy, for instance, for a memory/disk layer or a broker/remote server layer.

Web spam can significantly deteriorate the quality of search engine results. Thus there is a large incentive for commercial search engines to detect spam pages efficiently and accurately. In this paper we present a spam detection system that combines link-based and content-based features, and uses the topology of the Web graph by exploiting the link dependencies among the Web pages. We find that linked hosts tend to belong to the same class: either both are spam or both are non-spam. We demonstrate three methods of incorporating the Web graph topology into the predictions obtained by our base classifier: (i) clustering the host graph, and assigning the label of all hosts in the cluster by majority vote, (ii) propagating the predicted labels to neighboring hosts, and (iii) using the predicted labels of neighboring hosts as new features and retraining the classifier. The result is an accurate system for detecting Web spam, tested on a large and public dataset, using algorithms that can be applied in practice to large-scale Web data.

The problem of assessing the significance of data mining results on high-dimensional 0--1 datasets has been studied extensively in the literature. For problems such as mining frequent sets and finding correlations, significance testing can be done by standard statistical tests such as chi-square, or other methods. However, the results of such tests depend only on the specific attributes and not on the dataset as a whole. Moreover, the tests are difficult to apply to sets of patterns or other complex results of data mining algorithms. In this article, we consider a simple randomization technique that deals with this shortcoming. The approach consists of producing random datasets that have the same row and column margins as the given dataset, computing the results of interest on the randomized instances and comparing them to the results on the actual data. This randomization technique can be used to assess the results of many different types of data mining algorithms, such as frequent sets, clustering, and spectral analysis. To generate random datasets with given margins, we use variations of a Markov chain approach which is based on a simple swap operation. We give theoretical results on the efficiency of different randomization methods, and apply the swap randomization method to several well-known datasets. Our results indicate that for some datasets the structure discovered by the data mining algorithms is expected, given the row and column margins of the datasets, while for other datasets the discovered structure conveys information that is not captured by the margin counts.

We consider the following problem: given a set of clusterings, find a single clustering that agrees as much as possible with the input clusterings. This problem, clustering aggregation , appears naturally in various contexts. For example, clustering categorical data is an instance of the clustering aggregation problem; each categorical attribute can be viewed as a clustering of the input rows where rows are grouped together if they take the same value on that attribute. Clustering aggregation can also be used as a metaclustering method to improve the robustness of clustering by combining the output of multiple algorithms. Furthermore, the problem formulation does not require a priori information about the number of clusters; it is naturally determined by the optimization function. In this article, we give a formal statement of the clustering aggregation problem, and we propose a number of algorithms. Our algorithms make use of the connection between clustering aggregation and the problem of correlation clustering . Although the problems we consider are NP-hard, for several of our methods, we provide theoretical guarantees on the quality of the solutions. Our work provides the best deterministic approximation algorithm for the variation of the correlation clustering problem we consider. We also show how sampling can be used to scale the algorithms for large datasets. We give an extensive empirical evaluation demonstrating the usefulness of the problem and of the solutions.

Sequence data are abundant in application areas such as computational biology, environmental sciences, and telecommunication. Many real-life sequences have a strong segmental structure, with segments of different complexities. In this paper we study the description of sequence segments using variable length Markov chains (VLMCs), also known as tree models. We discover the segment boundaries of a sequence and at the same time we obtain a VLMC for each segment. Such a context tree contains the probability distribution vectors that capture the essential features of the corresponding segment. We use the Bayesian information criterion (BIC) and the Krichevsky-Trofimov probability (KT) to select the number of segments of a sequence. On DNA data the method selects segments that closely correspond to the annotated regions of the genes.

Many 0/1 datasets have a very large number of variables; however, they are sparse and the dependency structure of the variables is simpler than the number of variables would suggest. Defining the effective dimensionality of such a dataset is a nontrivial problem. We consider the problem of defining a robust measure of dimension for 0/1 datasets, and show that the basic idea of fractal dimension can be adapted for binary data. However, as such the fractal dimension is difficult to interpret. Hence we introduce the concept of normalized fractal dimension. For a dataset D, its normalized fractal dimension counts the number of independent columns needed to achieve the unnormalized fractal dimension of D. The normalized fractal dimension measures the degree of dependency structure of the data. We study the properties of the normalized fractal dimension and discuss its computation. We give empirical results on the normalized fractal dimension, comparing it against PCA.

