The increasingly connected world has catalyzed the fusion of networks from different domains, which facilitates the emergence of a new network model-multi-layered networks. Examples of such kind of network systems include critical infrastructure networks, biological systems, organization-level collaborations, cross-platform e-commerce, and so forth. One crucial structure that distances multi-layered network from other network models is its cross-layer dependency, which describes the associations between the nodes from different layers. Needless to say, the cross-layer dependency in the network plays an essential role in many data mining applications like system robustness analysis and complex network control. However, it remains a daunting task to know the exact dependency relationships due to noise, limited accessibility, and so forth. In this article, we tackle the cross-layer dependency inference problem by modeling it as a collective collaborative filtering problem. Based on this idea, we propose an effective algorithm Fascinate that can reveal unobserved dependencies with linear complexity. Moreover, we derive Fascinate-ZERO, an online variant of Fascinate that can respond to a newly added node timely by checking its neighborhood dependencies. We perform extensive evaluations on real datasets to substantiate the superiority of our proposed approaches.

Multi-view graph clustering aims to enhance clustering performance by integrating heterogeneous information collected in different domains. Each domain provides a different view of the data instances. Leveraging cross-domain information has been demonstrated an effective way to achieve better clustering results. Despite the previous success, existing multi-view graph clustering methods usually assume that different views are available for the set of instances. Thus instances in different domains can be treated as having strict relationship. In many real-life applications, however, data instances in one domain may correspond to multiple instances in another domain. Moreover, relationships between instances in different domains may be associated with weights based on prior (partial) knowledge. In this paper, we propose a flexible and robust framework, CGC (Co-regularized Graph Clustering), based on non-negative matrix factorization (NMF), to tackle these challenges. CGC has several advantages over the existing methods. First, it supports cross-domain instance relationship. Second, it incorporates weight on cross-domain relationship. Third, it allows partial cross-domain mapping so that graphs in different domains may have different sizes. Finally, it provides users with the extent to which the cross-domain instance relationship violates the in-domain clustering structure, and thus enables users to re-evaluate the consistency of the relationship. We develop an efficient optimization method that guarantees to find the global optimal solution with a given confidence requirement. The proposed method can automatically identify noisy domains and assign smaller weights to them. This helps to obtain optimal graph partition for the focused domain. Extensive experimental results on UCI benchmark data sets, newsgroup data sets and biological interaction networks demonstrate the effectiveness of our approach.

Bayesian models are generally computed with Markov Chain Monte Carlo (MCMC) methods. The main disadvantage about MCMC methods is the large number of iterations they need to sample the posterior distributions of model parameters, especially for large data sets. On the other hand, variable selection remains a challenging problem due to its combinatorial search space, where Bayesian models are a promising solution. In this work, we study how to accelerate Bayesian model computation for variable selection in linear regression. We propose a fast Gibbs sampler algorithm, a widely used MCMC method, that incorporates several optimizations. We use non-informative and conjugate prior distributions on several model parameters, which enable data set summarization in one pass exploiting an augmented set of sufficient statistics. Thereafter the algorithm can iterate in main memory. Sufficient statistics are indexed with a sparse binary vector to efficiently compute matrix projections based on selected variables. Discovered variable subsets probabilities, selecting and discarding each variable, are stored on a hash table for fast retrieval in future iterations. We study how to integrate our algorithm into a database management system (DBMS), exploiting aggregate User-Defined Functions for parallel data summarization and stored procedures to manipulate matrices with arrays. An experimental evaluation with real data sets evaluates accuracy and time performance, comparing our DBMS-based algorithm, with the R package. Our algorithm is shown to produce accurate results, scale linearly on data set size and run orders of magnitude faster than the R package.

A key task in analyzing social networks and other complex networks is role analysis: describing and categorizing nodes according to how they interact with other nodes. Two nodes have the same role if they interact with sets of neighbors. The most fundamental role equivalence is automorphic equivalence. Unfortunately, the fastest algorithms known for graph automorphism are nonpolynomial. Moreover, since exact equivalence is rare, a more meaningful task is measuring the role between any two nodes. This task is closely related to the structural or link-based similarity problem that SimRank addresses. However, SimRank and other existing similarity measures are not sufficient because they do not guarantee to recognize automorphically or structurally equivalent nodes. This paper makes two contributions. First, we present and justify several axiomatic properties necessary for a role similarity measure or metric. Second, we present RoleSim, a new similarity metric which satisfies these axioms and which can be computed with a simple iterative algorithm. We rigorously prove that RoleSim satisfies all these axiomatic properties. We also introduce Iceberg RoleSim, a scalable algorithm which discovers all pairs with RoleSim scores above a user-defined threshold θ. We demonstrate the interpretative power of RoleSim on both both synthetic and real datasets.

