Graph neural networks (GNNs) are deep learning models designed for graph-structured data that have achieved strong results across domains--social networks, knowledge graphs, bioinformatics, transportation, World Wide Web, and finance--on tasks such as node and graph classification, link prediction, entity resolution, question answering, recommendation, and fraud detection. Explaining the decisions of high-performing, yet ''black-box'' GNNs remains both challenging and essential. The initial five years have produced tremendous progress with many GNN explainers (e.g., GNNExplainer, PGExplainer, SubgraphX, PGMExplainer, GraphLime, GCFExplainer, CF2, GNN-LRP) that identify the influential nodes, edges, subgraphs, and features aiming to explain the output of GNNs.

We present GERN, a novel scalable framework for training GNNs in node classification tasks, based on effective resistance, a standard tool in spectral graph theory. Our method progressively refines the GNN weights on a sequence of random spanning trees suitably transformed into path graphs which, despite their simplicity, are shown to retain essential topological and node information of the original input graph. The sparse nature of these path graphs substantially lightens the computational burden of GNN training. This not only enhances scalability but also improves accuracy in subsequent test phases, especially under small training set regimes, which are of great practical importance, as in many real-world scenarios labels may be hard to obtain. In these settings, our framework yields very good results as it effectively counters the training deterioration caused by overfitting when the training set is small. Our method also addresses common issues like over-squashing and over-smoothing while avoiding under-reaching phenomena.

Counterfactual learning is emerging as an important paradigm, rooted in causality, which promises to alleviate common issues of graph neural networks (GNNs), such as fairness and interpretability. However, as in many real-world application domains where conducting randomized controlled trials is impractical, one has to rely on available observational (factual) data to detect counterfactuals. In this paper, we introduce and tackle the problem of searching for counterfactual evidences for the GNN-based node classification task. A counterfactual evidence is a pair of nodes such that, regardless they exhibit great similarity both in the features and in their neighborhood subgraph structures, they are classified differently by the GNN. We develop effective and efficient search algorithms and a novel indexing solution that leverages both node features and structural information to identify counterfactual evidences, and generalizes beyond any specific GNN. Through various downstream applications, we demonstrate the potential of counterfactual evidences to enhance fairness and accuracy of GNNs.

User navigation on social media platforms is often driven by recommendation algorithms . A growing body of literature questions whether these recommendation systems may exacerbate detrimental phenomena, perpetrate intrinsic biases, and alter user preferences in the long-term. Driven by this premise, the present study formalizes the concept of “ algorithmic drift ”, further introducing a novel framework and two metrics to quantify it. Our methodology involves a simulation process that models user behavior through random walks , reflecting user navigation under the influence and guidance of recommendation systems. This approach highlights that each user may respond differently to such stimuli, varying in both resistance to recommendation influence and inertia in selecting new steps in the random walk. The proposed metrics measure the drift in user behavior and item consumption over time in the random walks. We conduct a comprehensive evaluation over both synthetic and real-world datasets to validate the framework’s ability to measure drift across different parameter settings. All code and data used in our experimentation are publicly accessible online. 1

Traditionally, route recommendation systems focused on minimizing distance (or time) to travel between two points. However, recent attention has shifted to other factors beyond mere length. This paper addresses the challenge of ensuring a fair distribution of visits among network nodes when handling a high volume of point-to-point path queries. In doing so, we adopt a Rawlsian notion of individual-level fairness exploiting the power of randomization. Specifically, we aim to create a probabilistic distribution over paths that maximizes the minimum probability of any eligible node being included in the recommended path. A key idea of our work is the notion of forward paths , i.e., paths where travelling along any edge decreases the distance to the destination. In unweighted graphs forward paths and shortest paths coincide, but in weighted graphs forward paths provide a richer set of alternative routes, involving many more nodes while remaining close in length to the shortest path. Thus, they offer diversity and a wider basis for fairness, while maintaining near-optimal path lengths. We devise an algorithm that extracts a directed acyclic graph (DAG) containing all the forward paths in the input graph, with the same computational runtime as solving a single shortest-path query. This avoids enumerating all possible forward paths, which can be exponential in the number of nodes. We then design a flow problem on this DAG to derive the probabilistic distribution over forward paths with the desired fairness property, solvable in polynomial time through a sequence of small linear programs. Our experiments on real-world datasets validate our theoretical results, demonstrating that our technique provides individual node satisfaction while maintaining near-optimal path lengths. Moreover, our experiments show that our method can handle networks with millions of nodes and edges on a commodity laptop, and scales better than the baselines when there is a large volume of path queries for the same source and destination pair.

While accuracy has long been prioritized as the primary metric for Recommender Systems (RSs), it is increasingly accepted that the system’s overall quality is not solely determined by this factor. Reachability, the ease with which users can navigate the whole content catalog through recommendations, emerges as a pivotal yet under-explored concept: not only it ensures a smooth experience for users, but it also provides more equitable exposure for the items, avoiding that only a small fraction of popular items get the bulk of the attention. Despite its importance, the few existing studies analyze reachability without attempting a proper optimization. In this article, we study the problem of optimizing the overall reachability of a RS while maintaining high-quality recommendations. We model a user browsing session as a random walk on a recommendation graph, where the links and the transition probabilities are defined based on the relevance score of the recommendation list that the user gets at every step. In this setting, reachability is modeled as the expected length of a path to reach a given item. We introduce two optimization problems, one discrete and one continuous, and characterize their theoretical properties. We then devise two algorithms that outperform non-trivial baseline methods in enhancing reachability while maintaining a high Normalized Discounted Cumulative Gain (nDCG) score. Our experimental results show that, in some settings, our methods are able to improve the reachability metric by 80% while only compromising nDCG by 5%. Moreover, our empirical analysis shows that optimizing for reachability provides positive effects also on other prevalent “beyond-accuracy” metrics.

Networks in many real-world applications come with an inherent uncertainty in their structure, due to, for example, noisy measurements, inference and prediction models, or for privacy purposes. Modeling and analyzing uncertain graphs have attracted a great deal of attention. Among the various graph analytic tasks studied, the extraction of dense substructures, such as cores or trusses, has a central role. In this article, we study the problem of ( k , γ)-truss indexing and querying over an uncertain graph \({\mathcal {G}}\) . A ( k , γ)-truss is the largest subgraph of \({\mathcal {G}}\) such that the probability of each edge being contained in at least k -2 triangles is no less than γ. Our first proposal, CPT-index, keeps all the ( kz , γ)-trusses: retrieval for any given k and γ can be executed in an optimal linear time w.r.t. the graph size of the queried ( k , γ)-truss. We develop a bottom-up CPT-indexconstruction scheme and an improved algorithm for fast CPT-indexconstruction using top-down graph partitions. For trading off between ( k ,γ)-truss offline indexing and online querying, we further develop an approximate indexing approach ε , Δ r -APXequipped with two parameters, ε and Δ r , that govern tolerated errors. In addition, we further investigate the problem of maintaining ( k , γ)-truss indexes over dynamic uncertain graphs, where the update of vertex/edge insertions/deletions and also edge probability increments/decrements may frequently occur. We propose a comprehensive solution for CPT-indexand (ε , Δ r -APXmaintenance by addressing one fundamental task of one edge’s probability increment/decrement. To reduce the scope of affected edges that have trussness changed, we categorize three types of candidate edges and propose tight lower/upper bounds for trussness refinement, which can efficiently accomplish CPT-indexmaintenance in a local update scheme. Our proposed techniques for one single edge change can also be extended to handle a batch update of multiple edges. Extensive experiments using large-scale uncertain graphs with 261 million edges validate the efficiency of our proposed indexing and querying algorithms, as well as our ( k ,γ)-truss index maintenance algorithms, against state-of-the-art methods. Case studies on real-world graphs demonstrate the significant efficiency improvement by our proposed solutions as well as interesting discoveries.

Signed Graph Neural Networks (SGNNs) have recently gained attention as an effective tool for several learning tasks on signed networks, i.e., graphs where edges have an associated polarity. One of these tasks is to predict the polarity of the links for which this information is missing, starting from the network structure and the other available polarities. However, when the available polarities are few and potentially noisy, such a task becomes challenging. In this work, we devise a semi-supervised learning framework that builds around the novel concept of \emph{multiscale social balance} to improve the prediction of link polarities in settings characterized by limited data quantity and quality. Our model-agnostic approach can seamlessly integrate with any SGNN architecture, dynamically reweighting the importance of each data sample while making strategic use of the structural information from unlabeled edges combined with social balance theory. Empirical validation demonstrates that our approach outperforms established baseline models, effectively addressing the limitations imposed by noisy and sparse data. This result underlines the benefits of incorporating multiscale social balance into SGNNs, opening new avenues for robust and accurate predictions in signed network analysis.

Computing basic network properties and machine learning (ML) model outputs, e.g., reachability, shortest path distance, triangle count, node classification, etc., are key to understand large and complex graphs. We study two fundamental problems: (1) Given a graph with uncertain edges and a real-valued network property or an ML model, estimate the uncertainty associated with evaluating the property or the ML model's output over the uncertain graph. (2) Given a limited budget on the number of edges, find the$k-\mathbf{best}$edges whose probability update will reduce the aforementioned uncertainty maximally. We formulate both problems using the information-theoretic notion of entropy and then characterize the hardness of our problems. We next devise approximate solutions with theoretical soundness and greedy subgraph selection-based efficient algorithms. Our empirical evaluation and case study with real-world and synthetic datasets demonstrate that the proposed solutions are more effective and efficient than baselines and are several orders of magnitude faster than exact approaches.

Centrality measures, quantifying the importance of vertices or edges, play a fundamental role in network analysis. To date, triggered by some positive approximability results, a large body of work has been devoted to studying centrality maximization, where the goal is to maximize the centrality score of a target vertex by manipulating the structure of a given network. On the other hand, due to the lack of such results, only very little attention has been paid to centrality minimization, despite its practical usefulness.

Abstract Human feedback is often used, either directly or indirectly, as input to algorithmic decision making. However, humans are biased: if the algorithm that takes as input the human feedback does not control for potential biases, this might result in biased algorithmic decision making, which can have a tangible impact on people’s lives. In this paper, we study how to detect and correct for evaluators’ bias in the task of ranking people (or items) from pairwise comparisons. Specifically, we assume we are given pairwise comparisons of the items to be ranked produced by a set of evaluators. While the pairwise assessments of the evaluators should reflect to a certain extent the latent (unobservable) true quality scores of the items, they might be affected by each evaluator’s own bias against, or in favor, of some groups of items. By detecting and amending evaluators’ biases, we aim to produce a ranking of the items that is, as much as possible, in accordance with the ranking one would produce by having access to the latent quality scores. Our proposal is a novel method that extends the classic Bradley-Terry model by having a bias parameter for each evaluator which distorts the true quality score of each item, depending on the group the item belongs to. Thanks to the simplicity of the model, we are able to write explicitly its log-likelihood w.r.t. the parameters (i.e., items’ latent scores and evaluators’ bias) and optimize by means of the alternating approach. Our experiments on synthetic and real-world data confirm that our method is able to reconstruct the bias of each single evaluator extremely well and thus to outperform several non-trivial competitors in the task of producing a ranking which is as much as possible close to the unbiased ranking.

