We introduce a manifold analysis technique for neural network representations. Normalized Space Alignment (NSA) compares pairwise distances between two point clouds derived from the same source and having the same size, while potentially possessing differing dimensionalities. NSA can act as both an analytical tool and a differentiable loss function, providing a robust means of comparing and aligning representations across different layers and models. It satisfies the criteria necessary for both a dissimilarity metric and a neural network loss function. We showcase NSA's versatility by illustrating its utility as a representation space analysis metric and a structure-preserving loss function. NSA is not only computationally efficient, but it can also approximate the global structural discrepancy during mini-batching, facilitating its use in a wide variety of neural network training paradigms.

Link prediction is a fundamental problem in graph data. In its most realistic setting, the problem consists of predicting missing or future links between random pairs of nodes from the set of disconnected pairs. Graph Neural Networks (GNNs) have become the predominant framework for link prediction. GNN-based methods treat link prediction as a binary classification problem and handle the extreme class imbalance---real graphs are very sparse---by sampling (uniformly at random) a balanced number of disconnected pairs not only for training but also for evaluation. However, we show that the reported performance of GNNs for link prediction in the balanced setting does not translate to the more realistic imbalanced setting and that simpler topology-based approaches are often better at handling sparsity. These findings motivate Gelato, a similarity-based link-prediction method that applies (1) graph learning based on node attributes to enhance a topological heuristic, (2) a ranking loss for addressing class imbalance, and (3) a negative sampling scheme that efficiently selects hard training pairs via graph partitioning. Experiments show that Gelato outperforms existing GNN-based alternatives.

The problem of maximizing the adoption of a product through viral marketing in social networks has been studied heavily through postulated network models. We present a novel data-driven formulation of the problem. We use Graph Neural Networks (GNNs) to model the adoption of products by utilizing both topological and attribute information. The resulting Dynamic Viral Marketing (DVM) problem seeks to find the minimum budget and minimal set of dynamic topological and attribute changes in order to attain a specified adoption goal. We show that DVM is NP-Hard and is related to the existing influence maximization problem. Motivated by this connection, we develop the idea of Dynamic Gradient Influencing (DGI) that uses gradient ranking to find optimal perturbations and targets low-budget and high influence non-adopters in discrete steps. We use an efficient strategy for computing node budgets and develop the ''Meta-Influence'' heuristic for assessing a node's downstream influence. We evaluate DGI against multiple baselines and demonstrate gains on average of 24% on budget and 37% on AUC on real-world attributed networks. Our code is publicly available at https://github.com/saurabhsharma1993/dynamic_viral_marketing.

Graph neural networks (GNNs) find applications in various domains such as computational biology, natural language processing, and computer security. Owing to their popularity, there is an increasing need to explain GNN predictions since GNNs are black-box machine learning models. One way to address this issue involves using counterfactual reasoning where the objective is to alter the GNN prediction by minimal changes in the input graph. Existing methods for counterfactual explanation of GNNs are limited to instance-specific local reasoning. This approach has two major limitations of not being able to offer global recourse policies and overloading human cognitive ability with too much information. In this work, we study the global explainability of GNNs through global counterfactual reasoning. Specifically, we want to find a small set of representative counterfactual graphs that explains all input graphs. Toward this goal, we propose GCFExplainer , a novel algorithm powered by vertex-reinforced random walks on an edit map of graphs with a greedy summary . Extensive experiments on real graph datasets show that the global explanation from GCFExplainer provides important high-level insights of the model behavior and achieves a 46.9% gain in recourse coverage, a 9.5% reduction in recourse cost compared to the state-of-the-art local counterfactual explainers. We also demonstrate that GCFExplainer generates explanations that are more consistent with input dataset characteristics, and is robust under adversarial attacks. In addition, K-GCFExplainer , which incorporates a graph clustering component into GCFExplainer , is introduced as a more competitive extension for datasets with a clustering structure, leading to superior performance in three out of four datasets in the experiments and better scalability.

Counterfactual explanations of Graph Neural Networks (GNNs) offer a powerful way to understand data that can naturally be represented by a graph structure. Furthermore, in many domains, it is highly desirable to derive data-driven global explanations or rules that can better explain the high-level properties of the models and data in question. However, evaluating global counterfactual explanations is hard in real-world datasets due to a lack of human-annotated ground truth, which limits their use in areas like molecular sciences. Additionally, the increasing scale of these datasets provides a challenge for random search-based methods. In this paper, we develop a novel global explanation model RLHEX for molecular property prediction. It aligns the counterfactual explanations with human-defined principles, making the explanations more interpretable and easy for experts to evaluate. RLHEX includes a VAE-based graph generator to generate global explanations and an adapter to adjust the latent representation space to human-defined principles. Optimized by Proximal Policy Optimization (PPO), the global explanations produced by RLHEX cover 4.12% more input graphs and reduce the distance between the counterfactual explanation set and the input set by 0.47% on average across three molecular datasets. RLHEX provides a flexible framework to incorporate different human-designed principles into the counterfactual explanation generation process, aligning these explanations with domain expertise. The code and data are released at https://github.com/dqwang122/RLHEX.

R-convolution graph kernels are positive-semidefinite functions that decompose graphs into substructures and compare them. One problem in the effective implementation of this idea is that the substructures are not independent, which leads to high-dimensional feature space. In addition, graph kernels cannot capture the high-order complex interactions between vertices. To mitigate these two problems, we propose a framework called DeepMap to learn deep representations for graph feature maps used in graph kernels. The learned deep representation for a graph is a dense and low-dimensional vector that captures complex high-order interactions in a vertex neighborhood. We empirically validate DeepMap on various graph classification benchmarks and demonstrate that it achieves state-of-the-art performance.

In contrast to global graph clustering, local graph clustering aims to find only one cluster that is concentrating on the given seed vertex (and also on the designated attributes for attributed graphs). Currently, very few methods can deal with this kind of task. To this end, we propose two quality measures for a local graph cluster: Graph Unimodality (GU) and Attribute Unimodality (AU). They measure the homogeneity/unimodality of the graph structure and the subspace that is composed of the designated attributes, respectively. We call their linear combination Compactness. Further, we propose LOCLU to optimize the Compactness score in order to find a good local graph cluster. The local graph cluster detected by LOCLU concentrates on the region of interest, provides efficient information flow in the graph, and exhibits a unimodal data distribution in the subspace of the designated attributes.

Graph neural networks (GNNs) find applications in various domains such as computational biology, natural language processing, and computer security. Owing to their popularity, there is an increasing need to explain GNN predictions since GNNs are black-box machine learning models. One way to address this is counterfactual reasoning where the objective is to change the GNN prediction by minimal changes in the input graph. Existing methods for counterfactual explanation of GNNs are limited to instance-specific local reasoning. This approach has two major limitations of not being able to offer global recourse policies and overloading human cognitive ability with too much information. In this work, we study the global explainability of GNNs through global counterfactual reasoning. Specifically, we want to find a small set of representative counterfactual graphs that explains all input graphs. Towards this goal, we propose GCFExplainer, a novel algorithm powered by vertex-reinforced random walks on an edit map of graphs with a greedy summary. Extensive experiments on real graph datasets show that the global explanation from GCFExplainer provides important high-level insights of the model behavior and achieves a 46.9% gain in recourse coverage and a 9.5% reduction in recourse cost compared to the state-of-the-art local counterfactual explainers.

Flow graphs capture the directed flow of a quantity of interest (e.g., water, power, vehicles) being transported through an underlying network. Modeling and generating realistic flow graphs is key in many applications in infrastructure design, transportation, and biomedical and social sciences. However, they pose a great challenge to existing generative models due to a complex dynamics that is often governed by domain-specific physical laws or patterns. We introduce FlowGEN, an implicit generative model for flow graphs, that learns how to jointly generate graph topologies and flows with diverse dynamics directly from data using a novel (flow) graph neural network. Experiments show that our approach is able to effectively reproduce relevant local and global properties of flow graphs, including flow conservation, cyclic trends, and congestion around hotspots.

Finding an appropriate representation of dynamic activities in the brain is crucial for many downstream applications. Due to its highly dynamic nature, temporally averaged fMRI (functional magnetic resonance imaging) can only provide a narrow view of underlying brain activities. Previous works lack the ability to learn and interpret the latent dynamics in brain architectures. This paper builds an efficient graph neural network model that incorporates both region-mapped fMRI sequences and structural connectivities obtained from DWI (diffusion-weighted imaging) as inputs. We find good representations of the latent brain dynamics through learning sample-level adaptive adjacency matrices and performing a novel multi-resolution inner cluster smoothing. We also attribute inputs with integrated gradients, which enables us to infer (1) highly involved brain connections and subnetworks for each task, (2) temporal keyframes of imaging sequences that characterize tasks, and (3) subnetworks that discriminate between individual subjects. This ability to identify critical subnetworks that characterize signal states across heterogeneous tasks and individuals is of great importance to neuroscience and other scientific domains. Extensive experiments and ablation studies demonstrate our proposed method's superiority and efficiency in spatial-temporal graph signal modeling with insightful interpretations of brain dynamics.