The problem of assessing the significance of data mining results on high-dimensional 0-1 data sets has been studied extensively in the literature. For problems such as mining frequent sets and finding correlations, significance testing can be done by, e.g., chi-square tests, or many other methods. However, the results of such tests depend only on the specific attributes and not on the dataset as a whole. Moreover, the tests are more difficult to apply to sets of patterns or other complex results of data mining. In this paper, we consider a simple randomization technique that deals with this shortcoming. The approach consists of producing random datasets that have the same row and column margins with the given dataset, computing the results of interest on the randomized instances, and comparing them against the results on the actual data. This randomization technique can be used to assess the results of many different types of data mining algorithms, such as frequent sets, clustering, and rankings. To generate random datasets with given margins, we use variations of a Markov chain approach, which is based on a simple swap operation. We give theoretical results on the efficiency of different randomization methods, and apply the swap randomization method to several well-known datasets. Our results indicate that for some datasets the structure discovered by the data mining algorithms is a random artifact, while for other datasets the discovered structure conveys meaningful information.

Ordering and ranking items of different types are important tasks in various applications, such as query processing and scientific data mining. A total order for the items can be misleading, since there are groups of items that have practically equal ranks.We consider bucket orders, i.e., total orders with ties. They can be used to capture the essential order information without overfitting the data: they form a useful concept class between total orders and arbitrary partial orders. We address the question of finding a bucket order for a set of items, given pairwise precedence information between the items. We also discuss methods for computing the pairwise precedence data.We describe simple and efficient algorithms for finding good bucket orders. Several of the algorithms have a provable approximation guarantee, and they scale well to large datasets. We provide experimental results on artificial and a real data that show the usefulness of bucket orders and demonstrate the accuracy and efficiency of the algorithms.

Sequence segmentation and dimensionality reduction have been used as methods for studying high-dimensional sequences — they both reduce the complexity of the representation of the original data. In this paper we study the interplay of these two techniques. We formulate the problem of segmenting a sequence while modeling it with a basis of small size, thus essentially reducing the dimension of the input sequence. We give three different algorithms for this problem: all combine existing methods for sequence segmentation and dimensionality reduction. For two of the proposed algorithms we prove guarantees for the quality of the solutions obtained. We describe experimental results on synthetic and real datasets, including data on exchange rates and genomic sequences. Our experiments show that the algorithms indeed discover underlying structure in the data, including both segmental structure and interdependencies between the dimensions.

We consider the following problem: given a set of clusterings, find a clustering that agrees as much as possible with the given clusterings. This problem, clustering aggregation, appears naturally in various contexts. For example, clustering categorical data is an instance of the problem: each categorical variable can be viewed as a clustering of the input rows. Moreover, clustering aggregation can be used as a meta-clustering method to improve the robustness of clusterings. The problem formulation does not require a-priori information about the number of clusters, and it gives a natural way for handling missing values. We give a formal statement of the clustering-aggregation problem, we discuss related work, and we suggest a number of algorithms. For several of the methods we provide theoretical guarantees on the quality of the solutions. We also show how sampling can be used to scale the algorithms for large data sets. We give an extensive empirical evaluation demonstrating the usefulness of the problem and of the solutions.

Traditional data mining applications consider the problem of mining a single relation between two attributes. For example, in a scientific bibliography database, authors are related to papers, and we may be interested in discovering association rules between authors. However, in real life, we often have multiple attributes related though chains of relations. For example, authors write papers, and papers concern one or more topics. Mining such relational chains poses additional challenges. In this paper we consider the following problem: given a chain of two relations R/sub 1/ (A, P) and R/sub 2/(P, T) we want to find selectors for the objects in T such that the projected relation between A and P satisfies a specific property. The motivation for our approach is that a given property might not hold on the whole dataset, but it might hold when projecting the data on a selector set. We discuss various algorithms and we examine the conditions under which the a priori technique can be used. We experimentally demonstrate the effectiveness of our methods.