Abstract Societal biases encoded in real-world data can contaminate algorithmic decisions, perpetuating preexisting inequalities in domains such as employment and education. In the fair ranking literature, following the doctrine of affirmative action, fairness is enforced by means of a group-fairness constraint requiring “enough” individuals from protected groups in the top-k positions, for a ranking to be considered valid. However, which are the groups that need to be protected? And how much representation is “enough”? As the biases affecting the process may not always be directly observable nor measurable, these questions might be hard to answer in a principled way, especially when many different potentially discriminated subgroups exist. This paper addresses this issue by automatically identifying the disadvantaged groups in the data and mitigating their disparate representation in the final ranking. Our proposal leverages the notion of divergence to automatically identify which subgroups, defined as combination of sensitive attributes, show a statistically significant deviation, in terms of ranking utility, compared to the overall population. Subgroups with negative divergence experience a disadvantage. We formulate the problem of re-ranking instances to maximize the minimum subgroup divergence, while maintaining the new ranking as close as possible to the original one. We develop a method which is based on identifying the divergent subgroups and applying a re-ranking procedure which is monotonic w.r.t. the goal of maximizing the minimum divergence. Our experimental results show that our method effectively eliminates the existence of disadvantaged subgroups while producing rankings which are very close to the original ones.

Finding dense subgraphs in large (hyper)graphs is a key primitive in a variety of real-world application domains, encompassing social network analytics, event detection, biology, and finance. In most such applications, one typically aims at finding several (possibly overlapping) dense subgraphs, which might correspond to communities in social networks or interesting events. While a large amount of work is devoted to finding a single densest subgraph, perhaps surprisingly, the problem of finding several dense subgraphs in weighted hypergraphs with limited overlap has not been studied in a principled way, to the best of our knowledge. In this work, we define and study a natural generalization of the densest subgraph problem in weighted hypergraphs, where the main goal is to find at most k subgraphs with maximum total aggregate density, while satisfying an upper bound on the pairwise weighted Jaccard coefficient, i.e., the ratio of weights of intersection divided by weights of union on two nodes sets of the subgraphs. After showing that such a problem is NP-Hard, we devise an efficient algorithm that comes with provable guarantees in some cases of interest, as well as, an efficient practical heuristic. Our extensive evaluation on large real-world hypergraphs confirms the efficiency and effectiveness of our algorithms.

Counterfactual explanations are a natural way for humans to gain understanding and trust in the outcomes of complex machine learning algorithms. In the context of natural language processing, generating counterfactuals is particularly challenging as it requires the generated text to be fluent, grammatically correct, and meaningful. In this study, we improve the current state of the art for the generation of such counterfactual explanations for text classifiers. Our approach, named RELITC (Relevance-based Infilling for Textual Counterfactuals), builds on the idea of masking a fraction of text tokens based on their importance in a given prediction task and employs a novel strategy, based on the entropy of their associated probability distributions, to determine the infilling order of these tokens. Our method uses less time than competing methods to generate counterfactuals that require less changes, are closer to the original text and preserve its content better, while being competitive in terms of fluency. We demonstrate the effectiveness of the method on four different datasets and show the quality of its outcomes in a comparison with human generated counterfactuals.

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.

While much attention has been devoted to the causes of opinion change, little is known about its consequences. Our study moves a first step in this direction by looking at Reddit, and in particular to the subreddit r/ChangeMyView, a community dedicated to debating one’s own opinions on a wide array of topics. We analyze changes in online information consumption behavior that arise after a self-reported opinion change, by looking at the participation to a set of sociopolitical communities. We find that people who self-report an opinion change are significantly more likely to change their future participation in a specific subset of those communities. Specifically, there is a significant association (Pearson r = 0.46) between using propaganda-like language in a community and the increase in chances of leaving it. Comparable results (Pearson r = 0.39) hold for the opposite direction, i.e., joining these same communities. In addition, the textual content of the post associated with opinion change is indicative of which communities will be joined or left: a predictive model based only on the text of this post can pinpoint these communities with an average precision@5 of 0.20. Our results establish a link between opinion change and information consumption, and highlight how online propagandistic communities act as a first gateway to internalize a shift in one’s sociopolitical opinion.

Despite echo chambers in social media have been under considerable scrutiny, general models for their detection and analysis are missing. In this work, we aim to fill this gap by proposing a probabilistic generative model that explains social media footprints---i.e., social network structure and propagations of information---through a set of latent communities, characterized by a degree of echo-chamber behavior and by an opinion polarity. Specifically, echo chambers are modeled as communities that are permeable to pieces of information with similar ideological polarity, and impermeable to information of opposed leaning: this allows discriminating echo chambers from communities that lack a clear ideological alignment.

Dense subgraph discovery is a fundamental problem in graph mining whose goal is to extract a dense subgraph from a given graph, and it has a wide range of applications [18]. However, numerous real-world applications, ranging from computational biology and computational neuroscience to computational social science, take as input a dual graph, namely a pair of graphs on the same set of nodes. Despite the large number of such applications, research on dense subgraph discovery has focused on a single graph input, with few notable exceptions [9, 22, 35, 36]. In this work, we contribute to this line of research by studying the following novel algorithmic problem: Given a pair of graphs G, H on the same set of nodes V, how do we find a subset of nodes S ⊆ V that induces a well-connected subgraph in G and a dense subgraph in H? Our formulation generalizes previous research [11, 44, 45], by enabling to control the connectivity constraint on G. We propose a mathematical formulation and prove that it is solvable exactly in polynomial time. We compare our method to state-of-the-art competitors and find empirically that controlling the connectivity constraint enables the practitioner to obtain information that is otherwise inaccessible. Finally, we show that our proposed mining tool can be used to better understand how users interact on Twitter and connectivity aspects of human brain networks with and without Autism Spectrum Disorder (ASD).

Recommender systems typically suggest to users content similar to what they consumed in the past. If a user happens to be exposed to strongly polarized content, she might subsequently receive recommendations which may steer her towards more and more radicalized content, eventually being trapped in what we call a “radicalization pathway”. In this paper, we study the problem of mitigating radicalization pathways using a graph-based approach. Specifically, we model the set of recommendations of a “what-to-watch-next” recommender as a d-regular directed graph where nodes correspond to content items, links to recommendations, and paths to possible user sessions.

Simplicial complexes are a generalization of graphs that model higher-order relations. In this paper, we introduce simplicial patterns —that we call simplets— and generalize the task of frequent pattern mining from the realm of graphs to that of simplicial complexes. Our task is particularly challenging due to the enormous search space and the need for higher-order isomorphism. We show that finding the occurrences of simplets in a complex can be reduced to a bipartite graph isomorphism problem, in linear time and at most quadratic space. We then propose an anti-monotonic frequency measure that allows us to start the exploration from small simplets and stop expanding a simplet as soon as its frequency falls below the minimum frequency threshold. Equipped with these ideas and a clever data structure, we develop a memory-conscious algorithm that, by carefully exploiting the relationships among the simplices in the complex and among the simplets, achieves efficiency and scalability for our complex mining task. Our algorithm, FreSCo, comes in two flavors: it can compute the exact frequency of the simplets or, more quickly, it can determine whether a simplet is frequent, without having to compute the exact frequency. Experimental results prove the ability of FreSCo to mine frequent simplets in complexes of various size and dimension, and the significance of the simplets with respect to the traditional graph patterns.

Detecting niches of polarization in social media is a first step towards deploying mitigation strategies and avoiding radicalization. In this paper, we model polarization niches as close-knit dense communities of users, which are under the influence of some well-known sources of misinformation, and isolated from authoritative information sources. Based on this intuition we define the problem of finding a subgraph that maximizes a combination of ( i ) density, ( ii ) proximity to a small set of nodes A (named Attractors ), and ( iii ) distance from another small set of nodes R (named Repulsers ). Deviating from the bulk of the literature on detecting polarization, we do not exploit text mining or sentiment analysis, nor we track the propagation of information: we only exploit the network structure and the background knowledge about the sets A and R , which are given as input. We build on recent algorithmic advances in supermodular maximization to provide an iterative greedy algorithm, dubbed Down in the Hollow (dith), that converges fast to a near-optimal solution. Thanks to a novel theoretical upper bound, we are able to equip dith with a practical device that allows to terminate as soon as a solution with a user-specified approximation factor is found, making our algorithm very efficient in practice. Our experiments on very large networks confirm that our algorithm always returns a solution with an approximation factor better or equal to the one specified by the user, and it is scalable. Our case-studies in polarized settings, confirm the usefulness of our algorithmic primitive in detecting polarization niches.

Graph summarization is beneficial in a wide range of applications, such as visualization, interactive and exploratory analysis, approximate query processing, reducing the on-disk storage footprint, and graph processing in modern hardware. However, the bulk of the literature on graph summarization surprisingly overlooks the possibility of having edges of different types. In this article, we study the novel problem of producing summaries of multi-relation networks, i.e., graphs where multiple edges of different types may exist between any pair of nodes. Multi-relation graphs are an expressive model of real-world activities, in which a relation can be a topic in social networks, an interaction type in genetic networks, or a snapshot in temporal graphs. The first approach that we consider for multi-relation graph summarization is a two-step method based on summarizing each relation in isolation, and then aggregating the resulting summaries in some clever way to produce a final unique summary. In doing this, as a side contribution, we provide the first polynomial-time approximation algorithm based on the k -Median clustering for the classic problem of lossless single-relation graph summarization. Then, we demonstrate the shortcomings of these two-step methods, and propose holistic approaches, both approximate and heuristic algorithms, to compute a summary directly for multi-relation graphs. In particular, we prove that the approximation bound of k -Median clustering for the single relation solution can be maintained in a multi-relation graph with proper aggregation operation over adjacency matrices corresponding to its multiple relations. Experimental results and case studies (on co-authorship networks and brain networks) validate the effectiveness and efficiency of the proposed algorithms.

Modeling information cascades in a social network through the lenses of the ideological leaning of its users can help understanding phenomena such as misinformation propagation and confirmation bias, and devising techniques for mitigating their toxic effects.