From the 2016 U.S. presidential election to the 2021 Capitol riots to the spread of misinformation related to COVID-19, many have blamed social media for today's deeply divided society. Recent advances in machine learning for signed networks hold the promise to guide small interventions with the goal of reducing polarization in social media. However, existing models are especially ineffective in predicting conflicts (or negative links) among users. This is due to a strong correlation between link signs and the network structure, where negative links between polarized communities are too sparse to be predicted even by state-of-the-art approaches. To address this problem, we first design a partition-agnostic polarization measure for signed graphs based on the signed random-walk and show that many real-world graphs are highly polarized. Then, we propose POLE (POLarized Embedding for signed networks), a signed embedding method for polarized graphs that captures both topological and signed similarities jointly via signed autocovariance. Through extensive experiments, we show that POLE significantly outperforms state-of-the-art methods in signed link prediction, particularly for negative links with gains of up to one order of magnitude.

Personalized item search has become an essential tool for online platforms---where users interact with a large corpus of items (e.g., click, purchase, like) via a search query---to provide their users with a more satisfactory search experience. The record (or history) of users' past interactions serves as a valuable asset to achieve personalization. While user history data can span over a long period of time, only a part of the history is relevant to a user's current search intent. Moreover, since historical interactions take place at aperiodic points in time, modeling their relevance to the current search query entangles complex temporal dependencies. We propose multi-resolution attention to address these challenges for personalized item search. Our approach captures higher-order temporal relations between user queries and their history across several temporal subspaces (i.e., resolutions), each corresponding to distinct temporal ranges with adaptive time boundaries that are also learned directly from data. We achieve this by coupling the conventional multi-head attention module with a differentiable soft-thresholding mechanism, which essentially operates as a masking function in the temporal domain. Comparisons with strong baselines on an open-source benchmark dataset confirm the efficacy of our approach.

Online social networks have become major battlegrounds for political campaigns, viral marketing, and the dissemination of news. As a consequence, “bad actors” are increasingly exploiting these platforms, which is a key challenge for their administrators, businesses and society in general. The spread of fake news is a classical example of the abuse of social networks by these bad actors. While some have advocated for stricter policies to control the spread of misinformation in social networks, this often happens in detriment of their democratic and organic structure. In this paper, we aim to limit the influence of a target group in a social network via the removal of a few users/links. We formulate the influence limitation problem in a data-driven fashion, by taking into account past propagation traces. More specifically, our algorithms find critical edges to be removed in order to decrease the influence of a target group based on past data. The idea is to control the diffusion processes while minimizing the amount of disturbance in the network structure. Moreover, we consider two types of constraints over edge removals, a budget constraint and also a, more general, set of matroid constraints. These problems lead to interesting challenges in terms of algorithm design. For instance, we are able to show that influence limitation is APX-hard and propose deterministic and probabilistic approximation algorithms for the budgeted and the matroid version of the problem, respectively. Experiments show that the proposed approaches outperform several baselines.

Graph-structured data arise in many scenarios. A fundamental problem is to quantify the similarities of graphs for tasks such as classification. R-convolution graph kernels are positive-semidefinite functions that decompose graphs into substructures and compare them. One problem in the effective implementation of this idea is that the substructures are not independent, which leads to high-dimensional feature space. In addition, graph kernels cannot capture the high-order complex interactions between vertices. To mitigate these two problems, we propose a framework calledDeepMapto learn deep representations for graph feature maps. The learned deep representation for a graph is a dense and low-dimensional vector that captures complex high-order interactions in a vertex neighborhood.DeepMapextends Convolutional Neural Networks (CNNs) to arbitrary graphs by generating aligned vertex sequences and building the receptive field for each vertex. We empirically validateDeepMapon various graph classification benchmarks and demonstrate that it achieves state-of-the-art performance.

Graph embedding based on random-walks supports effective solutions for many graph-related downstream tasks. However, the abundance of embedding literature has made it increasingly difficult to compare existing methods and to identify opportunities to advance the state-of-the-art. Meanwhile, existing work has left several fundamental questions---such as how embeddings capture different structural scales and how they should be applied for effective link prediction---unanswered. This paper addresses these challenges with an analytical framework for random-walk based graph embedding that consists of three components: a random-walk process, a similarity function, and an embedding algorithm. Our framework not only categorizes many existing approaches but naturally motivates new ones. With it, we illustrate novel ways to incorporate embeddings at multiple scales to improve downstream task performance. We also show that embeddings based on autocovariance similarity, when paired with dot product ranking for link prediction, outperform state-of-the-art methods based on Pointwise Mutual Information similarity by up to 100%.

Graph clustering has been studied extensively on both plain graphs and attributed graphs. However, all these methods need to partition the whole graph to find cluster structures. Sometimes, based on domain knowledge, people may have information about a specific target region in the graph and only want to find a single cluster concentrated on this local region. Such a task is called local clustering. In contrast to global clustering, local clustering aims to find only one cluster that is concentrating on the given seed vertex (and also on the designated attributes for attributed graphs). Currently, very few methods can deal with this kind of task. To this end, we propose two quality measures for a local cluster: Graph Unimodality (GU) and Attribute Unimodality (AU). The former measures the homogeneity of the graph structure while the latter measures the homogeneity of the subspace that is composed of the designated attributes. We call their linear combination asCompactness. Further, we propose LOCLU to optimize theCompactnessscore. The local cluster detected by LOCLU concentrates on the region of interest, provides efficient information flow in the graph and exhibits a unimodal data distribution in the subspace of the designated attributes.

Graph-structured data arise ubiquitously in many application domains. A fundamental problem is to quantify their similarities. Graph kernels are often used for this purpose, which decompose graphs into substructures and compare these substructures. However, most of the existing graph kernels do not have the property of scale-adaptivity, i.e., they cannot compare graphs at multiple levels of granularities. Many real-world graphs such as molecules exhibit structure at varying levels of granularities. To tackle this problem, we propose a new graph kernel called Tree++ in this paper. At the heart of Tree++ is a graph kernel called the path-pattern graph kernel. The path-pattern graph kernel first builds a truncated BFS tree rooted at each vertex and then uses paths from the root to every vertex in the truncated BFS tree as features to represent graphs. The path-pattern graph kernel can only capture graph similarity at fine granularities. In order to capture graph similarity at coarse granularities, we incorporate a new concept called super path into it. The super path contains truncated BFS trees rooted at the vertices in a path. Our evaluation on a variety of real-world graphs demonstrates that Tree++ achieves the best classification accuracy compared with previous graph kernels.

Network regularization is an effective tool for incorporating structural prior knowledge to learn coherent models over networks, and has yielded provably accurate estimates in applications ranging from spatial economics to neuroimaging studies. Recently, there has been an increasing interest in extending network regularization to the spatio-temporal case to accommodate the evolution of networks. However, in both static and spatio-temporal cases, missing or corrupted edge weights can compromise the ability of network regularization to discover desired solutions. To address these gaps, we propose a novel approach—discrepancy-aware network regularization (DANR)—that is robust to inadequate regularizations and effectively captures model evolution and structural changes over spatio-temporal networks. We develop a distributed and scalable algorithm based on alternating direction method of multipliers (ADMM) to solve the proposed problem with guaranteed convergence to global optimum solutions. Experimental results on both synthetic and real-world networks demonstrate that our approach achieves improved performance on various tasks, and enables interpretation of model changes in evolving networks.

The process of opinion formation is inherently a network process, with user opinions in a social network being driven to a certain average opinion. One simple and intuitive incarnation of this opinion attractor is the average of user opinions weighted by the users' eigenvector centralities. This value is a lucrative target for control, as altering it essentially changes the mass opinion in the network. Since any potentially malicious influence upon the opinion distribution in a society is undesirable, it is important to design methods to prevent external attacks upon it. In this work, we assume that the adversary aims to maliciously change the network's average opinion by altering the opinions of some unknown users. We, then, state an NP-hard problem of disabling such opinion control attempts via strategically altering the network's users' eigencentralities by recommending a limited number of links to the users. Relying on Markov chain theory, we provide perturbation analysis that shows how eigencentrality and, hence, our problem's objective change in response to a link's addition to the network. The latter leads to the design of a pseudo-linear-time heuristic, relying on efficient estimation of mean first passage times in Markov chains. We have confirmed our theoretical and algorithmic findings, and studied effectiveness and efficiency of our heuristic in experiments with synthetic and real networks.

Analysis of opinion dynamics in social networks plays an important role in today’s life. For predicting users’ political preference, it is particularly important to be able to analyze the dynamics of competing polar opinions, such as pro-Democrat vs. pro-Republican. While observing the evolution of polar opinions in a social network over time, can we tell when the network evolved abnormally? Furthermore, can we predict how the opinions of the users will change in the future? To answer such questions, it is insufficient to study individual user behavior, since opinions can spread beyond users’ ego-networks. Instead, we need to consider the opinion dynamics of all users simultaneously and capture the connection between the individuals’ behavior and the global evolution pattern of the social network. In this work, we introduce the Social Network Distance (SND)—a distance measure that quantifies the likelihood of evolution of one snapshot of a social network into another snapshot under a chosen model of polar opinion dynamics. SND has a rich semantics of a transportation problem, yet, is computable in time linear in the number of users and, as such, is applicable to large-scale online social networks. In our experiments with synthetic and Twitter data, we demonstrate the utility of our distance measure for anomalous event detection. It achieves a true positive rate of 0.83, twice as high as that of alternatives. The same predictions presented in precision-recall space show that SND retains perfect precision for recall up to 0.2. Its precision then decreases while maintaining more than 2-fold improvement over alternatives for recall up to 0.95. When used for opinion prediction in Twitter data, SND’s accuracy is 75.6%, which is 7.5% higher than that of the next best method.