Along with increasing popularity of social websites, online users rely more on the trustworthiness information to make decisions, extract and filter information, and tag and build connections with other users. However, such social network data often suffer from severe data sparsity and are not able to provide users with enough information. Therefore, trust prediction has emerged as an important topic in social network research. Traditional approaches are primarily based on exploring trust graph topology itself. However, research in sociology and our life experience suggest that people who are in the same social circle often exhibit similar behaviors and tastes. To take advantage of the ancillary information for trust prediction, the challenge then becomes what to transfer and how to transfer. In this article, we address this problem by aggregating heterogeneous social networks and propose a novel joint social networks mining (JSNM) method. Our new joint learning model explores the user-group-level similarity between correlated graphs and simultaneously learns the individual graph structure; therefore, the shared structures and patterns from multiple social networks can be utilized to enhance the prediction tasks. As a result, we not only improve the trust prediction in the target graph but also facilitate other information retrieval tasks in the auxiliary graphs. To optimize the proposed objective function, we use the alternative technique to break down the objective function into several manageable subproblems. We further introduce the auxiliary function to solve the optimization problems with rigorously proved convergence. The extensive experiments have been conducted on both synthetic and real- world data. All empirical results demonstrate the effectiveness of our method.

Most time series data mining algorithms use similarity search as a core subroutine, and thus the time taken for similarity search is the bottleneck for virtually all time series data mining algorithms, including classification, clustering, motif discovery, anomaly detection, and so on. The difficulty of scaling a search to large datasets explains to a great extent why most academic work on time series data mining has plateaued at considering a few millions of time series objects, while much of industry and science sits on billions of time series objects waiting to be explored. In this work we show that by using a combination of four novel ideas we can search and mine massive time series for the first time. We demonstrate the following unintuitive fact: in large datasets we can exactly search under Dynamic Time Warping (DTW) much more quickly than the current state-of-the-art search algorithms. We demonstrate our work on the largest set of time series experiments ever attempted. In particular, the largest dataset we consider is larger than the combined size of all of the time series datasets considered in all data mining papers ever published. We explain how our ideas allow us to solve higher-level time series data mining problems such as motif discovery and clustering at scales that would otherwise be untenable. Moreover, we show how our ideas allow us to efficiently support the uniform scaling distance measure, a measure whose utility seems to be underappreciated, but which we demonstrate here. In addition to mining massive datasets with up to one trillion datapoints, we will show that our ideas also have implications for real-time monitoring of data streams, allowing us to handle much faster arrival rates and/or use cheaper and lower powered devices than are currently possible.

We consider the problem of learning incoherent sparse and low-rank patterns from multiple tasks. Our approach is based on a linear multi-task learning formulation, in which the sparse and low-rank patterns are induced by a cardinality regularization term and a low-rank constraint, respectively. This formulation is non-convex; we convert it into its convex surrogate, which can be routinely solved via semidefinite programming for small-size problems. We propose to employ the general projected gradient scheme to efficiently solve such a convex surrogate; however, in the optimization formulation, the objective function is non-differentiable and the feasible domain is non-trivial. We present the procedures for computing the projected gradient and ensuring the global convergence of the projected gradient scheme. The computation of projected gradient involves a constrained optimization problem; we show that the optimal solution to such a problem can be obtained via solving an unconstrained optimization subproblem and an Euclidean projection subproblem. We also present two projected gradient algorithms and analyze their rates of convergence in details. In addition, we illustrate the use of the presented projected gradient algorithms for the proposed multi-task learning formulation using the least squares loss. Experimental results on a collection of real-world data sets demonstrate the effectiveness of the proposed multi-task learning formulation and the efficiency of the proposed projected gradient algorithms.