Training graph classifiers able to distinguish between healthy brains and dysfunctional ones, can help identifying substructures associated to specific cognitive phenotypes. However, the mere predictive power of the graph classifier is of limited interest to the neuroscientists, which have plenty of tools for the diagnosis of specific mental disorders. What matters is the interpretation of the model, as it can provide novel insights and new hypotheses. In this paper we propose counterfactual graphs as a way to produce local post-hoc explanations of any black-box graph classifier. Given a graph and a black-box, a counterfactual is a graph which, while having high structural similarity with the original graph, is classified by the black-box in a different class. We propose and empirically compare several strategies for counterfactual graph search. Our experiments against a white-box classifier with known optimal counterfactual, show that our methods, although heuristic, can produce counterfactuals very close to the optimal one. Finally, we show how to use counterfactual graphs to build global explanations correctly capturing the behaviour of different black-box classifiers and providing interesting insights for the neuroscientists.

We study a novel problem of fairness in ranking aimed at minimizing the amount of individual unfairness introduced when enforcing group-fairness constraints. Our proposal is rooted in the distributional maxmin fairness theory, which uses randomization to maximize the expected satisfaction of the worst-off individuals. We devise an exact polynomial-time algorithm to find maxmin-fair distributions of general search problems (including, but not limited to, ranking), and show that our algorithm can produce rankings which, while satisfying the given group-fairness constraints, ensure that the maximum possible value is to individuals.

Studying information propagation in social media is an important task with plenty of applications for business and science. Generating realistic synthetic information cascades can help the research community in developing new methods and applications, testing sociological hypotheses and different what-if scenarios by simply changing few parameters. We demonstrate womg, a synthetic data generator which combines topic modeling and a topic-aware propagation model to create realistic information-rich cascades, whose shape depends on many factors, including the topic of the item and its virality, the homophily of the social network, the interests of its users and their social influence.

A simplicial complex is a generalization of a graph: a collection of n-ary relationships (instead of binary as the edges of a graph), named simplices. In this paper, we develop a new tool to study the structure of simplicial complexes: we generalize the graph notion of truss decomposition to complexes, and show that this more powerful representation gives rise to different properties compared to the graph-based one. This power, however, comes with important computational challenges derived from the combinatorial explosion caused by the downward closure property of complexes.

Networks in many real-world applications come with an inherent uncertainty in their structure, due to e.g., noisy measurements, inference and prediction models, or for privacy purposes. Modeling and analyzing uncertain graphs has attracted a great deal of attention. Among the various graph analytic tasks studied, the extraction of dense substructures, such as cores or trusses, has a central role.

Computing the shortest path between a pair of nodes is a fundamental graph primitive, which has critical applications in vehicle routing, finding functional pathways in biological networks, survivable network design, among many others. In this work, we study shortest-path queries over uncertain networks, i.e., graphs where every edge is associated with a probability of existence. We show that, for a given path, it is # P -hard to compute the probability of it being the shortest path, and we also derive other interesting properties highlighting the complexity of computing the Most Probable Shortest Paths (MPSPs). We thus devise sampling-based efficient algorithms, with end-to-end accuracy guarantees, to compute the MPSP. As a concrete application, we show how to compute a novel concept of betweenness centrality in an uncertain graph using MPSPs. Our thorough experimental results and rich real-world case studies on sensor networks and brain networks validate the effectiveness, efficiency, scalability, and usefulness of our solution.

Data are building blocks to information and, subsequently, they are vital input to knowledge. Today, in the midst of the digital era, vast quantities of highly-complex data are being collected and processed at an unprecedented scale. This abundance of data has highlighted the importance of efficient and effective knowledge-discovery algorithms to identify patterns hidden in the data with the ultimate aim of uncovering valuable knowledge and shape our understanding of the world around us. To capitalize on the opportunities offered by massive amounts of data as well as modern computing power, for many years, research in knowledge discovery and related areas has introduced algorithms that are increasingly efficient and effective, but also more and more opaque and unpredictable. Recently, growing interest in the ethical dimensions of algorithms has drawn attention to the limitations of opaque algorithms and has emphasized a need for trustworthy algorithms particularly when such algorithms are used to support high-stakes decision making. In order to be trustworthy, algorithms should solve a clearly defined problem via a clear sequence of instructions, they should not be utterly unsuccessful in any particular case and they should be easy to understand and interpret for humans so that no harmful biases can be hidden. In this thesis, we pursue the goal of developing novel knowledge-discovery algorithmic methods that are not only highly efficient to face the challenges and opportunities posed by modern data, but also trustworthy. In particular, we propose efficient and trustworthy methods for a collection of popular knowledgediscovery tasks. First, we consider tasks of exact inference in Bayesian networks and hidden Markov models. Trustworthy approaches for such tasks exist. However, their applicability may be severely limited by time or memory requirements. Therefore, we propose novel methods to reduce the time or memory resources that are needed by existing approaches for the considered exact inference tasks. Beside exact inference tasks, we also consider two different knowledge-discovery tasks that arise naturally in modern data: multi-label classification and community search in temporal graphs. Regarding multi-label classification, we propose an efficient and accurate rule-based multi-label classifier that drastically improves upon the interpretability of existing solutions. For community search in temporal graphs, we formalise the task for the first time, and we propose a solution that guarantees high efficiency and interpretability. In designing knowledge-discovery methods, we often rely on existing database-management and probabilistic methods. Methods for database management are valuable to address the large dimension and high complexity of modern data, while probabilistic methods are essential to methodologically handle uncertainty in the data.

Community search is a well-studied problem which, given a static graph and a query set of vertices, requires to find a cohesive (or dense) subgraph containing the query vertices. In this paper we study the problem of community search in temporal dynamic networks. We adapt to the temporal setting the notion of network inefficiency which is based on the pairwise shortest-path distance among all the vertices in a solution. For this purpose we define the notion of shortest-fastest-path distance: a linear combination of the temporal and spatial dimensions governed by a user-defined parameter. We thus define the MINIMUM TEMPORAL-INEFFICIENCY SUBGRAPH problem and show that it is NP-hard. We develop an algorithm which exploits a careful transformation of the temporal network to a static directed and weighted graph, and some recent approximation algorithm for finding the minimum Directed Steiner Tree. We finally generalize our framework to the streaming setting in which new snapshots of the temporal graph keep arriving continuously and our goal is to produce a community search solution for the temporal graph corresponding to a sliding time window.

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.

Opinion dynamics the research field dealing with how people's opinions form and evolve in a social context? traditionally uses agent-based models to validate the implications of sociological theories. These models encode the causal mechanism that drives the opinion formation process, and have the advantage of being easy to interpret. However, as they do not exploit the availability of data, their predictive power is limited. Moreover, parameter calibration and model selection are manual and difficult tasks.

Correlation clustering is arguably the most natural formulation of clustering. Given n objects and a pairwise similarity measure, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same cluster and dissimilar objects are put in different clusters.

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.

Reidentification-risk analysis and anonymity have received a great deal of attention in the last two decades. While the research community has been developing several privacy notions and the algorithms to achieve them, these tools have faced difficulties in being transferred to the wider audience of practitioners, for they require a considerable amount of data privacy technical knowledge. We demonstrate X 2 R 2 (Explainable Explorative Reidentification Risk), a data anonymization tool for the laymen. X 2 R 2 guides the user through a transparent explorative process, during which the existing reidentification risks are explained and quantified, possible data transformation options are recommended, and the consequences of these operations, in terms of privacy risk and data utility, are clearly shown.

Multilayer networks are a powerful paradigm to model complex systems, where multiple relations occur between the same entities. Despite the keen interest in a variety of tasks, algorithms, and analyses in this type of network, the problem of extracting dense subgraphs has remained largely unexplored so far. As a first step in this direction, in this work, we study the problem of core decomposition of a multilayer network . Unlike the single-layer counterpart in which cores are all nested into one another and can be computed in linear time, the multilayer context is much more challenging as no total order exists among multilayer cores; rather, they form a lattice whose size is exponential in the number of layers. In this setting, we devise three algorithms, which differ in the way they visit the core lattice and in their pruning techniques. We assess time and space efficiency of the three algorithms on a large variety of real-world multilayer networks. We then move a step forward and study the problem of extracting the inner-most (also known as maximal ) cores, i.e., the cores that are not dominated by any other core in terms of their core index in all the layers. inner-most cores are typically orders of magnitude less than all the cores. Motivated by this, we devise an algorithm that effectively exploits the maximality property and extracts inner-most cores directly, without first computing a complete decomposition. This allows for a consistent speed up over a naïve method that simply filters out non-inner-most ones from all the cores. Finally, we showcase the multilayer core-decomposition tool in a variety of scenarios and problems. We start by considering the problem of densest-subgraph extraction in multilayer networks . We introduce a definition of multilayer densest subgraph that tradesoff between high density and number of layers in which the high density holds, and exploit multilayer core decomposition to approximate this problem with quality guarantees. As further applications, we show how to utilize multilayer core decomposition to speed-up the extraction of frequent cross-graph quasi-cliques and to generalize the community-search problem to the multilayer setting.

Large-scale dynamic interaction graphs can be challenging to process and store, due to their size and the continuous change of communication patterns between nodes. In this work, we address the problem of summarizing large-scale dynamic graphs, while maintaining the evolution of their structure and interactions. Our approach is based on grouping the nodes of the graph in supernodes according to their connectivity and communication patterns. The resulting summary graph preserves the information about the evolution of the graph within a time window. We propose two online algorithms for summarizing this type of graphs. Our baseline algorithm kC based on clustering is fast but rather memory expensive. The second method we propose, named /LC, reduces the memory requirements by introducing an intermediate step that keeps statistics of the clustering of the previous rounds. Our algorithms are distributed by design, and we implement them over the Apache Spark framework, so as to address the problem of scalability for large-scale graphs and massive streams. We apply our methods to several dynamic graphs, and show that we can efficiently use the summary graphs to answer temporal and probabilistic graph queries.

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.

Uncertain graphs are prevalent in several applications including communications systems, biological databases and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely expensive. Sparsification has often been used to reduce the size of deterministic graphs by maintaining only the important edges. However, adaptation of deterministic sparsification methods fails in the uncertain setting. To overcome this problem, we introduce the first sparsification techniques aimed explicitly at uncertain graphs. The proposed methods reduce the number of edges and redistribute their probabilities in order to decrease the graph size, while preserving its underlying structure. The resulting graph can be used to efficiently and accurately approximate any query and mining tasks on the original graph, including clustering coefficient, page rank, reliability and shortest path distance.

The k-core of a graph is defined as the maximal subgraph in which every vertex is connected to at least k other vertices within that subgraph. In this work we introduce a distance-based generalization of the notion of k-core, which we refer to as the $(k,h)$-core, i.e., the maximal subgraph in which every vertex has at least k other vertices at distance $łeq h$ within that subgraph. We study the properties of the $(k,h)$-core showing that it preserves many of the nice features of the classic core decomposition (e.g., its connection with the notion of distance-generalized chromatic number ) and it preserves its usefulness to speed-up or approximate distance-generalized notions of dense structures, such as h-club. Computing the distance-generalized core decomposition over large networks is intrinsically complex. However, by exploiting clever upper and lower bounds we can partition the computation in a set of totally independent subcomputations, opening the door to top-down exploration and to multithreading, and thus achieving an efficient algorithm.