In many real-world big data applications, the data distribution is not homogeneous over entire data, but instead varies across groups/clusters of data samples. Although a model's predictive performance remains vital, there is also a need to learn succinct sets of features that evolve and capture smooth variations in data distribution. These small sets of features not only lead to high prediction accuracy, but also discover the important underlying processes. We investigate this challenging problem by developing a novel multi-task learning paradigm that trains multiple support vector machine (SVM) classifiers over a set of related data clusters, and directly imposes smoothness constraints on adjacent classifiers. We show that such patterns can be effectively learned in the dual form of the classical SVM, and further show that a parsimonious solution can be achieved in the primal form. Although a solution can be effectively optimized via gradient descent, the technical development is not straightforward, requiring a relaxation over the loss function of SVMs. We demonstrate the performance of our algorithm in two practical application domains: team performance and road traffic prediction. Empirical results show our model not only achieves competitive prediction accuracy, but its discovered patterns truly capture and give intuition about the variation in the data distribution across multiple data clusters.

Understanding and modeling complex network processes is an important task in many real-world applications. The first challenge is to discover patterns in such complex data. In this work, our goal is to summarize different processes in a network by a small yet interpretable set of network patterns, each of which represents a local community of connected nodes frequently participating in the same network processes. We formulate this problem as a Boolean Matrix Factorization with a network constraint, which we prove to be NP-hard. We then propose an efficient algorithm that incrementally adds the best patterns and achieve scalability with two further improvements. First, to decide which network processes contain which network patterns, we introduce two mapping algorithms with linear costs. Second, to systematically mine the exponential subgraph search space for good patterns, we devise two sampling algorithms based on Monte Carlo Markov Chain. Experimental results on both synthetic and real-world datasets show that our solutions are scalable and find network patterns that effectively summarize network processes.

Network centrality plays an important role in many applications. Central nodes in social networks can be influential, driving opinions and spreading news or rumors. In hyperlinked environments, such as the Web, where users navigate via clicks, central content receives high traffic, becoming target for advertising campaigns. While there is an extensive amount of work on centrality measures and their efficient computation, controlling nodes' centrality via network updates is a more recent and challenging task. Performing minimal modifications to a network to achieve a desired property falls under the umbrella of network design problems. This paper is focused on improving group (coverage and betweenness) centrality, which is a function of the shortest paths passing through a set of nodes, by adding edges to the network. Several variations of the problem, which are NP-hard as well as APX-hard, are introduced. We present a greedy algorithm, and even faster sampling algorithms, for group centrality maximization with theoretical quality guarantees under realistic constraints. The experimental results show that our sampling algorithms outperform the best baseline solution in terms of centrality by up to 5 times while being 2–3 orders of magnitude faster than our greedy approach.

The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of graph cuts include community detection and computer vision. However, cut problems were originally proposed for static graphs, an assumption that does not hold in many modern applications where graphs are highly dynamic. In this paper, we introduce sparsest and normalized cuts in temporal graphs, which generalize their standard definitions by enforcing the smoothness of cuts over time. We propose novel formulations and algorithms for computing temporal cuts using spectral graph theory, divide-and-conquer and low-rank matrix approximation. Furthermore, we extend temporal cuts to dynamic graph signals, where vertices have attributes. Experiments show that our solutions are accurate and scalable, enabling the discovery of dynamic communities and the analysis of dynamic graph processes.

In several domains, the flow of data is governed by an underlying network. Reduction of delays in end-to-end data flow is an important network optimization task. Reduced delays enable shorter travel times for vehicles in road networks, faster information flow in social networks, and increased rate of packets in communication networks. While techniques for network delay minimization have been proposed, they fail to provide any noticeable reduction in individual data flows. Furthermore, they treat all nodes as equally important, which is often not the case in real-world networks. In this paper, we incorporate these practical aspects and propose a network design problem where the goal is to perform k network upgrades such that it maximizes the number of flows in the network with a noticeable reduction in delay. We show that the problem is NP-hard, APX-hard, and non-submodular. We overcome these computational challenges by designing an importance sampling based algorithm with provable quality guarantees. Through extensive experiments on real and synthetic data sets, we establish that importance sampling imparts up to 1000 times speed-up over the greedy approach, and provides up to 70 times the improvement achieved by the state-of-the-art technique.

Reduction of end-to-end network delay is an optimization task with applications in multiple domains. Low delays enable improved information flow in social networks, quick spread of ideas in collaboration networks, low travel times for vehicles on road networks, and increased rate of packets in the case of communication networks. Delay reduction can be achieved by both improving the propagation capabilities of individual nodes and adding additional edges in the network. One of the main challenges in such network design problems is that the effects of local changes are not independent, and as a consequence, there is a combinatorial search-space of possible improvements. Thus, minimizing the cumulative propagation delay requires novel scalable and data-driven approaches. We consider the problem of network delay minimization via node upgrades. We show that the problem is NP-hard and prove strong inapproximability results about it (i.e., APX-hard) even for equal vertex delays. On the positive side, probabilistic approximations for a restricted version of the problem can be obtained. We propose a greedy heuristic to solve the general problem setting which has good quality in practice, but does not scale to very large instances. To enable scalability to real-world networks, we develop approximations for Greedy with probabilistic guarantees for every iteration, tailored to different models of delay distribution and network structures. Our methods scale almost linearly with the graph size and consistently outperform competitors in quality. We evaluate our approaches on several real-world graphs from different genres. We achieve up to two orders of magnitude speed-up compared to alternatives from the literature on moderate size networks, and obtain high-quality results in minutes on large datasets while competitors from the literature require more than four hours.

Modeling and predicting people's opinions plays an important role in today's life. For viral marketing and political strategy design, it is particularly important to be able to analyze competing opinions, such as pro-Democrat vs. pro-Republican. While observing the evolution of polar opinions in a social network over time, can we tell when the network "behaved"' abnormally? Furthermore, can we predict how the opinions of individual users will change in the future? To answer such questions, it is insufficient to study individual user behavior, since opinions spread beyond users' ego-networks. Instead, we need to consider the opinion dynamics of all users simultaneously. In this work, we introduce the Social Network Distance (SND)-a distance measure that quantifies the likelihood of evolution of one snapshot of a social network into another snapshot under a chosen opinion dynamics model. SND has a rich semantics of a transportation problem, yet, is computable in pseudo-linear time, thereby, being applicable to large-scale social networks analysis. We demonstrate the effectiveness of SND in experiments with Twitter data.

In many real-world applications, data is represented in the form of networks with structures and attributes changing over time. The dynamic changes not only happen at nodes/edges, forming local subnetwork processes, but also eventually influence global states of networks. The need to understand what these local network processes are, how they evolve and consequently govern the progression of global network states has become increasingly important. In this paper, we explore these questions and develop a novel algorithm for mining a succinct set of subnetworks that are predictive and evolve along with the progression of global network states. Our algorithm is designed in the framework of logistic regression that fits a model for multi-states of network samples. Its objective function considers both the spatial network topology and temporal smooth transition between adjacent global network states, and we show that its global optimum solution can be achieved via steepest descent. Extensive experimental analysis on both synthetic and real world datasets demonstrates the effectiveness of our algorithm against competing methods, not only in the prediction accuracy but also in terms of domain relevance of the discovered subnetworks.

Predicting the popularity of online content in social networks is important in many applications, ranging from ad campaign design, web content caching and prefetching, to web-search result ranking. Earlier studies target this problem by learning models that either generalize behaviors of the entire network population or capture behaviors of each individual user. In this paper, we claim that a novel approach based on group-level popularity is necessary and more practical, given that users naturally organize themselves into clusters and that users within a cluster react to online content in a uniform manner. We develop a novel framework by first grouping users into cohesive clusters, and then adopt tensor decomposition to make predictions. In order to minimize the impact of noisy data and be more flexible in capturing changes in users' interests, our framework exploits both the network topology and interaction among users in learning a robust user clustering. The PARAFAC tensor decomposition is adapted to work with hierarchical constraint over user groups, and we show that optimizing this constrained function via gradient descent achieves faster convergence and leads to more stable solutions. Extensive experimental results over two social networks demonstrate that our framework is scalable, finds meaningful user groups, and significantly outperforms eight baseline methods in terms of prediction accuracy.

Predicting the movement of crowds in a city is strategically important for traffic management, risk assessment, and public safety. In this paper, we propose predicting two types of flows of crowds in every region of a city based on big data, including human mobility data, weather conditions, and road network data. To develop a practical solution for citywide traffic prediction, we first partition the map of a city into regions using both its road network and historical records of human mobility. Our problem is different than the predictions of each individual's movements and each road segment's traffic conditions, which are computationally costly and not necessary from the perspective of public safety on a citywide scale. To model the multiple complex factors affecting crowd flows, we decompose flows into three components: seasonal (periodic patterns), trend (changes in periodic patterns), and residual flows (instantaneous changes). The seasonal and trend models are built as intrinsic Gaussian Markov random fields which can cope with noisy and missing data, whereas a residual model exploits the spatio-temporal dependence among different flows and regions, as well as the effect of weather. Experiment results on three real-world datasets show that our method is scalable and outperforms all baselines significantly in terms of accuracy.

Detecting a small number of outliers from a set of data observations is always challenging. This problem is more difficult in the setting of multiple network samples, where computing the anomalous degree of a network sample is generally not sufficient. In fact, explaining why a given network is exceptional, expressed in the form of subnetwork, is also equally important. We develop a novel algorithm to address these two key problems. We treat each network sample as a potential outlier and identify subnetworks that help discriminate it from nearby samples. The algorithm is developed in the framework of network regression combined with the constraints on both network topology and L1-norm shrinkage to perform subnetwork discovery. Our method thus goes beyond subspace/subgraph discovery. We also show that the developed method converges to a global optimum. Empirical evaluation on various real-world network datasets demonstrates the advantages of our algorithm over various baseline methods.