Consider spatial data consisting of a set of binary features taking values over a collection of spatial extents (grid cells). We propose a method that simultaneously finds spatial correlation and feature co-occurrence patterns, without any parameters. In particular, we employ the minimum description length (MDL) principle coupled with a natural way of compressing regions. This defines what "good" means: a feature co-occurrence pattern is good, if it helps us better compress the set of locations for these features. Conversely, a spatial correlation is good, if it helps us better compress the set of features in the corresponding region. Our approach is scalable for large datasets (both number of locations and of features). We evaluate our method on both real and synthetic datasets.

It is commonly assumed that high-dimensional datasets contain points most of which are located in low-dimensional manifolds. Detection of low-dimensional clusters is an extremely useful task for performing operations such as clustering and classification, however, it is a challenging computational problem. In this paper we study the problem of finding subsets of points with low intrinsic dimensionality. Our main contribution is to extend the definition of fractal correlation dimension, which measures average volume growth rate, in order to estimate the intrinsic dimensionality of the data in local neighborhoods. We provide a careful analysis of several key examples in order to demonstrate the properties of our measure. Based on our proposed measure, we introduce a novel approach to discover clusters with low dimensionality. The resulting algorithms extend previous density based measures, which have been successfully used for clustering. We demonstrate the effectiveness of our algorithms for discovering low-dimensional m-flats embedded in high dimensional spaces, and for detecting low-rank sub-matrices.

We study the problem of segmenting a sequence into k pieces so that the resulting segmentation satisfies monotonicity or unimodality constraints. Unimodal functions can be used to model phenomena in which a measured variable first increases to a certain level and then decreases. We combine a well-known unimodal regression algorithm with a simple dynamic-programming approach to obtain an optimal quadratic-time algorithm for the problem of unimodal k-segmentation. In addition, we describe a more efficient greedy-merging heuristic that is experimentally shown to give solutions very close to the optimal. As a concrete application of our algorithms, we describe two methods for testing if a sequence behaves unimodally or not. Our experimental evaluation shows that our algorithms and the proposed unimodality tests give very intuitive results.

One of the most well-studied problems in data mining is computing the collection of frequent item sets in large transactional databases. One obstacle for the applicability of frequent-set mining is that the size of the output collection can be far too large to be carefully examined and understood by the users. Even restricting the output to the border of the frequent item-set collection does not help much in alleviating the problem.In this paper we address the issue of overwhelmingly large output size by introducing and studying the following problem: What are the k sets that best approximate a collection of frequent item sets? Our measure of approximating a collection of sets by k sets is defined to be the size of the collection covered by the the k sets, i.e., the part of the collection that is included in one of the k sets. We also specify a bound on the number of extra sets that are allowed to be covered. We examine different problem variants for which we demonstrate the hardness of the corresponding problems and we provide simple polynomial-time approximation algorithms. We give empirical evidence showing that the approximation methods work well in practice.

Massive-scale self-administered networks like Peer-to-Peer and Sensor Networks have data distributed across thousands of participant hosts. These networks are highly dynamic with short-lived hosts being the norm rather than an exception. In recent years, researchers have investigated best-effort algorithms to efficiently process aggregate queries (e.g., sum, count, average, minimum and maximum) [6, 13, 21, 34, 35, 37] on these networks. Unfortunately, query semantics for best-effort algorithms are ill-defined, making it hard to reason about guarantees associated with the result returned. In this paper, we specify a correctness condition, single-site validity, with respect to which the above algorithms are best-effort. We present a class of algorithms that guarantee validity in dynamic networks. Experiments on real-life and synthetic network topologies validate performance of our algorithms, revealing the hitherto unknown price of validity.