As data science and artificial intelligence become ubiquitous, they have an increasing impact on society. While many of these impacts are beneficial, others may not be. So understanding and managing these impacts is required of every responsible data scientist. Nevertheless, most human decision-makers use algorithms for efficiency purposes and not to make a better (i.e., fairer) decisions. Even the task of risk assessment in the criminal justice system enables efficiency instead of (and often at the expense of) fairness. So we need to frame the problem with fairness, and other societal impacts, as primary objectives. In this context, most attention has been paid to the machine learning of a model for a task, such as recognition, prediction, or classification. However, issues arise in all parts of the data eco-system, from data acquisition to data presentation. For example, the majority of the population is not white and male, yet this demographic is over-represented in the training data. It is challenging for a data scientist to satisfactorily discharge this broad responsibility.

Mastering the dynamics of social influence requires separating, in a database of information propagation traces, the genuine causal processes from temporal correlation, i.e., homophily and other spurious causes. However, most studies to characterize social influence, and, in general, most data-science analyses focus on correlations, statistical independence, or conditional independence. Only recently, there has been a resurgence of interest in "causal data science,'' e.g., grounded on causality theories. In this paper we adopt a principled causal approach to the analysis of social influence from information-propagation data, rooted in the theory of probabilistic causation. Our approach consists of two phases. In the first one, in order to avoid the pitfalls of misinterpreting causation when the data spans a mixture of several subtypes ("Simpson's paradox''), we partition the set of propagation traces into groups, in such a way that each group is as less contradictory as possible in terms of the hierarchical structure of information propagation. To achieve this goal, we borrow the notion of "agony'' and define the Agony-bounded Partitioning problem, which we prove being hard, and for which we develop two efficient algorithms with approximation guarantees. In the second phase, for each group from the first phase, we apply a constrained MLE approach to ultimately learn a minimal causal topology. Experiments on synthetic data show that our method is able to retrieve the genuine causal arcs w.r.t. a ground-truth generative model. Experiments on real data show that, by focusing only on the extracted causal structures instead of the whole social graph, the effectiveness of predicting influence spread is significantly improved.

This paper provides an overview of the workshops co-located with the 27th ACM International Conference on Information and Knowledge Management (CIKM 2018), held during October 22-26, 2018 in Turin, Italy.

When analyzing temporal networks, a fundamental task is the identification of dense structures (i.e., groups of vertices that exhibit a large number of links), together with their temporal span (i.e., the period of time for which the high density holds). We tackle this task by introducing a notion of temporal core decomposition where each core is associated with its span: we call such cores span-cores. As the total number of time intervals is quadratic in the size of the temporal domain T under analysis, the total number of span-cores is quadratic in $|T|$ as well. Our first contribution is an algorithm that, by exploiting containment properties among span-cores, computes all the span-cores efficiently. Then, we focus on the problem of finding only the maximal span-cores, i.e., span-cores that are not dominated by any other span-core by both the coreness property and the span. We devise a very efficient algorithm that exploits theoretical findings on the maximality condition to directly compute the maximal ones without computing all span-cores. Experimentation on several real-world temporal networks confirms the efficiency and scalability of our methods. Applications on temporal networks, gathered by a proximity-sensing infrastructure recording face-to-face interactions in schools, highlight the relevance of the notion of (maximal) span-core in analyzing social dynamics and detecting/correcting anomalies in the data.

Recent advances in computing resources have made it possible to collect enormous amounts of interconnected data, such as social media interactions, web activity, knowledge bases, product and service purchases, autonomous vehicle routing, smart home sensor data, and more. The massive scale and complexity of this data, however, not only vastly surpasses human processing power, but also goes beyond limitations with regard to computation and storage. That is, there is an urgent need for methods and tools that summarize large interconnected data to enable faster computations, storage reduction, interactive large-scale visualization and understanding, and pattern discovery. Network summarization-which aims to find a small representation of an original, larger graph-features a variety of methods with different goals and for different input data representations (e.g., attributed graphs, time-evolving or streaming graphs, heterogeneous graphs). The objective of this tutorial is to give a systematic overview of methods for summarizing and explaining graphs at different scales: the node-group level, the network level, and the multi-network level. We emphasize the current challenges, present real-world applications, and highlight the open research problems in this vibrant research area.

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.

Network reliability is a well-studied problem that requires to measure the probability that a target node is reachable from a source node in a probabilistic (or uncertain) graph, i.e., a graph where every edge is assigned a probability of existence. Many approaches and problem variants have been considered in the literature, with the majority of them assuming that edge-existence probabilities are fixed. Nevertheless, in real-world graphs, edge probabilities typically depend on external conditions. In metabolic networks, a protein can be converted into another protein with some probability depending on the presence of certain enzymes. In social influence networks, the probability that a tweet of some user will be re-tweeted by her followers depends on whether the tweet contains specific hashtags. In transportation networks, the probability that a network segment will work properly or not, might depend on external conditions such as weather or time of the day. In this paper, we overcome this limitation and focus onconditional reliability, that is, assessing reliability when edge-existence probabilities depend on a set of conditions. In particular, we study the problem of determining the top-$k$conditions that maximize the reliability between two nodes. We deeply characterize our problem and show that, even employing polynomial-time reliability-estimation methods, it is$\mathbf {NP}$-hard, does not admit any$\mathbf {PTAS}$, and the underlying objective function is non-submodular. We then devise a practical method that targets both accuracy and efficiency. We also study natural generalizations of the problem with multiple source and target nodes. An extensive empirical evaluation on several large, real-life graphs demonstrates effectiveness and scalability of our methods.

Uncertain graphs are prevalent in several applications including communications systems, biological databases, and social networks. The ever increasing size of the underlying data renders both graph storage and query processing extremely expensive. Sparsification has often been used to reduce the size of deterministic graphs by maintaining only the important edges. However, adaptation of deterministic sparsification methods fails in the uncertain setting. To overcome this problem, we introduce the first sparsification techniques aimed explicitly at uncertain graphs. The proposed methods reduce the number of edges and redistribute their probabilities in order to decrease the graph size, while preserving its underlying structure. The resulting graph can be used to efficiently and accurately approximate any query and mining tasks on the original graph. An extensive experimental evaluation with real and synthetic datasets illustrates the effectiveness of our techniques on several common graph tasks, including clustering coefficient, page rank, reliability, and shortest path distance.

Multilayer networks are a powerful paradigm to model complex systems, where various relations might occur among the same set of entities. Despite the keen interest in a variety of problems, algorithms, and analysis methods in this type of network, the problem of extracting dense subgraphs has remained largely unexplored.

We study the problem of extracting a selective connector for a given set of query vertices Q subset of V in a graph G = (V,E). A selective connector is a subgraph of G which exhibits some cohesiveness property, and contains the query vertices but does not necessarily connect them all. Relaxing the connectedness requirement allows the connector to detect multiple communities and to be tolerant to outliers. We achieve this by introducing the new measure of network inefficiency and by instantiating our search for a selective connector as the problem of finding the minimum inefficiency subgraph.

In this work, we define and solve the Fair Top-k Ranking problem, in which we want to determine a subset of k candidates from a large pool of n » k candidates, maximizing utility (i.e., select the "best" candidates) subject to group fairness criteria.

Consider a multi-layered graph, where the different layers correspond to different proprietary social networks on the same ground set of users. Suppose that the owners of the different networks (called hosts) are mutually non-trusting parties: how can they compute a centrality score for each of the users using all the layers, but without disclosing information about their private graphs?

Incentivized social advertising, an emerging marketing model, provides monetization opportunities not only to the owners of the social networking platforms but also to their influential users by offering a "cut" on the advertising revenue. We consider a social network (the host) that sells ad-engagements to advertisers by inserting their ads, in the form of promoted posts, into the feeds of carefully selected "initial endorsers" or seed users: these users receive monetary incentives in exchange for their endorsements. The endorsements help propagate the ads to the feeds of their followers. Whenever any user engages with an ad, the host is paid some fixed amount by the advertiser, and the ad further propagates to the feed of her followers, potentially recursively. In this context, the problem for the host is is to allocate ads to influential users, taking into account the propensity of ads for viral propagation, and carefully apportioning the monetary budget of each of the advertisers between incentives to influential users and ad-engagement costs, with the rational goal of maximizing its own revenue. We show that, taking all important factors into account, the problem of revenue maximization in incentivized social advertising corresponds to the problem of monotone submodular function maximization, subject to a partition matroid constraint on the ads-to-seeds allocation, and submodular knapsack constraints on the advertisers' budgets. We show that this problem is NP-hard and devise two greedy algorithms with provable approximation guarantees, which differ in their sensitivity to seed user incentive costs. Our approximation algorithms require repeatedly estimating the expected marginal gain in revenue as well as in advertiser payment. By exploiting a connection to the recent advances made in scalable estimation of expected influence spread, we devise efficient and scalable versions of our two greedy algorithms. An extensive experimental assessment confirms the high quality of our proposal.

Large-scale, highly-interconnected networks pervade our society and the natural world around us, including the World Wide Web, social networks, knowledge graphs, genome and scientific databases, medical and government records. The massive scale of graph data often surpasses the available computation and storage resources. Besides, users get overwhelmed by the daunting task of understanding and using such graphs due to their sheer volume and complexity. Hence, there is a critical need to summarize large graphs into concise forms that can be more easily visualized, processed, and managed. Graph summarization has indeed attracted a lot of interests from various research communities, such as sociology, physics, chemistry, bioinformatics, and computer science. Different ways of summarizing graphs have been invented that are often complementary to each other. In this tutorial, we discuss algorithmic advances on graph summarization in the context of both classical (e.g., static graphs) and emerging (e.g., dynamic and stream graphs) applications. We emphasize the current challenges and highlight some future research directions.

We study the problem of detecting social communities when the social graph is not available but instead we have access to a log of user activity, that is, a dataset of tuples ( u , i , t ) recording the fact that user u “adopted” item i at time t . We propose a stochastic framework that assumes that the adoption of items is governed by an underlying diffusion process over the unobserved social network and that such a diffusion model is based on community-level influence . That is, we aim at modeling communities through the lenses of social contagion . By fitting the model parameters to the user activity log, we learn the community membership and the level of influence of each user in each community. The general framework is instantiated with two different diffusion models, one with discrete time and one with continuous time, and we show that the computational complexity of both approaches is linear in the number of users and in the size of the propagation log. Experiments on synthetic data with planted community structure show that our methods outperform non-trivial baselines. The effectiveness of the proposed techniques is further validated on real-word data, on which our methods are able to detect high-quality communities.