Reduction of end-to-end network delays is an optimization task with applications in multiple domains. Low delays enable improved information flow in social networks, quick spread of ideas in collaboration networks, low travel times for vehicles on road networks and increased rate of packets in communication networks. Delay reduction can be achieved by both improving the propagation capabilities of individual nodes and adding additional edges in the network. One of the main challenges in such design problems is that the effects of local changes are not independent, and as a consequence, there is a combinatorial search space of possible improvements. Thus, minimizing the cumulative propagation delay requires novel scalable and data-driven approaches. In this paper, we consider the problem of network delay minimization via node upgrades. Although the problem is NP-hard, we show that probabilistic approximation for a restricted version can be obtained. We design scalable and high-quality techniques for the general setting based on sampling that are targeted to different models of delay distribution. Our methods scale almost linearly with the graph size and consistently outperform competitors in quality.

Modeling information that resides on vertices of large graphs is a key problem in several real-life applications, ranging from social networks to the Internet-of-things. Signal Processing on Graphs and, in particular, graph wavelets can exploit the intrinsic smoothness of these datasets in order to represent them in a compact and accurate manner. However, how to discover wavelet bases that capture the geometry of the data with respect to the signal as well as the graph structure remains an open problem. In this paper, we study the problem of computing graph wavelet bases via sparse cuts in order to produce low-dimensional encodings of data-driven bases. This problem is connected to known hard problems in graph theory (e.g. multiway cuts) and thus requires an efficient heuristic. We formulate the basis discovery task as a relaxation of a vector optimization problem, which leads to an elegant solution as a regularized eigenvalue computation. Moreover, we propose several strategies in order to scale our algorithm to large graphs. Experimental results show that the proposed algorithm can effectively encode both the graph structure and signal, producing compressed and accurate representations for vertex values in a wide range of datasets (e.g. sensor and gene networks) and significantly outperforming the best baseline.

Keyword-based search in text-rich multi-dimensional datasets facilitates many novel applications and tools. In this paper, we consider objects that are tagged with keywords and are embedded in a vector space. For these datasets, we study queries that ask for the tightest groups of points satisfying a given set of keywords. We propose a novel method called ProMiSH (Projection and Multi Scale Hashing) that uses random projection and hash-based index structures, and achieves high scalability and speedup. We present an exact and an approximate version of the algorithm. Our experimental results on real and synthetic datasets show that ProMiSH has up to 60 times of speedup over state-of-the-art tree-based techniques.

Many real-world complex systems can be modeled as dynamic networks with real-valued vertex/edge attributes. Examples include users' opinions in social networks and average speeds in a road system. When managing these large dynamic networks, compressing attribute values becomes a key requirement, since it enables the answering of attribute-based queries regarding a node/edge or network region based on a compact representation of the data. To address this problem, we introduce a lossy network compression scheme called Slice Tree (ST), which partitions a network into smooth regions with respect to node/edge values and compresses each value as the average of its region. ST applies a compact representation for network partitions, called slices, that are defined as a center node and radius distance. We propose an importance sampling algorithm to efficiently prune the search space of candidate slices in the ST construction by biasing the sampling process towards the node values that most affect the compression error. The effectiveness of ST in terms of compression error, compression rate, and running time is demonstrated using synthetic and real datasets. ST scales to million-node instances and removes up to 87% of the error in attribute values with a 103compression ratio. We also illustrate how ST captures relevant phenomena in real networks, such as research collaboration patterns and traffic congestions.

Learning a succinct set of substructures that predicts global network properties plays a key role in understanding complex network data. Existing approaches address this problem by sampling the exponential space of all possible subnetworks to find ones of high prediction accuracy. In this paper, we develop a novel framework that avoids sampling by formulating the problem of predictive subnetwork learning as node selection, subject to network-constrained regularization. Our framework involves two steps: (i) subspace learning, and (ii) predictive substructures discovery with network regularization. The framework is developed based upon two mathematically sound techniques of spectral graph learning and gradient descent optimization, and we show that their solutions converge to a global optimum solution - a desired property that cannot be guaranteed by sampling approaches. Through experimental analysis on a number of real world datasets, we demonstrate the performance of our framework against state-of-the-art algorithms, not only based on prediction accuracy but also in terms of domain relevance of the discovered substructures.

Complex network phenomena -- such as information cascades in online social networks -- are hard to fully observe, model, and forecast. In forecasting, a recent trend has been to forgo the use of parsimonious models in favor of models with increasingly large degrees of freedom that are trained to learn the behavior of a process from historical data. Extrapolating this trend into the future, eventually we would renounce models all together. But is it possible to forecast the evolution of a complex stochastic process directly from the data without a model? In this work we show that model-free forecasting is possible. We present SED, an algorithm that forecasts process statistics based on relationships of statistical equivalence using two general axioms and historical data. To the best of our knowledge, SED is the first method that can perform axiomatic, model-free forecasts of complex stochastic processes. Our simulations using simple and complex evolving processes and tests performed on a large real-world dataset show promising results.

Computer system monitoring generates huge amounts of logs that record the interaction of system entities. How to query such data to better understand system behaviors and identify potential system risks and malicious behaviors becomes a challenging task for system administrators due to the dynamics and heterogeneity of the data. System monitoring data are essentially heterogeneous temporal graphs with nodes being system entities and edges being their interactions over time. Given the complexity of such graphs, it becomes time-consuming for system administrators to manually formulate useful queries in order to examine abnormal activities, attacks, and vulnerabilities in computer systems. In this work, we investigate how to query temporal graphs and treat query formulation as a discriminative temporal graph pattern mining problem. We introduce TGMiner to mine discriminative patterns from system logs, and these patterns can be taken as templates for building more complex queries. TGMiner leverages temporal information in graphs to prune graph patterns that share similar growth trend without compromising pattern quality. Experimental results on real system data show that TGMiner is 6-32 times faster than baseline methods. The discovered patterns were verified by system experts; they achieved high precision (97%) and recall (91%).

Fast service placement, finding a set of nodes with enough free capacity of computation, storage, and network connectivity, is a routine task in daily cloud administration. In this work, we formulate this as a subgraph matching problem. Different from the traditional setting, including approximate and probabilistic graphs, subgraph matching on data-center networks has two unique properties. (1) Node/edge labels representing vacant CPU cycles and network bandwidth change rapidly, while the network topology varies little. (2) There is a partial order on node/edge labels. Basically, one needs to place service in nodes with enough free capacity. Existing graph indexing techniques have not considered very frequent label updates, and none of them supports partial order on numeric labels. Therefore, we resort to a new graph index framework, Gradin, to address both challenges. Gradin encodes subgraphs into multi-dimensional vectors and organizes them with indices such that it can efficiently search the matches of a query's subgraphs and combine them to form a full match. In particular, we analyze how the index parameters affect update and search performance with theoretical results. Moreover, a revised pruning algorithm is introduced to reduce unnecessary search during the combination of partial matches. Using both real and synthetic datasets, we demonstrate that Gradin outperforms the baseline approaches up to 10 times.

Performance monitor software for data centers typically generates a great number of alert sequences. These alert sequences indicate abnormal network events. Given a set of observed alert sequences, it is important to identify the most critical alerts that are potentially the causes of others. While the need for mining critical alerts over large scale alert sequences is evident, most alert analysis techniques stop at modeling and mining the causal relations among the alerts.

Given a function that classifies a data object as relevant or irrelevant, we consider the task of selecting k objects that best represent all relevant objects in the underlying database. This problem occurs naturally when analysts want to familiarize themselves with the relevant objects in a database using a small set of k exemplars. In this paper, we solve the problem of top-k representative queries on graph databases. While graph databases model a wide range of scientific data, solving the problem in the context of graphs presents us with unique challenges due to the inherent complexity of matching structures. Furthermore, top-k representative queries map to the classic Set Cover problem, making it NP-hard. To overcome these challenges, we develop a greedy approximation with theoretical guarantees on the quality of the answer set, noting that a better approximation is not feasible in polynomial time. To further optimize the quadratic computational cost of the greedy algorithm, we propose an index structure called NB-Index to index the \theta-neighborhoods of the database graphs by employing a novel combination of Lipschitz embedding and agglomerative clustering. Extensive experiments on real graph datasets validate the efficiency and effectiveness of the proposed techniques that achieve up to two orders of magnitude speed-up over state-of-the-art algorithms.

Information propagation in social media depends not only on the static follower structure but also on the topic-specific user behavior. Hence novel models incorporating dynamic user behavior are needed. To this end, we propose a model for individual social media users, termed a genotype. The genotype is a per-topic summary of a user's interest, activity and susceptibility to adopt new information. We demonstrate that user genotypes remain invariant within a topic by adopting them for classification of new information spread in large-scale real networks. Furthermore, we extract topic-specific influence backbone structures based on information adoption and show that they differ significantly from the static follower network. When employed for influence prediction of new content spread, our genotype model and influence backbones enable more than 20% improvement, compared to purely structural features. We also demonstrate that knowledge of user genotypes and influence backbones allow for the design of effective strategies for latency minimization of topic-specific information spread.