High-dimensional collections of 0--1 data occur in many applications. The attributes in such data sets are typically considered to be unordered. However, in many cases there is a natural total or partial order ≺ underlying the variables of the data set. Examples of variables for which such orders exist include terms in documents, courses in enrollment data, and paleontological sites in fossil data collections. The observations in such applications are flat, unordered sets; however, the data sets respect the underlying ordering of the variables. By this we mean that if A ≺ B ≺ C are three variables respecting the underlying ordering ≺, and both of variables A and C appear in an observation, then, up to noise levels, variable B also appears in this observation. Similarly, if A1 ≺ A2 ≺ … ≺ Al-1 ≺ Ai is a longer sequence of variables, we do not expect to see many observations for which there are indices i < j < k such that Ai and Ak occur in the observation but Aj does not.In this paper we study the problem of discovering fragments of orders of variables implicit in collections of unordered observations. We define measures that capture how well a given order agrees with the observed data. We describe a simple and efficient algorithm for finding all the fragments that satisfy certain conditions. We also discuss the sometimes necessary postprocessing for selecting only the best fragments of order. Also, we relate our method with a sequencing approach that uses a spectral algorithm, and with the consecutive ones problem. We present experimental results on some real data sets (author lists of database papers, exam results data, and paleontological data).

Finding pages on the Web that are similar to a query page (Related Pages) is an important component of modern search engines. A variety of strategies have been proposed for answering Related Pages queries, but comparative evaluation by user studies is expensive, especially when large strategy spaces must be searched (e.g., when tuning parameters). We present a technique for automatically evaluating strategies using Web hierarchies, such as Open Directory, in place of user feedback. We apply this evaluation methodology to a mix of document representation strategies, including the use of text, anchor-text, and links. We discuss the relative advantages and disadvantages of the various approaches examined. Finally, we describe how to e#ciently construct a similarity index out of our chosen strategies, and provide sample results from our index.

Set value attributes are a concise and natural way to model complex data sets. Modern Object Relational systems support set value attributes and allow various query capabilities on them. In this paper we initiate a formal study of indexing techniques for set value attributes based on similarity, for suitably defined notions of similarity between sets. Such techniques are necessary in modern applications such as recommendations through collaborative filtering and automated advertising. Our techniques are probabilistic and approximate in nature. As a design principle we create structures that make use of well known and widely used data structuring techniques, as a means to ease integration with existing infrastructure.

Association-rule mining has heretofore relied on the condition of high support to do its work efficiently. In particular, the well-known a priori algorithm is only effective when the only rules of interest are relationships that occur very frequently. However, there are a number of applications, such as data mining, identification of similar Web documents, clustering, and collaborative filtering, where the rules of interest have comparatively few instances in the data. In these cases, we must look for highly correlated items, or possibly even causal relationships between infrequent items. We develop a family of algorithms for solving this problem, employing a combination of random sampling and hashing techniques. We provide analysis of the algorithms developed and conduct experiments on real and synthetic data to obtain a comparative performance analysis.

Association rule mining has heretofore relied on the condition of high support to do its work efficiently. In particular, the well-known a-priori algorithm is only effective when the only rules of interest are relationships that occur very frequently. However, there are a number of applications, such as data mining, identification of similar Web documents, clustering and collaborative filtering, where the rules of interest have comparatively few instances in the data. In these cases, we must look for highly correlated items, or possibly even causal relationships between infrequent items. We develop a family of algorithms for solving this problem, employing a combination of random sampling and hashing techniques. We provide an analysis of the algorithms developed and conduct experiments on real and synthetic data to obtain a comparative performance analysis.

XML is rapidly emerging as the new standard for data representation and exchange on the Web. An XML document can be accompanied by a Document Type Descriptor (DTD) which plays the role of a schema for an XML data collection. DTDs contain valuable information on the structure of documents and thus have a crucial role in the efficient storage of XML data, as well as the effective formulation and optimization of XML queries. In this paper, we propose XTRACT, a novel system for inferring a DTD schema for a database of XML documents. Since the DTD syntax incorporates the full expressive power of regular expressions, naive approaches typically fail to produce concise and intuitive DTDs. Instead, the XTRACT inference algorithms employ a sequence of sophisticated steps that involve: (1) finding patterns in the input sequences and replacing them with regular expressions to generate “general” candidate DTDs, (2) factoring candidate DTDs using adaptations of algorithms from the logic optimization literature, and (3) applying the Minimum Description Length (MDL) principle to find the best DTD among the candidates. The results of our experiments with real-life and synthetic DTDs demonstrate the effectiveness of XTRACT's approach in inferring concise and semantically meaningful DTD schemas for XML databases.