Large-scale dynamic graphs can be challenging to process and store, due to their size and the continuous change of communication patterns between nodes. In this work we address the problem of summarizing large-scale dynamic graphs, maintaining the evolution of their structure and the communication patterns. Our approach is based on grouping the nodes of the graph in supernodes according to their connectivity and communication patterns. The resulting summary graph preserves the information about the evolution of the graph within a time window. We propose two online, distributed, and tunable algorithms for summarizing this type of graphs. We apply our methods to several real-world and synthetic dynamic graphs, and we show that they scale well on the number of nodes and produce high-quality summaries.

Betweenness centrality measures the importance of an element of a graph, either a vertex or an edge, by the fraction of shortest paths that pass through it [1]. This measure is notoriously expensive to compute, and the best known algorithm, proposed by Brandes [2], runs in O(nm) time. The problems of efficiency and scalability are exacerbated in a dynamic setting, where the input is an evolving graph seen edge by edge, and the goal is to keep the betweenness centrality up to date. In this paper [8] we propose the first truly scalable and practical framework for computing vertex and edge betweenness centrality of large evolving graphs, incrementally and online.

Algorithms and decision making based on Big Data have become pervasive in all aspects of our daily lives lives (offline and online), as they have become essential tools in personal finance, health care, hiring, housing, education, and policies. It is therefore of societal and ethical importance to ask whether these algorithms can be discriminative on grounds such as gender, ethnicity, or health status. It turns out that the answer is positive: for instance, recent studies in the context of online advertising show that ads for high-income jobs are presented to men much more often than to women [Datta et al., 2015]; and ads for arrest records are significantly more likely to show up on searches for distinctively black names [Sweeney, 2013]. This algorithmic bias exists even when there is no discrimination intention in the developer of the algorithm. Sometimes it may be inherent to the data sources used (software making decisions based on data can reflect, or even amplify, the results of historical discrimination), but even when the sensitive attributes have been suppressed from the input, a well trained machine learning algorithm may still discriminate on the basis of such sensitive attributes because of correlations existing in the data. These considerations call for the development of data mining systems which are discrimination-conscious by-design. This is a novel and challenging research area for the data mining community.

What is the set of nodes of a social network that, under a probabilistic contagion model, would get infected if a given node $s$ gets infected? We call this set the sphere of influence of s. Due to the stochastic nature of the contagion model we need to define a notion of "expected" or "typical" cascade: this is a set of nodes which is the closest to all the possible cascades starting from s. We thus formalize the Typical Cascade problem which requires, for a given source node s, to find the set of nodes minimizing the expected Jaccard distance to all the possible cascades from s. The expected cost of a typical cascade also provides us a measure of the stability of cascade propagation, i.e., how much random cascades from a source node s deviate from the "typical" cascade. In this sense source nodes with lower expected costs are more reliable.

Story identification from online user-generated content has recently raised increasing attention. Existing approaches fall into two categories. Approaches in the first category extract stories as cohesive substructures in a graph representing the strength of association between terms. The latter category includes approaches that analyze the temporal evolution of individual terms and identify stories by grouping terms with similar anomalous temporal behavior. Both categories have limitations. In this work we advance the literature on story identification by devising a novel method that profitably combines the peculiarities of the two main existing approaches, thus also addressing their weaknesses. Experiments on a dataset extracted from a real-world web-search log demonstrate the superiority of the proposed method over the state of the art.

Community-based question answering (CQA) platforms are crowd-sourced services for sharing user expertise on various topics, from mechanical repairs to parenting. While they naturally build-in an online social network infrastructure, they carry a very different purpose from Facebook-like social networks, where users "hang-out" with their friends and tend to share more personal information. It is unclear, thus, how the privacy concerns and their correlation with user behavior in an online social network translate into a CQA platform. This study analyzes one year of recorded traces from a mature CQA platform to understand the association between users' privacy concerns as manifested by their account settings and their activity in the platform. The results show that privacy preference is correlated with behavior in the community in terms of engagement, retention, accomplishments and deviance from the norm. We find privacy-concerned users have higher qualitative and quantitative contributions, show higher retention, report more abuses, have higher perception on answer quality and have larger social circles. However, at the same time, these users also exhibit more deviant behavior than the users with public profiles.

We study the fundamental problem of finding the set of top-k edge colors that maximizes the reliability between a source node and a destination node in an uncertain and edge-colored graph. Our top-k reliable color set problem naturally arises in a variety of real-world applications including pathway finding in biological networks, topic-aware influence maximization, and team formation in social networks, among many others. In addition to the #P-completeness of the classical reliability finding problem between a source and a destination node over an uncertain graph, we prove that our problem is also NP-hard, and neither sub-modular, nor super-modular. To this end, we aim at designing effective and scalable solutions for the top-k reliable color set problem. We first introduce two baselines following the idea of repetitive inclusion of the next best edge colors, and we later develop a more efficient and effective algorithm that directly finds the highly-reliable paths while maintaining the budget on the number of edge-colors. An extensive empirical evaluation on various large-scale and real-world graph datasets illustrates that our proposed techniques are both scalable and highly accurate.

We study a problem of graph-query reformulation enabling explorative query-driven discovery in graph databases. Given a query issued by the user, the system, apart from returning the result patterns, also proposes a number of specializations (i.e., supergraphs) of the original query to facilitate the exploration of the results.

The Wiener index of a graph is the sum of all pairwise shortest-path distances between its vertices. In this paper we study the novel problem of finding a minimum Wiener connector: given a connected graph G=(V,E) and a set Q ⊆ V of query vertices, find a subgraph of G that connects all query vertices and has minimum Wiener index.

Finding dense subgraphs in large graphs is a key primitive in a variety of real-world application domains, encompassing social network analytics, event detection, biology, and finance. In most such applications, one typically aims at finding several (possibly overlapping) dense subgraphs which might correspond to communities in social networks or interesting events. While a large amount of work is devoted to finding a single densest subgraph, perhaps surprisingly, the problem of finding several dense subgraphs with limited overlap has not been studied in a principled way, to the best of our knowledge. In this work we define and study a natural generalization of the densest subgraph problem, where the main goal is to find at most $k$ subgraphs with maximum total aggregate density, while satisfying an upper bound on the pairwise Jaccard coefficient between the sets of nodes of the subgraphs. After showing that such a problem is NP-Hard, we devise an efficient algorithm that comes with provable guarantees in some cases of interest, as well as, an efficient practical heuristic. Our extensive evaluation on large real-world graphs confirms the efficiency and effectiveness of our algorithms.

Community-based question answering platforms can be rich sources of information on a variety of specialized topics, from finance to cooking. The usefulness of such platforms depends heavily on user contributions (questions and answers), but also on respecting the community rules. As a crowd-sourced service, such platforms rely on their users for monitoring and flagging content that violates community rules. Common wisdom is to eliminate the users who receive many flags. Our analysis of a year of traces from a mature Q&A site shows that the number of flags does not tell the full story: on one hand, users with many flags may still contribute positively to the community. On the other hand, users who never get flagged are found to violate community rules and get their accounts suspended. This analysis, however, also shows that abusive users are betrayed by their network properties: we find strong evidence of homophilous behavior and use this finding to detect abusive users who go under the community radar. Based on our empirical observations, we build a classifier that is able to detect abusive users with an accuracy as high as 83%.

Social advertisement is one of the fastest growing sectors in the digital advertisement landscape: ads in the form of promoted posts are shown in the feed of users of a social networking platform, along with normal social posts; if a user clicks on a promoted post, the host (social network owner) is paid a fixed amount from the advertiser. In this context, allocating ads to users is typically performed by maximizing click-through-rate, i.e., the likelihood that the user will click on the ad. However, this simple strategy fails to leverage the fact the ads can propagate virally through the network, from endorsing users to their followers. In this paper, we study the problem of allocating ads to users through the viral-marketing lenses. We show that allocation that takes into account the propensity of ads for viral propagation can achieve significantly better performance. However, uncontrolled virality could be undesirable for the host as it creates room for exploitation by the advertisers: hoping to tap uncontrolled virality, an advertiser might declare a lower budget for its marketing campaign, aiming at the same large outcome with a smaller cost. This creates a challenging trade-off: on the one hand, the host aims at leveraging virality and the network effect to improve advertising efficacy, while on the other hand the host wants to avoid giving away free service due to uncontrolled virality. We formalize this as the problem of ad allocation with minimum regret, which we show is NP-hard and inapproximable w.r.t. any factor. However, we devise an algorithm that provides approximation guarantees w.r.t. the total budget of all advertisers. We develop a scalable version of our approximation algorithm, which we extensively test on four real-world data sets, confirming that our algorithm delivers high quality solutions, is scalable, and significantly outperforms several natural baselines.

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.

Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best known algorithm runs in O(nm) time. The problems of efficiency and scalability are exacerbated in a dynamic setting, where the input is an evolving graph seen edge by edge, and the goal is to keep the betweenness centrality up to date. In this paper, we propose the first truly scalable algorithm for online computation of betweenness centrality of both vertices and edges in an evolving graph where new edges are added and existing edges are removed. Our algorithm is carefully engineered with out-of-core techniques and tailored for modern parallel stream processing engines that run on clusters of shared-nothing commodity hardware. Hence, it is amenable to real-world deployment. We experiment on graphs that are two orders of magnitude larger than previous studies. Our method is able to keep the betweenness centrality measures up-to-date online, i.e., the time to update the measures is smaller than the inter-arrival time between two consecutive updates.

Data in several applications can be represented as an uncertain graph whose edges are labeled with a probability of existence. Exact query processing on uncertain graphs is prohibitive for most applications, as it involves evaluation over an exponential number of instantiations. Thus, typical approaches employ Monte-Carlo sampling, which (i) draws a number of possible graphs (samples), (ii) evaluates the query on each of them, and (iii) aggregates the individual answers to generate the final result. However, this approach can also be extremely time consuming for large uncertain graphs commonly found in practice. To facilitate efficiency, we study the problem of extracting a single representative instance from an uncertain graph. Conventional processing techniques can then be applied on this representative to closely approximate the result on the original graph. In order to maintain data utility, the representative instance should preserve structural characteristics of the uncertain graph. We start with representatives that capture the expected vertex degrees, as this is a fundamental property of the graph topology. We then generalize the notion of vertex degree to the concept of n -clique cardinality, that is, the number of cliques of size n that contain a vertex. For the first problem, we propose two methods: Average Degree Rewiring (ADR), which is based on random edge rewiring, and Approximate B-Matching (ABM), which applies graph matching techniques. For the second problem, we develop a greedy approach and a game-theoretic framework. We experimentally demonstrate, with real uncertain graphs, that indeed the representative instances can be used to answer, efficiently and accurately, queries based on several metrics such as shortest path distance, clustering coefficient, and betweenness centrality.