The study of influence, persuasion, and user sentiment dynamics within online communities has recently emerged as a highly active area of research. In this paper, we focus on analyzing and modeling user sentiment dynamics within a real-world social media such as Twitter. Beyond text and connectivity, we are interested in exploring the level of topical user posting activity and its effect on sentiment change. We perform topic-wise analysis of tweeting behavior that reveals a strong relationship between users' activity acceleration and topic sentiment change. Inspired by this empirical observation, we develop a new generative and predictive model that extends classical neighborhood-based influence propagation with the notion of user activation. We fit the parameters of our model to a large, real-world Twitter dataset and evaluate its utility to predict future sentiment change. Our model outperforms significantly (1 order of magnitude in accuracy) existing alternatives in identifying the individuals who are most likely to change sentiment based on past information. When predicting the next sentiment of users who actually change their opinion (a relatively rare event), our model is twice more accurate than alternatives, while its overall network accuracy is 94% on average. We also study the effect of inactive users on consensus efficiency in the opinion dynamics process both analytically and in simulation within the context of our model.

Nearest neighbor proximity search in large graphs is an important analysis primitive with a variety of applications in graph data from different domains. We propose a novel proximity measure for weighted graphs called Effective Importance which incorporates multiple paths between nodes and captures the inherent structural clusters within a network. We develop effective bounds on the EI value using a modified small subnetwork around a query node, enabling scalable exact nearest neighbor (NN) search at query time. Our NN search does not require heavy offline analysis or holistic knowledge of the graph, making our method suitable for very large dynamically changing networks or composite network overlays.

Accurately estimating the current positions of moving objects is a challenging task due to the various forms of data uncertainty (e.g. limited sensor precision, periodic updates from continuously moving objects). However, in many cases, groups of objects tend to exhibit similarities in their movement behavior. For example, vehicles in a convoy or animals in a herd both exhibit tightly coupled movement behavior within the group. While such statistical dependencies often increase the computational complexity necessary for capturing this additional structure, they also provide useful information which can be utilized to provide more accurate location estimates. In this paper, we propose a novel model for accurately tracking coordinated groups of mobile uncertain objects. We introduce an exact and more efficient approximate inference algorithm for updating the current location of each object upon the arrival of new (uncertain) location observations. Additionally, we derive probability bounds over the groups in order to process probabilistic threshold range queries more efficiently. Our experimental evaluation shows that our proposed model can provide 4X improvements in tracking accuracy over competing models which do not consider group behavior. We also show that our bounds enable us to prune up to 50% of the database, resulting in more efficient processing over a linear scan.

Processes within real world networks evolve according to the underlying graph structure. A number of examples exists in diverse network genres: botnet communication growth, moving traffic jams [1], information foraging [2] in document networks (WWW and Wikipedia), and spread of viral memes or opinions in social networks. The network structure in all the above examples remains relatively fixed, while the shape, size and position of the affected network regions change gradually with time. Traffic jams grow, move, shrink and eventually disappear. Public attention shifts among current hot topics inducing a similar shift of highly accessed Wikipedia articles. Discovery of such smoothly evolving network processes has the potential to expose the intrinsic mechanisms of complex network dynamics, enable new data-driven models and improve network design. We introduce the novel problem of Mining smoothly evolving processes (MINESMOOTH) in networks with dynamic real-valued node/edge weights. We show that ensuring smooth transitions in the solution is NP-hard even on restricted network structures such as trees. We propose an efficient filtering based framework, called LEGATO. It achieves 3-7 times higher scores (i.e. larger and more significant processes) compared to alternatives on real networks, and above 80% accuracy in discovering realistic "embedded" processes in synthetic networks. In transportation networks, LEGATO discovers processes that conform to existing traffic jams models. Its results in Wikipedia reveal the temporal evolution of information seeking of Internet users.

Global-state networks provide a powerful mechanism to model the increasing heterogeneity in data generated by current systems. Such a network comprises of a series of network snapshots with dynamic local states at nodes, and a global network state indicating the occurrence of an event. Mining discriminative subgraphs from global-state networks allows us to identify the influential sub-networks that have maximum impact on the global state and unearth the complex relationships between the local entities of a network and their collective behavior. In this paper, we explore this problem and design a technique called MINDS to mine minimally discriminative subgraphs from large global-state networks. To combat the exponential subgraph search space, we derive the concept of an edit map and perform Metropolis Hastings sampling on it to compute the answer set. Furthermore, we formulate the idea of network-constrained decision trees to learn prediction models that adhere to the underlying network structure. Extensive experiments on real datasets demonstrate excellent accuracy in terms of prediction quality. Additionally, MINDS achieves a speed-up of at least four orders of magnitude over baseline techniques.

How to spot and summarize anomalies in dynamic networks such as road networks, communication networks and social networks? An anomalous event, such as a traffic accident, a denial of service attack or a chemical spill, can affect several near-by edges and make them behave abnormally, over several consecutive time-ticks. We focus on spotting and summarizing such significant anomalous regions, spanning space (i.e. nearby edges), as well as time. Our first contribution is the problem formulation, namely finding all such Significant Anomalous Regions (SAR). The next contribution is the design of novel algorithms: an expensive, exhaustive algorithm, as well as an efficient approximation, called NETSPOT. Compared to the exhaustive algorithm, NETSPOT is up to one order of magnitude faster in real data, while achieving less than 4% average relative error rate. In synthetic datasets, it is more than 30 times faster and solves large problem instances that are otherwise infeasible. The final contribution is the validation on real data: we demonstrate the utility of NETSPOT for inferring accidents on road networks and detecting patterns of anomalous access to subnetworks of Wikipedia. We also study NETSPOT'S scalability in large social, transportation and synthetic evolving networks, spanning in total up to 50 million edges.

Real-life graphs not only contain nodes and edges, but also have events taking place, e.g., product sales in social networks. Among different events, some exhibit strong correlations with the network structure, while others do not. Such structural correlations will shed light on viral influence existing in the corresponding network. Unfortunately, the traditional association mining concept is not applicable in graphs because it only works on homogeneous data sets like transactions and baskets. We propose a novel measure for assessing such structural correlations in heterogeneous graph data sets with events. The measure applies hitting time to aggregate the proximity among nodes that have the same event. To calculate the correlation scores for many events in a large network, we develop a scalable framework, called gScore, using sampling and approximation. By comparing to the situation where events are randomly distributed in the same network, our method is able to discover events that are highly correlated with the graph structure. We test gScore's effectiveness by synthetic events on the DBLP coauthor network and report interesting correlation results in a social network extracted from TaoBao.com, the largest online shopping network in China. Scalability of gScore is tested on the Twitter network. Since an event is essentially a temporal phenomenon, we also propose a dynamic measure, which reveals structural correlations at specific time steps and can be used for discovering detailed evolutionary patterns.

Increased availability of large repositories of chemical compounds has created new challenges and opportunities for the application of data-mining and indexing techniques to problems in chemical informatics. The primary goal in analysis of molecular databases is to identify structural patterns that can predict biological activity. Two of the most popular approaches to representing molecular topologies are graphs and 3D geometries. As a result, the problem of indexing and mining structural patterns map to indexing and mining patterns from graph and 3D geometric databases.

Near neighbor search in high dimensional spaces is useful in many applications. Existing techniques solve this problem efficiently only for the approximate cases. These solutions are designed to solve r-near neighbor queries for a fixed query range or for a set of query ranges with probabilistic guarantees, and then extended for nearest neighbor queries. Solutions supporting a set of query ranges suffer from prohibitive space cost. There are many applications which are quality sensitive and need to efficiently and accurately support near neighbor queries for all query ranges. In this paper, we propose a novel indexing and querying scheme called Spatial Intersection and Metric Pruning (SIMP). It efficiently supports r-near neighbor queries in very high dimensional spaces for all query ranges with 100% quality guarantee and with practical storage costs. Our empirical studies on three real datasets having dimensions between 32 and 256 and sizes up to 10 million show a superior performance of SIMP over LSH, Multi-Probe LSH, LSB tree, and iDistance. Our scalability tests on real datasets having as many as 100 million points of dimensions up to 256 establish that SIMP scales linearly with query range, dataset dimension, and dataset size.

In social networks, information and influence diffuse among users as cascades. While the importance of studying cascades has been recognized in various applications, it is difficult to observe the complete structure of cascades in practice. In this paper we study the cascade inference problem following the independent cascade model, and provide a full treatment from complexity to algorithms: (a) we propose the idea of consistent trees as the inferred structures for cascades, these trees connect source nodes and observed nodes with paths satisfying the constraints from the observed temporal information. (b) We introduce metrics to measure the likelihood of consistent trees as inferred cascades, as well as several optimization problems for finding them. (c) We show that the decision problems for consistent trees are in general NP-complete, and that the optimization problems are hard to approximate. (d) We provide approximation algorithms with performance guarantees on the quality of the inferred cascades, as well as heuristics. We experimentally verify the efficiency and effectiveness of our inference algorithms, using real and synthetic data.

Anomaly detection in dynamic networks has a rich gamut of application domains, such as road networks, communication networks and water distribution networks. An anomalous event, such as a traffic accident, denial of service attack or a chemical spill, can cause a local shift from normal behavior in the network state that persists over an interval of time. Detecting such anomalous regions of network and time extent in large real-world networks is a challenging task. Existing anomaly detection techniques focus on either the time series associated with individual network edges or on global anomalies that affect the entire network. In order to detect anomalous regions, one needs to consider both the time and the affected network substructure jointly, which brings forth computational challenges due to the combinatorial nature of possible solutions.