In this article, we propose a methodology for identifying predictive physiological patterns in the absence of prior knowledge. We use the principle of conservation to identify activity that consistently precedes an outcome in patients, and describe a two-stage process that allows us to efficiently search for such patterns in large datasets. This involves first transforming continuous physiological signals from patients into symbolic sequences, and then searching for patterns in these reduced representations that are strongly associated with an outcome.Our strategy of identifying conserved activity that is unlikely to have occurred purely by chance in symbolic data is analogous to the discovery of regulatory motifs in genomic datasets. We build upon existing work in this area, generalizing the notion of a regulatory motif and enhancing current techniques to operate robustly on non-genomic data. We also address two significant considerations associated with motif discovery in general: computational efficiency and robustness in the presence of degeneracy and noise. To deal with these issues, we introduce the concept of active regions and new subset-based techniques such as a two-layer Gibbs sampling algorithm. These extensions allow for a framework for information inference, where precursors are identified as approximately conserved activity of arbitrary complexity preceding multiple occurrences of an event.We evaluated our solution on a population of patients who experienced sudden cardiac death and attempted to discover electrocardiographic activity that may be associated with the endpoint of death. To assess the predictive patterns discovered, we compared likelihood scores for motifs in the sudden death population against control populations of normal individuals and those with non-fatal supraventricular arrhythmias. Our results suggest that predictive motif discovery may be able to identify clinically relevant information even in the absence of significant prior knowledge.

BACKGROUND: We recently described "Author-ity," a model for estimating the probability that two articles in MEDLINE, sharing the same author name, were written by the same individual. Features include shared title words, journal name, coauthors, medical subject headings, language, affiliations, and author name features (middle initial, suffix, and prevalence in MEDLINE). Here we test the hypothesis that the Author-ity model will suffice to disambiguate author names for the vast majority of articles in MEDLINE. METHODS: Enhancements include: (a) incorporating first names and their variants, email addresses, and correlations between specific last names and affiliation words; (b) new methods of generating large unbiased training sets; (c) new methods for estimating the prior probability; (d) a weighted least squares algorithm for correcting transitivity violations; and (e) a maximum likelihood based agglomerative algorithm for computing clusters of articles that represent inferred author-individuals. RESULTS: Pairwise comparisons were computed for all author names on all 15.3 million articles in MEDLINE (2006 baseline), that share last name and first initial, to create Author-ity 2006, a database that has each name on each article assigned to one of 6.7 million inferred author-individual clusters. Recall is estimated at ~98.8%. Lumping (putting two different individuals into the same cluster) affects ~0.5% of clusters, whereas splitting (assigning articles written by the same individual to >1 cluster) affects ~2% of articles. IMPACT: The Author-ity model can be applied generally to other bibliographic databases. Author name disambiguation allows information retrieval and data integration to become person-centered, not just document-centered, setting the stage for new data mining and social network tools that will facilitate the analysis of scholarly publishing and collaboration behavior. AVAILABILITY: The Author-ity 2006 database is available for nonprofit academic research, and can be freely queried via http://arrowsmith.psych.uic.edu.

Gene expression in a developing embryo occurs in particular cells (spatial patterns) in a time-specific manner (temporal patterns), which leads to the differentiation of cell fates. Images of a Drosophila melanogaster embryo at a given developmental stage, showing a particular gene expression pattern revealed by a gene-specific probe, can be compared for spatial overlaps. The comparison is fundamentally important to formulating and testing gene interaction hypotheses. Expression pattern comparison is most biologically meaningful when images from a similar time point (developmental stage) are compared. In this paper, we present LdaPath, a novel formulation of Linear Discriminant Analysis (LDA) for automatic developmental stage range classification. It employs multivariate linear regression with the L(1)-norm penalty controlled by a regularization parameter for feature extraction and visualization. LdaPath computes an entire solution path for all values of regularization parameter with essentially the same computational cost as fitting one LDA model. Thus, it facilitates efficient model selection. It is based on the equivalence relationship between LDA and the least squares method for multi-class classifications. This equivalence relationship is established under a mild condition, which we show empirically to hold for many high-dimensional datasets, such as expression pattern images. Our experiments on a collection of 2705 expression pattern images show the effectiveness of the proposed algorithm. Results also show that the LDA model resulting from LdaPath is sparse, and irrelevant features may be removed. Thus, LdaPath provides a general framework for simultaneous feature selection and feature extraction.