Influence maximization is the key algorithmic problem behind viral marketing: it requires to identify a set of influential users in a social network, who, when convinced to adopt a product, shall influence other users in the network, leading to a large number of adoptions. Although real world users evidently have di↵erent degrees of interest and authoritativeness on di↵erent topics, the bulk of the literature on influence maximization is topic-blind, in the sense that it treats all items as they were the same. In this paper we study Topic-aware Influence Maximization (TIM) queries: given a directed social graph, where the arcs are associated with a topic-dependent user-to-user social influence strength, and given a budget k, the problem requires to find a set of k users (named seed set) that we shall target in a viral marketing campaign for a given new item (described as a distribution over topics) in order to maximize its adoption. Our goal is to answer such queries in milliseconds, thus enabling online social influence analytics, what-if simulation, and marketing decision making. The main challenge here is the enormous number of potential queries: any possible distribution over the topic space (i.e., any possible item) induces a di↵erent probabilistic graph, and thus a di↵erent instance of the standard influence maximization problem, for which eciency and scalability are still unsolved problems. Given these computational challenges, we propose to build an index over pre-computed solutions for a limited number of possible queries. Our proposal, INFLEX, employs a treebased index for similarity search with Bregman divergences, to eciently retrieve a good-enough set of neighbor points for the query item. Then it performs rank aggregation on their seed sets to produce the final answer to the query. Experimental results on real data show that INFLEX can provide in few milliseconds a solution very similar (Kendall⌧ distance < 0.1) to the one produced by the best known o✏ine computation (which usually takes several days).

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.

Exploiting word-of-mouth effect to create viral cascades in social networks is a very appealing possibility from the mar-keting standpoint. However, in order to set up an effective viral marketing campaign, one has first to accurately esti-mate social influence. This is usually done by analyzing user activity data. As we point out in this paper, the data anal-ysis and sharing that is needed to estimate social influence raises important privacy issues that may jeopardize the le-gal, ethical and societal acceptability of such practice, and in turn, the concrete applicability of viral marketing in the real world. In this paper we devise secure multiparty protocols that allow a group of service providers and a social networking platform to jointly compute social influence, in a privacy preserving manner. 1.

We study the data mining problem of modeling adoptions and the stages of the diffusion of an innovation. For our aim we propose a stochastic model which decomposes a diffusion trace (sequence of adoptions) in an ordered sequence of stages, where each stage is intuitively built around two dimensions: users and relative speed at which adoptions happen. Each stage is characterized by a specific rate of adoption and it involves different users to different extent, while the sequentiality in the diffusion is guaranteed by constraining the transition probabilities among stages. An empirical evaluation on synthetic and real-world adoption logs shows the effectiveness of the proposed framework in summarizing the adoption process, enabling several analysis tasks such as the identification of adopter categories, clustering and characterization of diffusion traces, and prediction of which users will adopt an item in the next future.

We study the problem of graph summarization. Given a large graph we aim at producing a concise lossy representation that can be stored in main memory and used to approximately answer queries about the original graph much faster than by using the exact representation. In this paper we study a very natural type of summary: the original set of vertices is partitioned into a small number of super nodes connected by super edges to form a complete weighted graph. The super edge weights are the edge densities between vertices in the corresponding super nodes. The goal is to produce a summary that minimizes the reconstruction error w.r.t. The original graph. By exposing a connection between graph summarization and geometric clustering problems (i.e., k-means and k-median), we develop the first polynomial-time approximation algorithm to compute the best possible summary of a given size.

User recommender systems are a key component in any on-line social networking platform: they help the users growing their network faster, thus driving engagement and loyalty.

Core decomposition has proven to be a useful primitive for a wide range of graph analyses. One of its most appealing features is that, unlike other notions of dense subgraphs, it can be computed linearly in the size of the input graph. In this paper we provide an analogous tool for uncertain graphs, i.e., graphs whose edges are assigned a probability of existence. The fact that core decomposition can be computed efficiently in deterministic graphs does not guarantee efficiency in uncertain graphs, where even the simplest graph operations may become computationally intensive. Here we show that core decomposition of uncertain graphs can be carried out efficiently as well.

Correlation clustering is arguably the most natural formulation of clustering. Given a set of objects and a pairwise similarity measure between them, the goal is to cluster the objects so that, to the best possible extent, similar objects are put in the same cluster and dissimilar objects are put in different clusters. As it just needs a definition of similarity, its broad generality makes it applicable to a wide range of problems in different contexts, and in particular makes it naturally suitable to clustering structured objects for which feature vectors can be difficult to obtain.

Product design and viral marketing are two popular concepts in the marketing literature that, although following different paths, aim at the same goal: maximizing the adoption of a new product. While the effect of the social network is nowadays kept in great consideration in any marketing-related activity, the interplay between product design and social influence is surprisingly still largely unexplored. In this paper we move a first step in this direction and study the problem of designing the features of a novel product such that its adoption, fueled by peer influence and “word-of-mouth” effect, is maximized. We model the viral process of product adoption on the basis of social influence and the features of the product, and devise an improved iterative scaling procedure to learn the parameters that maximize the likelihood of our novel feature-aware propagation model. In order to design an effective algorithm for our problem, we study the property of the underlying propagation model. In particular we show that the expected spread, i.e., the objective function to maximize, is monotone and submodular when we fix the features of the product and seek for the set of users to target in the viral marketing campaign. Instead, when we fix the set of users and try to find the optimal features for the product, then the expected spread is neither submodular nor monotone (as it is the case, in general, for product design). Therefore, we develop an algorithm based on an alternating optimization between selecting the features of the product, and the set of users to target in the campaign. Our experimental evaluation on real-world data from the domain of social music consumption (LastFM) and social movie consumption (Flixster) confirms the effectiveness of the proposed framework in integrating product design in viral marketing.

Data in several applications can be represented as an uncertain graph, whose edges are labeled with a probability of existence. Exact query processing on uncertain graphs is prohibitive for most applications, as it involves evaluation over an exponential number of instantiations. Even approximate processing based on sampling is usually extremely expensive since it requires a vast number of samples to achieve reasonable quality guarantees. To overcome these problems, we propose algorithms for creating deterministic representative instances of uncertain graphs that maintain the underlying graph properties. Specifically, our algorithms aim at preserving the expected vertex degrees because they capture well the graph topology. Conventional processing techniques can then be applied on these instances to closely approximate the result on the uncertain graph. We experimentally demonstrate, with real and synthetic uncertain graphs, that indeed the representative instances can be used to answer, efficiently and accurately, queries based on several properties such as shortest path distance, clustering coefficient and betweenness centrality.

Traditional approaches to community detection, as studied by physicists, sociologists, and more recently computer scientists, aim at simply partitioning the social network graph. However, with the advent of online social networking sites, richer data has become available: beyond the link information, each user in the network is annotated with additional information, for example, demographics, shopping behavior, or interests. In this context, it is therefore important to develop mining methods which can take advantage of all available information. In the case of community detection, this means finding good communities (a set of nodes cohesive in the social graph) which are associated with good descriptions in terms of user information (node attributes). Having good descriptions associated to our models make them understandable by domain experts and thus more useful in real-world applications. Another requirement dictated by real-world applications, is to develop methods that can use, when available, any domain-specific background knowledge. In the case of community detection the background knowledge could be a vague description of the communities sought in a specific application, or some prototypical nodes (e.g., good customers in the past), that represent what the analyst is looking for (a community of similar users). Towards this goal, in this article, we define and study the problem of finding a diverse set of cohesive communities with concise descriptions. We propose an effective algorithm that alternates between two phases: a hill-climbing phase producing (possibly overlapping) communities, and a description induction phase which uses techniques from supervised pattern set mining. Our framework has the nice feature of being able to build well-described cohesive communities starting from any given description or seed set of nodes, which makes it very flexible and easily applicable in real-world applications. Our experimental evaluation confirms that the proposed method discovers cohesive communities with concise descriptions in realistic and large online social networks such as D elicious , F lickr , and L ast FM.

Users are often faced with the problem of finding complementary items that together achieve a single common goal (e.g., a starter kit for a novice astronomer, a collection of question/answers related to low-carb nutrition, a set of places to visit on holidays). In this paper, we argue that for some application scenarios returning item bundles is more appropriate than ranked lists. Thus we define composite retrieval as the problem of finding$k$bundles of complementary items. Beyond complementarity of items, the bundles must be valid w.r.t. a given budget, and the answer set of$k$bundles must exhibit diversity. We formally define the problem and show that in its general form is${\bf NP}$-hard and that also the special cases in which each bundle is formed by only one item, or only one bundle is sought, are hard. Our characterization however suggests how to adopt a two-phase approach (Produce-and-Choose, or PAC) in which we first produce many valid bundles, and then we choose$k$among them. For the first phase we devise two ad-hoc clustering algorithms, while for the second phase we adapt heuristics with approximation guarantees for a related problem. We also devise another approach which is based on first finding a$k$-clustering and then selecting a valid bundle from each of the produced clusters (Cluster-and-Pick, or CAP). We compare experimentally the proposed methods on two real-world data sets: the first data set is given by a sample of touristic attractions in 10 large European cities, while the second is a large database of user-generated restaurant reviews from Yahoo! Local. Our experiments show that when diversity is highly important, CAP is the best option, while when diversity is less important, a PAC approach constructing bundles around randomly chosen pivots, is better.

How can we detect communities when the social graphs is not available? We tackle this problem by modeling social contagion from a log of user activity, that is a dataset of tuples (u, i, t) recording the fact that user u "adopted" item i at time t. This is the only input to our problem. We propose a stochastic framework which assumes that item adoptions are governed by un underlying diffusion process over the unobserved social network, and that such diffusion model is based on community-level influence. By fitting the model parameters to the user activity log, we learn the community membership and the level of influence of each user in each community. This allows to identify for each community the "key" users, i.e., the leaders which are most likely to influence the rest of the community to adopt a certain item. The general framework can be instantiated with different diffusion models. In this paper we define two models: the extension to the community level of the classic (discrete time) Independent Cascade model, and a model that focuses on the time delay between adoptions. To the best of our knowledge, this is the first work studying community detection without the network.

Analyzing the traces left by a meme of information propagating through a social network or by a user browsing a website can help to unveil the structure and dynamics of such complex networks. This may in turn open the door to concrete applications, such as finding influential users for a topic in a social network, or detecting the typical structure of a web browsing session that leads to a product purchase. In this paper we define the problem of mining summaries of propagations as a constrained pattern-mining problem. A propagation is a DAG where an entity (e.g., information exchanged in a social network, or a user browsing a website) flows following the underlying hierarchical structure of the nodes. A summary is a set of propagations that (i) involve a similar population of nodes, and (ii) exhibit a coherent hierarchical structure when merged altogether to form a single graph. The first constraint is defined based on the Jaccard coefficient, while the definition of the second one relies on the graph-theoretic concept of "agony" of a graph. It turns out that both constraints satisfy the downward closure property, thus enabling Apriori-like algorithms. However, motivated by the fact that computing agony is much more expensive than computing Jaccard, we devise two algorithms that explore the search space differently. The first algorithm is an Apriori-like, bottom-up method that checks both the constraints level-by-level. The second algorithm consists of a first phase where the search space is pruned as much as possible by exploiting the Jaccard constraint only, while involving the second constraint only afterwards, in a subsequent phase. We test our algorithms on four real-world datasets. Quantitative results reveal that the choice of the most efficient algorithm depends on the selectivity of the two constraints. Qualitative results show the relevance of the extracted summaries in a number of real-world scenarios.