Social and communication networks across the world generate vast amounts of graph-like data each day. The modeling and prediction of how these communication structures evolve can be highly useful for many applications. Previous research in this area has focused largely on using past graph structure to predict future links. However, a useful observation is that many graph datasets have additional information associated with them beyond just their graph structure. In particular, communication graphs (such as email, twitter, blog graphs, etc.) have information content associated with their graph edges. In this paper we examine the link between information content and graph structure, proposing a new graph modeling approach, GC-Model, which combines both. We then apply this model to multiple real world communication graphs, demonstrating that the built models can be used effectively to predict future graph structure and information flow. On average, GC-Model's top predictions covered 19% more of the actual future graph communication structure when compared to other previously introduced algorithms, far outperforming multiple link prediction methods and several naive approaches.

Many real world applications produce data with uncertainties drawn from measurements over a continuous domain space. Recent research in the area of probabilistic databases has mainly focused on managing and querying discrete data in which the domain is limited to a small number of values (i.e. on the order of 10). When the size of the domain increases, current methods fail due to their nature of explicitly storing each value/probability pair. Such methods are not capable of extending their use to continuous-valued attributes. In this paper, we provide a scalable, accurate, space efficient probabilistic data synopsis for uncertain attributes defined over a continuous domain. Our synopsis construction methods are all error-aware to ensure that our synopsis provides an accurate representation of the underlying data given a limited space budget. Additionally, we are able to provide approximate query results over the synopsis with error bounds.

Networks from different genres are not static entities, but exhibit dynamic behavior. The congestion level of links in transportation networks varies in time depending on the traffic. Similarly, social and communication links are employed at varying rates as information cascades unfold. In recent years there has been an increase of interest in modeling and mining dynamic networks. However, limited attention has been placed in high-scoring sub graph discovery in time-evolving networks. We define the problem of finding the highest-scoring temporal sub graph in a dynamic network, termed Heaviest Dynamic Sub graph (HDS). We show that HDS is NP-hard even with edge weights in {-1,1} and devise an efficient approach for large graph instances that evolve over long time periods. While a naive approach would enumerate all O(t^2) sub-intervals, our solution performs an effective pruning of the sub-interval space by considering O(t*log(t)) groups of sub-intervals and computing an aggregate of each group in logarithmic time. We also define a fast heuristic and a tight upper bound for approximating the static version of HDS, and use them for further pruning the sub-interval space and quickly verifying candidate sub-intervals. We perform an extensive experimental evaluation of our algorithm on transportation, communication and social media networks for discovering sub graphs that correspond to traffic congestions, communication overflow and localized social discussions. Our method is two orders of magnitude faster than a naive approach and scales well with network size and time length.

Real-life graphs not only have nodes and edges, but also have events taking place, e.g., product sales in social networks and virus infection in communication networks. Among different events, some exhibit strong correlation with the network structure, while others do not. Such structural correlation will shed light on viral influence existing in the corresponding network. Unfortunately, the traditional association mining concept is not applicable in graphs since it only works on homogeneous datasets like transactions and baskets.

In this paper, we formulate a top-kquery that compares objects in a database to a user-provided query object on a novel scoring function. The proposed scoring function combines the idea ofattractiveandrepulsivedimensions into a general framework to overcome the weakness of traditional distance or similarity measures. We study the properties of the proposed class of scoring functions and develop efficient and scalable index structures that index the isolines of the function. We demonstrate various scenarios where the query finds application. Empirical evaluation demonstrates a performance gain of one to two orders of magnitude on querying time over existing state-of-the-art top-ktechniques. Further, a qualitative analysis is performed on a real dataset to highlight the potential of the proposed query in discovering hidden data characteristics.

Querying uncertain data sets (represented as probability distributions) presents many challenges due to the large amount of data involved and the difficulties comparing uncertainty between distributions. The Earth Mover's Distance (EMD) has increasingly been employed to compare uncertain data due to its ability to effectively capture the differences between two distributions. Computing the EMD entails finding a solution to the transportation problem, which is computationally intensive. In this paper, we propose a new lower bound to the EMD and an index structure to significantly improve the performance of EMD based K-- nearest neighbor (K--NN) queries on uncertain databases. We propose a new lower bound to the EMD that approximates the EMD on a projection vector. Each distribution is projected onto a vector and approximated by a normal distribution, as well as an accompanying error term. We then represent each normal as a point in a Hough transformed space. We then use the concept of stochastic dominance to implement an efficient index structure in the transformed space. We show that our method significantly decreases K--NN query time on uncertain databases. The index structure also scales well with database cardinality. It is well suited for heterogeneous data sets, helping to keep EMD based queries tractable as uncertain data sets become larger and more complex.

Spatial data are common in many scientific and commercial domains such as geographical information systems and gene/protein expression profiles. Querying for distribution patterns on such data can discover underlying spatial relationships and suggest avenues for further scientific exploration. Supporting such pattern retrieval requires not only the formulation of an appropriate scoring function for defining relevant connected subregions, but also the design of new access methods that can scale to large databases. In this paper, we propose a solution to this problem of querying significant sub-regions on spatial data provided as raster images. We design a scoring scheme to measure the similarity of subregions. All the raster images are tiled and each alignment of the query and a database image produces a tile score matrix. We show that the problem of finding the best connected subregion from this matrix is NP-hard and develop a dynamic programming heuristic. With this heuristic, we develop two index-based scalable search strategies, TARS and SPARS, to query patterns in large data repositories. Experimental results on real image datasets show that TARS offers an 87% improvement for small queries, and SPARS a 52% improvement in runtime for large queries, as compared to linear search. Qualitative tests on real datasets achieve precision of more than 80%.

The identification of clusters, well-connected components in a graph, is useful in many applications from biological function prediction to social community detection. However, finding these clusters can be difficult as graph sizes increase. Most current graph clustering algorithms scale poorly in terms of time or memory. An important insight is that many clustering applications need only the subset of best clusters, and not all clusters in the entire graph. In this paper we propose a new technique, Top Graph Clusters (TopGC), which probabilistically searches large, edge weighted, directed graphs for their best clusters in linear time. The algorithm is inherently parallelizable, and is able to find variable size, overlapping clusters. To increase scalability, a parameter is introduced that controls memory use. When compared with three other state-of-the art clustering techniques, TopGC achieves running time speedups of up to 70% on large scale real world datasets. In addition, the clusters returned by TopGC are consistently found to be better both in calculated score and when compared on real world benchmarks.

Graphs are being increasingly used to model a wide range of scientific data. Such widespread usage of graphs has generated considerable interest in mining patterns from graph databases. While an array of techniques exists to mine frequent patterns, we still lack a scalable approach to mine statistically significant patterns, specifically patterns with low p-values, that occur at low frequencies. We propose a highly scalable technique, called GraphSig, to mine significant subgraphs from large graph databases. We convert each graph into a set of feature vectors where each vector represents a region within the graph. Domain knowledge is used to select a meaningful feature set. Prior probabilities of features are computed empirically to evaluate statistical significance of patterns in the feature space. Following analysis in the feature space, only a small portion of the exponential search space is accessed for further analysis. This enables the use of existing frequent subgraph mining techniques to mine significant patterns in a scalable manner even when they are infrequent. Extensive experiments are carried out on the proposed techniques, and empirical results demonstrate that GraphSig is effective and efficient for mining significant patterns. To further demonstrate the power of significant patterns, we develop a classifier using patterns mined by GraphSig. Experimental results show that the proposed classifier achieves superior performance, both in terms of quality and computation cost, over state-of-the-art classifiers.

We develop a framework for minimizing the communication overhead of monitoring global system parameters in IP networks and sensor networks. A global system predicate is defined as a conjunction of the local properties of different network elements. A typical example is to identify the time windows when the outbound traffic from each network element exceeds a predefined threshold. Our main idea is to optimize the scheduling of local event reporting across network elements for a given network traffic load and local event frequencies. The system architecture consists of N distributed network elements coordinated by a central monitoring station. Each network element monitors a set of local properties and the central station is responsible for identifying the status of global parameters registered in the system. We design an optimal algorithm, the Partition and Rank (PAR) scheme, when the local events are independent; whereas, when they are dependent, we show that the problem is NP-complete and develop two efficient heuristics: the PAR for dependent events (PAR-D) and Adaptive (Ada) algorithms, which adapt well to changing network conditions, and outperform the current state of the art techniques in terms of communication cost.

Probabilistic data have recently become popular in applications such as scientific and geospatial databases. For images and other spatial datasets, probabilistic values can capture the uncertainty in extent and class of the objects in the images. Relating one such dataset to another by spatial joins is an important operation for data management systems. We consider probabilistic spatial join (PSJ) queries, which rank the results according to a score that incorporates both the uncertainties associated with the objects and the distances between them. We present algorithms for two kinds of PSJ queries: Threshold PSJ queries, which return all pairs that score above a given threshold, and top-k PSJ queries, which return the k top-scoring pairs. For threshold PSJ queries, we propose a plane sweep algorithm that, because it exploits the special structure of the problem, runs in 0(n (log n + k)) time, where n is the number of points and k is the number of results. We extend the algorithms to 2-D data and to top-k PSJ queries. To further speed up top-k PSJ queries, we develop a scheduling technique that estimates the scores at the level of blocks, then hands the blocks to the plane sweep algorithm. By finding high-scoring pairs early, the scheduling allows a large portion of the datasets to be pruned. Experiments demonstrate speed-ups of two orders of magnitude.

With the prevalence of graph data in a variety of domains, there is an increasing need for a language to query and manipulate graphs with heterogeneous attributes and structures. We propose a query language for graph databases that supports arbitrary attributes on nodes, edges, and graphs. In this language, graphs are the basic unit of information and each query manipulates one or more collections of graphs. To allow for flexible compositions of graph structures, we extend the notion of formal languages from strings to the graph domain. We present a graph algebra extended from the relational algebra in which the selection operator is generalized to graph pattern matching and a composition operator is introduced for rewriting matched graphs. Then, we investigate access methods of the selection operator. Pattern matching over large graphs is challenging due to the NP-completeness of subgraph isomorphism. We address this by a combination of techniques: use of neighborhood subgraphs and profiles, joint reduction of the search space, and optimization of the search order. Experimental results on real and synthetic large graphs demonstrate that our graph specific optimizations outperform an SQL-based implementation by orders of magnitude.

The ability to store and query uncertain information is of great benefit to databases that infer values from a set of observations, including databases of moving objects, sensor readings, historical business transactions, and biomedical images. These observations are often inexact to begin with, and even if they are exact, a set of observations of an attribute of an object is better represented by a probability distribution than by a single number, such as a mean. In this paper, we present adaptive, piecewise-linear approximations (APLAs), which represent arbitrary probability distributions compactly with guaranteed quality. We also present the APLA-tree, an index structure for APLAs. Because APLA is more precise than existing approximation techniques, the APLA-tree can answer probabilistic range queries twice as fast. APLA generalizes to multiple dimensions, and the APLA-tree can index multivariate distributions using either one-dimensional or multidimensional APLAs. Finally, we propose a new definition of k-NN queries on uncertain data. The new definition allows APLA and the APLA-tree to answer k-NN queries quickly, even on arbitrary probability distributions. No efficient k-NN search was previously possible on such distributions.

Graphs have become popular for modeling scientific data in recent years. As a result, techniques for mining graphs are extremely important for understanding inherent data and domain characteristics. One such exploratory mining paradigm is the k-MST (minimum spanning tree over k vertices) problem that can be used to discover significant local substructures. In this paper, we present an efficient approximation algorithm for the k-MST problem in large graphs. The algorithm has an O(radic/k) approximation ratio and O(n log n + in log m log k + nk2log k) running time, where n and m are the number of vertices and edges respectively. Experimental results on synthetic graphs and protein interaction networks show that the algorithm is scalable to large graphs and useful for discovering biological pathways. The highlight of the algorithm is that it offers both analytical guarantees and empirical evidence of good running time and quality.

Graphs have become popular for modeling structured data. As a result, graph queries are becoming common and graph indexing has come to play an essential role in query processing. We introduce the concept of a graph closure, a generalized graph that represents a number of graphs. Our indexing technique, called Closure-tree, organizes graphs hierarchically where each node summarizes its descendants by a graph closure. Closure-tree can efficiently support both subgraph queries and similarity queries. Subgraph queries find graphs that contain a specific subgraph, whereas similarity queries find graphs that are similar to a query graph. For subgraph queries, we propose a technique called pseudo subgraph isomorphism which approximates subgraph isomorphism with high accuracy. For similarity queries, we measure graph similarity through edit distance using heuristic graph mapping methods. We implement two kinds of similarity queries: K-NN query and range query. Our experiments on chemical compounds and synthetic graphs show that for subgraph queries, Closuretree outperforms existing techniques by up to two orders of magnitude in terms of candidate answer set size and index size. For similarity queries, our experiments validate the quality and efficiency of the presented algorithms.

In many domains, the similarity between two images depends on the spatial locations of their features. The earth mover’s distance (EMD), first proposed by Werman et al. [8], measures such similarity. It yields higher-quality image retrieval results than the Lp-norm, quadratic-form distance, and Jeffrey divergence [6], and has also been used for similarity search on contours [3], melodies [7], and graphs [2].

We propose a technique for evaluating the statistical significance of frequent subgraphs in a database. A graph is represented by a feature vector that is a histogram over a set of basis elements. The set of basis elements is chosen based on domain knowledge and consists generally of vertices, edges, or small graphs. A given subgraph is transformed to a feature vector and the significance of the subgraph is computed by considering the significance of occurrence of the corresponding vector. The probability of occurrence of the vector in a random vector is computed based on the prior probability of the basis elements. This is then used to obtain a probability distribution on the support of the vector in a database of random vectors. The statistical significance of the vector/subgraph is then defined as the p-value of its observed support. We develop efficient methods for computing p-values and lower bounds. A simplified model is further proposed to improve the efficiency. We also address the problem of feature vector mining, a generalization of item- set mining where counts are associated with items and the goal is to find significant sub-vectors. We present an algorithm that explores closed frequent sub-vectors to find significant ones. Experimental results show that the proposed techniques are effective, efficient, and useful for ranking frequent subgraphs by their statistical significance.

Because images of neurons show interweaved processes from multiple cells, it is hard to determine which pixels belong to each cell, and consequently to analyze the images automatically. To manage these difficulties, we introduce probabilistic segmentation, in which each pixel is assigned a probability of belonging to each cell instead of being categorically assigned to one cell. We propose a randomized algorithm for probabilistic segmentation. The algorithm is based on repeated, intensity-weighted random walks on the image, and leads to improved segmentation quality. Analysis and mining techniques can utilize the more nuanced and complete information that the probabilistic segmentation yields about an image. Such techniques can then compute probabilistic values, which indicate the level of confidence that can be placed in them.

Top-k preference queries with multiple attributes are critical for decision-making applications. Previous research has concentrated on improving the computational efficiency mainly by using novel index structures and search strategies. Since current applications need to scale to terabytes of data and thousands of users, performance of such systems is strongly impacted by the amount of available memory. This paper proposes a scalable approach for memory-bounded top-k query processing.

We consider the general problem of tracking moving objects in sensor networks. The specific application we consider is that of tracking a chemical plume moving over a large infrastructure network. We present a distributed index structure DIST that stores and updates distributed summaries as the plume moves. We present algorithms for range queries on the history of the plume. DIST localizes information with respect to time and space using a hierarchy that scales with the plume size. The highlight of our work is an analytical model to predict the cost of query algorithms based on the query location, query size, and plume's spatio-temporal distribution. Using this model, our adaptive scheme chooses the optimal scheme. Experimental results show that DIST outperforms alternative techniques in query, update, and storage costs, and scales well with the number of plumes.

Online monitoring of data streams poses a challenge in many data-centric applications, such as telecommunications networks, traffic management, trend-related analysis, Web-click streams, intrusion detection, and sensor networks. Mining techniques employed in these applications have to be efficient in terms of space usage and per-item processing time while providing a high quality of answers to (1) aggregate monitoring queries, such as finding surprising levels of a data stream, detecting bursts, and to (2) similarity queries, such as detecting correlations and finding interesting patterns. The most important aspect of these tasks is their need for flexible query lengths, i.e., it is difficult to set the appropriate lengths a priori. For example, bursts of events can occur at variable temporal modalities from hours to days to weeks. Correlated trends can occur at various temporal scales. The system has to discover "interesting" behavior online and monitor over flexible window sizes. In this paper, we propose a multi-resolution indexing scheme, which handles variable length queries efficiently. We demonstrate the effectiveness of our framework over existing techniques through an extensive set of experiments.

Given a large collection of medical images of several conditions and treatments, how can we succinctly describe the characteristics of each setting? For example, given a large collection of retinal images from several different experimental conditions (normal, detached, reattached, etc.), how can data mining help biologists focus on important regions in the images or on the differences between different experimental conditions? If the images were text documents, we could find the main terms and concepts for each condition by existing IR methods (e.g., tf/idf and LSI). We propose something analogous, but for the much more challenging case of an image collection: We propose to automatically develop a visual vocabulary by breaking images into n /spl times/ n tiles and deriving key tiles ("ViVos") for each image and condition. We experiment with numerous domain-independent ways of extracting features from tiles (color histograms, textures, etc.), and several ways of choosing characteristic tiles (PCA, ICA). We perform experiments on two disparate biomedical datasets. The quantitative measure of success is classification accuracy: Our "ViVos" achieve high classification accuracy (up to 83 %for a nine-class problem on feline retinal images). More importantly, qualitatively, our "ViVos" do an excellent job as "visual vocabulary terms": they have biological meaning, as corroborated by domain experts; they help spot characteristic regions of images, exactly like text vocabulary terms do for documents; and they highlight the differences between pairs of images.

We consider the problem of finding similar patterns in a time sequence. Typical applications of this problem involve large databases consisting of long time sequences of different lengths. Current time sequence search techniques work well for queries of a prespecified length, but not for arbitrary length queries. We propose a novel indexing technique that works well for arbitrary length queries. The proposed technique stores index structures at different resolutions for a given data set. We prove that this index structure is superior to existing index structures that use a single resolution. We propose a range query and nearest neighbor query technique on this index structure and prove the optimality of our index structure for these search techniques. The experimental results show that our method is 4 to 20 times faster than the current techniques, including sequential scan, for range queries and 3 times faster than sequential scan and other techniques for nearest neighbor queries. Because of the need to store information at multiple resolution levels, the storage requirement of our method could potentially be large. In the second part, we show how the index information can be compressed with minimal information loss. According to our experimental results, even after compressing the size of the index to one fifth, the total cost of our method is 3 to 15 times less than the current techniques.