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.

The key algorithmic problem in viral marketing is to identify a set of influential users (called seeds) in a social network, who, when convinced to adopt a product, shall influence other users in the network, leading to a large number of adoptions. When two or more players compete with similar products on the same network we talk about competitive viral marketing, which so far has been studied exclusively from the perspective of one of the competing players.

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.

Every day millions of users are connected through online social networks, generating a rich trove of data that allows us to study the mechanisms behind human interactions. Triadic closure has been treated as the major mechanism for creating social links: if Alice follows Bob and Bob follows Charlie, Alice will follow Charlie. Here we present an analysis of longitudinal micro-blogging data, revealing a more nuanced view of the strategies employed by users when expanding their social circles. While the network structure affects the spread of information among users, the network is in turn shaped by this communication activity. This suggests a link creation mechanism whereby Alice is more likely to follow Charlie after seeing many messages by Charlie. We characterize users with a set of parameters associated with different link creation strategies, estimated by a Maximum-Likelihood approach. Triadic closure does have a strong effect on link formation, but shortcuts based on traffic are another key factor in interpreting network evolution. However, individual strategies for following other users are highly heterogeneous. Link creation behaviors can be summarized by classifying users in different categories with distinct structural and behavioral characteristics. Users who are popular, active, and influential tend to create traffic-based shortcuts, making the information diffusion process more efficient in the network.

Given a directed social graph and a set of past informa- tion cascades observed over the graph, we study the novel problem of detecting modules of the graph (communities of nodes), that also explain the cascades. Our key observation is that both information propagation and social ties forma- tion in a social network can be explained according to the same latent factor, which ultimately guide a user behavior within the network. Based on this observation, we propose the Community-Cascade Network (CCN) model, a stochas- tic mixture membership generative model that can fit, at the same time, the social graph and the observed set of cas- cades. Our model produces overlapping communities and for each node, its level of authority and passive interest in each community it belongs. For learning the parameters of the CCN model, we devise a Generalized Expectation Maximization procedure. We then apply our model to real-world social networks and in- formation cascades: the results witness the validity of the proposed CCN model, providing useful insights on its signif- icance for analyzing social behavior.

We study the problem of anticipating user search needs, based on their browsing activity. Given the current web page p that a user is visiting we want to recommend a small and diverse set of search queries that are relevant to the content of p, but also non-obvious and serendipitous.

No abstract available.

Collaborative content creation and annotation creates vast repositories of all sorts of media, and user-defined tags play a central role as they are a simple yet powerful tool for organizing, searching and exploring the available resources. We observe that when a user annotates a resource with a set of tags, those tags are introduced one at a time. Therefore, when the fourth tag is introduced, a knowledge represented by the previous three tags, i.e., the context in which the fourth tag is produced, is available and exploitable for generating potential correction of the current tag. This context, together with the "wisdom of the crowd" represented by the co-occurrences of tags in all the resources of the repository, can be exploited to provide interactive tag spell check and correction. We develop this idea in a framework, based on a weighted tag co-occurrence graph and on nodes relatedness measures defined on weighted neighborhoods. We test our proposal on a dataset coming from YouTube. The results show that our framework is effective as it outperforms two important baselines. We also show that it is efficient, thus enabling its use in modern tagging services.

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 social influence from a topic modeling perspective. We introduce novel topic-aware influence-driven propagation models that experimentally result to be more accurate in describing real-world cascades than the standard propagation models studied in the literature. In particular, we first propose simple topic-aware extensions of the well-known Independent Cascade and Linear Threshold models. Next, we propose a different approach explicitly modeling authoritativeness, influence and relevance under a topic-aware perspective. We devise methods to learn the parameters of the models from a dataset of past propagations. Our experimentation confirms the high accuracy of the proposed models and learning schemes.

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.

We present a recommendation method based on the well-known concept of center-piece subgraph, that allows for the time/space efficient generation of suggestions also for rare, i.e., long-tail queries. Our method is scalable with respect to both the size of datasets from which the model is computed and the heavy workloads that current web search engines have to deal with. Basically, we relate terms contained into queries with highly correlated queries in a query-flow graph. This enables a novel recommendation generation method able to produce recommendations for approximately 99% of the workload of a real-world search engine. The method is based on a graph having term nodes, query nodes, and two kinds of connections: term-query and query-query. The first connects a term to the queries in which it is contained, the second connects two query nodes if the likelihood that a user submits the second query after having issued the first one is sufficiently high. On such large graph we need to compute the center-piece subgraph induced by terms contained into queries. In order to reduce the cost of the above computation, we introduce a novel and efficient method based on an inverted index representation of the model. We experiment our solution on two real-world query logs and we show that its effectiveness is comparable (and in some case better) than state-of-the-art methods for head-queries. More importantly, the quality of the recommendations generated remains very high also for long-tail queries, where other methods fail even to produce any suggestion. Finally, we extensively investigate scalability and efficiency issues and we show the viability of our method in real world search engines.

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.

Motivated by sensor networks, mobility data, biology and life sciences, the area of mining uncertain data has recently received a great deal of attention. While various papers have focused on efficiently mining frequent patterns from uncertain data, the problem of discovering a small set of interesting patterns that provide an accurate and condensed description of a probabilistic database is still unexplored. In this paper we study the problem of discovering characteristic patterns in uncertain data through information theoretic lenses. Adopting the possible worlds interpretation of probabilistic data and a compression scheme based on the MDL principle, we formalize the problem of mining patterns that compress the database well in expectation. Despite its huge search space, we show that this problem can be accurately approximated. In particular, we devise a sequence of three methods where each new method improves the memory requirements orders of magnitudes compared to its predecessor, while giving up only a little in terms of approximation accuracy. We empirically compare our methods on both synthetic data and real data from life science. Results show that from a probabilistic matrix with more than one million rows and columns, we can extract a small set of meaningful patterns that accurately characterize the data distribution of any probable world.

With the success of online social networks and microblogs such as Facebook, Flickr and Twitter, the phenomenon of influence exerted by users of such platforms on other users, and how it propagates in the network, has recently attracted the interest of computer scientists, information technologists, and marketing specialists. One of the key problems in this area is the identification of influential users, by targeting whom certain desirable marketing outcomes can be achieved. In this article we take a data mining perspective and we discuss what (and how) can be learned from the available traces of past propagations. While doing this we provide a brief overview of some recent progresses in this area and discuss some open problems. By no means this article must be intended as an exhaustive survey: it is instead (admittedly) a rather biased and personal perspective of the author on the topic of influence propagation in social networks.

Influence maximization is the problem of finding a set of users in a social network, such that by targeting this set, one maximizes the expected spread of influence in the network. Most of the literature on this topic has focused exclusively on the social graph, overlooking historical data, i.e., traces of past action propagations. In this paper, we study influence maximization from a novel data-based perspective. In particular, we introduce a new model, which we call credit distribution , that directly leverages available propagation traces to learn how influence flows in the network and uses this to estimate expected influence spread. Our approach also learns the different levels of influence-ability of users, and it is time-aware in the sense that it takes the temporal nature of influence into account. We show that influence maximization under the credit distribution model is NP -hard and that the function that defines expected spread under our model is submodular. Based on these, we develop an approximation algorithm for solving the influence maximization problem that at once enjoys high accuracy compared to the standard approach, while being several orders of magnitude faster and more scalable.

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.

In the traditional link prediction problem, a snapshot of a social network is used as a starting point to predict, by means of graph-theoretic measures, the links that are likely to appear in the future. In this paper, we introduce cold start link prediction as the problem of predicting the structure of a social network when the network itself is totally missing while some other information regarding the nodes is available. We propose a two-phase method based on the bootstrap probabilistic graph. The first phase generates an implicit social network under the form of a probabilistic graph. The second phase applies probabilistic graph-based measures to produce the final prediction. We assess our method empirically over a large data collection obtained from Flickr, using interest groups as the initial information. The experiments confirm the effectiveness of our approach.

Recently, there has been tremendous interest in the phenomenon of influence propagation in social networks. The studies in this area assume they have as input to their problems a social graph with edges labeled with probabilities of influence between users. However, the question of where these probabilities come from or how they can be computed from real social network data has been largely ignored until now. Thus it is interesting to ask whether from a social graph and a log of actions by its users, one can build models of influence. This is the main problem attacked in this paper. In addition to proposing models and algorithms for learning the model parameters and for testing the learned models to make predictions, we also develop techniques for predicting the time by which a user may be expected to perform an action. We validate our ideas and techniques using the Flickr data set consisting of a social graph with 1.3M nodes, 40M edges, and an action log consisting of 35M tuples referring to 300K distinct actions. Beyond showing that there is genuine influence happening in a real social network, we show that our techniques have excellent prediction performance.

Addressing user's information needs has been one of the main goals of Web search engines since their early days. In some cases, users cannot see their needs immediately answered by search results, simply because these needs are too complex and involve multiple aspects that are not covered by a single Web or search results page. This typically happens when users investigate a certain topic in domains such as education, travel or health, which often require collecting facts and information from many pages. We refer to this type of activities as "research missions". These research missions account for 10% of users' sessions and more than 25% of all query volume, as verified by a manual analysis that was conducted by Yahoo! editors.

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.

The process of discovering relevant patterns holding in a database was first indicated as a threat to database security by O'Leary in. Since then, many different approaches for knowledge hiding have emerged over the years, mainly in the context of association rules and frequent item sets mining. Following many real-world data and application demands, in this paper, we shift the problem of knowledge hiding to contexts where both the data and the extracted knowledge have a sequential structure. We define the problem of hiding sequential patterns and show its NP-hardness. Thus, we devise heuristics and a polynomial sanitization algorithm. Starting from this framework, we specialize it to the more complex case of spatiotemporal patterns extracted from moving objects databases. Finally, we discuss a possible kind of attack to our model, which exploits the knowledge of the underlying road network, and enhance our model to protect from this kind of attack. An exhaustive experiential analysis on real-world data sets shows the effectiveness of our proposal.

A voting system is a set of rules that a community adopts to take collective decisions. In this paper we study voting systems for a particular kind of community: electronically mediated social networks. In particular, we focus on delegative democracy (a.k.a. proxy voting) that has recently received increased interest for its ability to combine the benefits of direct and representative systems, and that seems also perfectly suited for electronically mediated social networks. In such a context, we consider a voting system in which users can only express their preference for one among the people they are explicitly connected with, and this preference can be propagated transitively, using an attenuation factor. We present this system and we study its properties. We also take into consideration the problem of missing votes, which is particularly relevant in online networks, as some recent case shows. Our experiments on real-world networks provide interesting insight into the significance and stability of the results obtained with the suggested voting system.

On photo sharing websites like Flickr and Zooomr, users are offered the possibility to assign tags to their uploaded pictures. Using these tags to find interesting groups of semantically related pictures in the result set of a given query is a problem with obvious applications. We analyse this problem from a Minimum Description Length (MDL) perspective and develop an algorithm that finds the most interesting groups. The method is based on Krimp, which finds small sets of patterns that characterise the data using compression. These patterns are sets of tags, often assigned together to photos. The better a database compresses, the more structure it contains and thus the more homogeneous it is. Following this observation we devise a compression-based measure. Our experiments on Flickr data show that the most interesting and homogeneous groups are found. We show extensive examples and compare to clusterings on the Flickr website.

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.

Moving object databases (MOD) have gained much interest in recent years due to the advances in mobile communications and positioning technologies. Study of MOD can reveal useful information (e.g., traffic patterns and congestion trends) that can be used in applications for the common benefit. In order to mine and/or analyze the data, MOD must be published, which can pose a threat to the location privacy of a user. Indeed, based on prior knowledge of a user's location at several time points, an attacker can potentially associate that user to a specific moving object (MOB) in the published database and learn her position information at other time points.

In this demo we introduce GuruMine, a pattern mining system for the discovery of leaders, i.e., influential users in social networks, and their tribes, i.e., a set of users usually influenced by the same leader over several actions. GuruMine is built upon a novel pattern mining framework for leaders discovery, that we introduced. In particular, we consider social networks where users perform actions. Actions may be as simple as tagging resources (URLS) as in del.icio.us, rating songs as in Yahoo! Music, or movies as in Yahoo! Movies, or users buying gadgets such as cameras, handholds, etc. and blogging a review on the gadgets. The assumption is that actions performed by a user can be seen by their network friends. Users seeing their friends actions are sometimes tempted to perform those actions. On the basis of the propagation of such influence, we provided various notion of leaders and developed algorithms for their efficient discovery. GuruMine provides users with a friendly graphical interface for selecting the actions of interest, and the kind of leaders to mine. The set of parameters driving the pattern discovery process can be iteratively refined, and the result is updated, if possible without incurring a completely new computation. Once a set of leaders has been extracted, GuruMine can easily validate them on a set of actions unseen during the pattern mining, by analyzing the portion of network reached by the influence of the selected leaders on the unseen actions. GuruMine also offers various visualizations over the social networks: the propagation of an action, the leaders, their tribes, and the interactions between different leaders and tribes. In this demo we will show: (i) how the pattern mining process can be driven towards the discovery of a good set of leaders, (ii) the ease of use of GuruMine system, and (iii) its outstanding performances on large real-world social networks and actions databases.

Understanding query reformulation patterns is a key step towards next generation web search engines: it can help improving users' web-search experience by predicting their intent, and thus helping them to locate information more effectively. As a step in this direction, we build an accurate model for classifying user query reformulations into broad classes (generalization, specialization, error correction or parallel move), achieving 92\% accuracy. We apply the model to automatically label two large query logs, creating annotated query-flow graphs. We study the resulting reformulation patterns, finding results consistent with previous studies done on smaller manually annotated datasets, and discovering new interesting patterns, including connections between reformulation types and topical categories. Finally, applying our findings to a third query log that is publicly available for research purposes, we demonstrate that our reformulation classifier leads to improved recommendations in a query recommendation system.

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 novel frequent pattern mining approach to discover leaders and tribes in social networks. In particular, we consider social networks where users perform actions. Actions may be as simple as tagging resources (urls) as in del.icio.us, rating songs as in Yahoo! Music, or movies as in Yahoo! Movies, or users buying gadgets such as cameras, handhelds, etc. and blogging a review on the gadgets. The assumption is that actions performed by a user can be seen by their network friends. Users seeing their friends' actions are sometimes tempted to perform those actions. We are interested in the problem of studying the propagation of such "influence", and on this basis, identifying which users are leaders when it comes to setting the trend for performing various actions. We consider alternative definitions of leaders based on frequent patterns and develop algorithms for their efficient discovery. Our definitions are based on observing the way influence propagates in a time window, as the window is moved in time. Given a social graph and a table of user actions, our algorithms can discover leaders of various flavors by making one pass over the actions table. We run detailed experiments to evaluate the utility and scalability of our algorithms on real-life data. The results of our experiments confirm on the one hand, the efficiency of the proposed algorithm, and on the other hand, the effectiveness and relevance of the overall framework. To the best of our knowledge, this the first frequent pattern based approach to social network mining.

Preserving individual privacy when publishing data is a problem that is receiving increasing attention. According to the fc-anonymity principle, each release of data must be such that each individual is indistinguishable from at least k - 1 other individuals. In this paper we study the problem of anonymity preserving data publishing in moving objects databases. We propose a novel concept of k-anonymity based on co-localization that exploits the inherent uncertainty of the moving object's whereabouts. Due to sampling and positioning systems (e.g., GPS) imprecision, the trajectory of a moving object is no longer a polyline in a three-dimensional space, instead it is a cylindrical volume, where its radius delta represents the possible location imprecision: we know that the trajectory of the moving object is within this cylinder, but we do not know exactly where. If another object moves within the same cylinder they are indistinguishable from each other. This leads to the definition of (k,delta) -anonymity for moving objects databases. We first characterize the (k, delta)-anonymity problem and discuss techniques to solve it. Then we focus on the most promising technique by the point of view of information preservation, namely space translation. We develop a suitable measure of the information distortion introduced by space translation, and we prove that the problem of achieving (k,delta) -anonymity by space translation with minimum distortion is NP-hard. Faced with the hardness of our problem we propose a greedy algorithm based on clustering and enhanced with ad hoc pre-processing and outlier removal techniques. The resulting method, named NWA (Never Walk .Alone), is empirically evaluated in terms of data quality and efficiency. Data quality is assessed both by means of objective measures of information distortion, and by comparing the results of the same spatio-temporal range queries executed on the original database and on the (k, delta)-anonymized one. Experimental results show that for a wide range of values of delta and k, the relative error introduced is kept low, confirming that NWA produces high quality (k, delta)-anonymized data.

In this paper we study the problem of mining frequent sequences satisfying a given regular expression. Previous approaches to solve this problem were focusing on its search space, pushing (in some way) the given regular expression to prune unpromising candidate patterns. On the contrary, we focus completely on the given input data and regular expression. We introduce sequence mining automata (SMA), a specialized kind of Petri Net that while reading input sequences, it produces for each sequence all and only the patterns contained in the sequence and that satisfy the given regular expression. Based on this automaton, we develop a family of algorithms. Our thorough experimentation on different datasets and application domains confirms that in many cases our methods outperform the current state of the art of frequent sequence mining algorithms using regular expressions (in some cases of orders of magnitude).

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.

Spatio-temporal, geo-referenced datasets are growing rapidly, and will be more in the near future. This phenomenon is mostly due to the daily collection of telecommunication data from mobile phones and other location-aware devices and is expected to enable novel classes of applications based on the extraction of behavioral patterns from mobility data. Such patterns could be used for instance in traffic and sustainable mobility management (e.g., to study the accessibility to services), urban planning, environmental monitoring, and collaborative location-based services. Clearly, in these applications privacy is a concern, since some knowledge may be sensitive, or an over-specific pattern may reveal the behaviour of groups of few individual. In this paper we focus on automated privacy-preserving methods we developed for extracting and sharing user- consumable forms of knowledge from large amounts of raw data referenced in space and in time.

ConQueSt is a constraint-based querying system devised with the aim of supporting the intrinsically exploratory nature of pattern discovery. It provides users with an expressive constraint-based query language which allows the discovery process to be effectively driven toward potentially interesting patterns. Constraints are also exploited to reduce the cost of pattern mining. The system is built around an efficient constraint-based mining engine which entails several data and search space reduction techniques, and allows new user-defined constraints to be easily added.

In this paper we study when the disclosure of data mining results represents, per se, a threat to the anonymity of the individuals recorded in the analyzed database. The novelty of our approach is that we focus on an objective definition of privacy compliance of patterns without any reference to a preconceived knowledge of what is sensitive and what is not, on the basis of the rather intuitive and realistic constraint that the anonymity of individuals should be guaranteed. In particular, the problem addressed here arises from the possibility of inferring from the output of frequent itemset mining (i.e., a set of item-sets with support larger than a threshold a), the existence of patterns with very low support (smaller than an anonymity threshold k)[M. Atzori et. al, 2005]. In the following we develop a simple methodology to block such inference opportunities by introducing distortion on the dangerous patterns.

Constrained frequent patterns and closed frequent patterns are two paradigms aimed at reducing the set of extracted patterns to a smaller, more interesting, subset. Although a lot of work has been done with both these paradigms, there is still confusion around the mining problem obtained by joining closed and constrained frequent patterns in a unique framework. In this paper, we shed light on this problem by providing a formal definition and a thorough characterization. We also study computational issues and show how to combine the most recent results in both paradigms, providing a very efficient algorithm which exploits the two requirements (satisfying constraints and being closed) together at mining time in order to reduce the computation as much as possible.

The key point is that, in frequent pattern mining, the most appropriate way of exploiting monotone constraints in conjunction with frequency is to use them in order to reduce the problem input together with the search space. Following this intuition, we introduce ExAMiner, a level-wise algorithm which exploits the real synergy of antimonotone and monotone constraints: the total benefit is greater than the sum of the two individual benefits. ExAMiner generalizes the basic idea of the preprocessing algorithm ExAnte [F. Bonchi et al., (2003)], embedding such ideas at all levels of an Apriori-like computation. The resulting algorithm is the generalization of the Apriori algorithm when a conjunction of monotone constraints is conjoined to the frequency antimonotone constraint. Experimental results confirm that this is, so far, the most efficient way of attacking the computational problem in analysis.

Planning adequate audit strategies is a key success factor in a posterion' fraud detection, e.g., in the fiscal and insurance domains, where audits are intended to detect tax evasion and fraudulent claims.A case study is presented in this paper, which illustrates how techniques based on classification can be used to support the task of planning audit strategies.The proposed approach is sensible to some conflicting issues of audit planning, e.g., the trade-off between maximizing audit benefits vs. minimizing audit costs.A methodological scenario, common to a whole class of similar applications, is then abstracted away from the case study.The limitations of available systems to support the identified overall KDD process, bring us to point out the key aspects of a logic-based database language, integrated with mining mechanisms, which is used to provide a uniform, highly expressive environment for the various steps in the construction of the considered case-study.