The problem of statistics and aggregate maintenance over data streams has gained popularity in recent years especially in telecommunications network monitoring, trend-related analysis, Web-click streams, stock tickers, and other time-variant data. The amount of data generated in such applications can become too large to store, or if stored too large to scan multiple times. We consider queries over data streams that are biased towards the more recent values. We develop a technique that summarizes a dynamic stream incrementally at multiple resolutions. This approximation can be used to answer point queries, range queries, and inner product queries. Moreover, the precision of answers can be changed adoptively by a client. Later, we extend the above technique to work in a distributed setting, specifically in a large network where a central site summarizes the stream and clients ask queries. We minimize the message overhead by deciding what and where to replicate by using an adaptive replication scheme. We maintain a hierarchy of approximations that change adoptively based on the query and update rates. We show experimentally that our technique performs better than existing techniques: up to 50 times better in terms of approximation quality, up to four orders of magnitude times better in response time, and up to five times better in terms of message complexity.

We consider the problem of joining massive datasets. We propose two techniques for minimizing disk I/O cost of join operations for both spatial and sequence data. Our techniques optimize the available buffer space using a global view of the datasets. We build a boolean matrix on the pages of the given datasets using a lower bounding distance predictor. The marked entries of this matrix represent candidate page pairs to be joined. Our first technique joins the marked pages iteratively. Our second technique clusters the marked entries using rectangular dense regions that have minimal perimeter and fit into buffer. These clusters are then ordered so that the total number of common pages between consecutive clusters is maximal. The clusters are then read from disk and joined. Our experimental results on various real datasets show that our techniques are 2 to 86 times faster than the competing techniques for spatial datasets, and 13 to 133 times faster than the competing techniques for sequence datasets.

We demonstrate an efficient algorithm for alignment of large genome strings. Our algorithm constructs a Boolean match table for a given query string and database string with the help of the MRS index structure. The size of the MRS index structure is approximately 1-2% of that of database. Each entry of the match table corresponds to a query/database substring pair. An entry in the match table is marked as True if the corresponding query substring and database substring potentially contain similar patterns. It is marked as False otherwise. The size of the match table is negligible compared to that of database. Once the match table is computed, we build hash tables on these strings. Once the hash table of a string is constructed the marked substrings of other string are read sequentially and exactly matching substrings of the prespecified size are found using this hash table. We call this technique MAP (match table based pruning). Experimental results show that MAP runs up to 97 times faster than BLAST.

We consider the problem of shift and scale invariant search for multi-attribute time sequences. Our work fills a void in the existing literature for time sequence similarity since the existing techniques do not consider the general symmetric formulation of the problem. We define a new distance function for mufti-attribute time sequences that is symmetric: the distance between two time sequences is defined to be the smallest Euclidean distance after scaling and shifting either one of the sequences to be as close to the other. We define two models for comparing mufti-attribute time sequences: in the first model, the scaling and shifting of the component sequences are dependent, and in the second model they are independent. We propose a novel index structure called CS-Index (cone slice) for shift and scale invariant comparison of time sequences.

We investigate the problem of searching similar multiattribute time sequences. Such sequences arise naturally in a number of medical, financial, video, weather forecast, and stock market databases where more than one attribute is of interest at a time instant. We first solve the simple case in which the distance is defined as the Euclidean distance. Later we extend it to shift and scale invariance. We formulate a new symmetric scale and shift invariant notion of distance for such sequences. We also propose a new index structure that transforms the data sequences and clusters them according to their shiftings and scalings. This clustering improves the efficiency considerably. According to our experiments with real and synthetic datasets, the index structure's performance is 5 to 45 times better than competing techniques, the exact speedup based on other optimizations such as caching and replication.

The performance of nearest neighbor (NN) queries degrades noticeably with increasing dimensionality of the data due to reduced selectivity of high-dimensional data and an increased number of seek operations during NN-query execution. If the NN-radii were known in advance, the disk accesses could be reordered such that seek operations are minimized. We therefore propose a new way of estimating the NN-radius based on the fractal dimensionality and sampling. It is applicable to any page-based index structure. We show that the estimation error is considerably lower than for previous approaches. In the second part of the paper, we present two applications of this technique. We show how the radius estimations can be used to transform k-NN queries into at most two range queries, and how it can be used to reduce the number of page reads during all-NN queries. In both cases, we observe significant speedups over traditional techniques for synthetic and real-world data.

Finding similar patterns in a time sequence is a well-studied problem. Most of the current techniques work well for queries of a prespecified length, but not for variable length queries. We propose a new indexing technique that works well for variable length queries. The central idea is to store index structures at different resolutions for a given dataset. The resolutions are based on wavelets. For a given query, a number of subqueries at different resolutions are generated. The ranges of the subqueries are progressively refined based on results from previous subqueries. Our experiments show that the total cost for our method is 4 to 20 times less than the current techniques including linear scan. Because of the need to store information at multiple resolution levels, the storage requirement of our method could potentially be large. In the second part of the paper we show how the index information can be compressed with minimal information loss. According to our experimental results, even after compressing the size of the index to one fifth, the total cost of our method is 3 to 15 times less than the current techniques.

A large number of index structures for high-dimensional data have been proposed previously. In order to tune and compare such index structures, it is vital to have efficient cost prediction techniques for these structures. Previous techniques either assume uniformity of the data or are not applicable to high-dimensional data. We propose the use of sampling to predict the number of accessed index pages during a query execution. Sampling is independent of the dimensionality and preserves clusters which is important for representing skewed data. We present a general model for estimating the index page layout using sampling and show how to compensate for errors. We then give an implementation of our model under restricted memory assumptions and show that it performs well even under these constraints. Errors are minimal and the overall prediction time is up to two orders of magnitude below the time for building and probing the full index without sampling. 1.

Databases are increasingly being used to store multi-media objects such as maps, images, audio and video. Storage and retrieval of these objects is accomplished using multi-dimensional index structures such as R*-trees and SS-trees. As dimensionality increases, query performance in these index structures degrades. This phenomenon, generally referred to as the dimensionality curse, can be circumvented by reducing the dimensionality of the data. Such a reduction is however accompanied by a loss of precision of query results. Current techniques such as QBIC use SVD transform-based dimensionality reduction to ensure high query precision. The drawback of this approach is that SVD is expensive to compute, and therefore not readily applicable to dynamic databases. In this paper, we propose novel techniques for performing SVD-based dimensionality reduction in dynamic databases. When the data distribution changes considerably so as to degrade query precision, we recompute the SVD transform and incorporate it in the existing index structure. For recomputing the SVD-transform, we propose a novel technique that uses aggregate data from the existing index rather than the entire data. This technique reduces the SVD-computation time without compromising query precision. We then explore efficient ways to incorporate the recomputed SVD-transform in the existing index structure without degrading subsequent query response times. These techniques reduce the computation time by a factor of 20 in experiments on color and texture image vectors. The error due to approximate computation of SVD is less than 10%.

Non-uniformity in data extents is a general characteristic of spatial data. Indexing such non-uniform data using conventional spatial index structures such as R/sup */-trees is inefficient for two reasons: (1) the non-uniformity increases the likelihood of overlapping index entries, and (2) clustering of non-uniform data is likely to index more dead space than clustering of uniform data. To reduce the impact of these anomalies, we propose a new scheme that promotes data objects to higher levels in tree-based index structures. We examine two criteria for promotion of data objects and evaluate their relative merits using an R*-tree. In experiments on cartographic data, we observe that our promotion criteria yield up to 45% improvement in query performance for an R*-tree.

We present incremental view maintenance algorithms for a data warehouse derived from multiple distributed autonomous data sources. We begin with a detailed framework for analyzing view maintenance algorithms for multiple data sources with concurrent updates. Earlier approaches for view maintenance in the presence of concurrent updates typically require two types of messages: one to compute the view change due to the initial update and the other to compensate the view change due to interfering concurrent updates. The algorithms developed in this paper instead perform the compensation locally by using the information that is already available at the data warehouse. The first algorithm, termed SWEEP, ensures complete consistency of the view at the data warehouse in the presence of concurrent updates. Previous algorithms for incremental view maintenance either required a quiescent state at the data warehouse or required an exponential number of messages in terms of the data sources. In contrast, this algorithm does not require that the data warehouse be in a quiescent state for incorporating the new views and also the message complexity is linear in the number of data sources. The second algorithm, termed Nested SWEEP, attempts to compute a composite view change for multiple updates that occur concurrently while maintaining strong consistency.

The Alexandria project has been initiated to build a digital library for map and satellite images.Designed for content-based retrieval, the relevant information in each image is encoded in the form of a multi-dimensional feature vector.Though representing images by feature vectors ~eatly facilitates user queries, indexing these vectors degrades performance when the number of dimensions is large.We consider 2 popular techniques (DFT and SVD) to reduce the dimension of feature vectors, and study their retrieval performance with respect to recall and precision.We End that though SVD generally out-performs DFT, DFT compares favorably in a limited range suitable for browsing large image databases.

The semantics of objects and transactions in database systems are investigated. User-defined predicates called consistency assertions are used to specify user programs. Three new correctness criteria are proposed. The first correctness criterion consistency is based solely on the users' specifications and admit nonserializable executions that are acceptable to the users. Integrity constraints of the database are maintained through consistency assertions. The second correctness criterion orderability is a generalization of view serializability and represents a weak notion of equivalence to a serial schedule. Finally, the third correctness criterion strong order-ability is introduced as a generalization of conflict serializability. Unlike consistency, the notions of orderability allow users to operate an isolation as maintenance of the integrity constrainst now becomes the responsibility of the database system.