Interaction graphs are ubiquitous in many fields such as bioinformatics, sociology and physical sciences. There have been many studies in the literature targeted at studying and mining these graphs. However, almost all of them have studied these graphs from a static point of view. The study of the evolution of these graphs over time can provide tremendous insight on the behavior of entities, communities and the flow of information among them. In this work, we present an event-based characterization of critical behavioral patterns for temporally varying interaction graphs. We use non-overlapping snapshots of interaction graphs and develop a framework for capturing and identifying interesting events from them. We use these events to characterize complex behavioral patterns of individuals and communities over time. We show how semantic information can be incorporated to reason about community-behavior events. We also demonstrate the application of behavioral patterns for the purposes of modeling evolution, link prediction and influence maximization. Finally, we present a diffusion model for evolving networks, based on our framework.

We discover communities from social network data, and analyze the community evolution. These communities are inherent characteristics of human interaction in online social networks, as well as paper citation networks. Also, communities may evolve over time, due to changes to individuals’ roles and social status in the network as well as changes to individuals ’ research interests. We present an innovative algorithm that deviates from the traditional two-step approach to analyze community evolutions. In the traditional approach, communities are first detected for each time slice, and then compared to determine correspondences. We argue that this approach is inappropriate in applications with noisy data. In this paper, we propose FacetNet for analyzing communities and their evolutions through a robust unified

A multi-mode network typically consists of multiple heterogeneous social actors among which various types of interactions could occur. Identifying communities in a multi-mode network can help understand the structural properties of the network, address the data shortage and unbalanced problems, and assist tasks like targeted marketing and finding influential actors within or between groups. In general, a network and the membership of groups often evolve gradually. In a dynamic multi-mode network, both actor membership and interactions can evolve, which poses a challenging problem of identifying community evolution. In this work, we try to address this issue by employing the temporal information to analyze a multi-mode network. A spectral framework and its scalability issue are carefully studied. Experiments on both synthetic data and real-world large scale networks demonstrate the efficacy of our algorithm and suggest its generality in solving problems with complex relationships.

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Given an author-conference network that evolves over time, which are the conferences that a given author is most closely related with, and how do they change over time? Large time-evolving bipartite graphs appear in many settings, such as social networks, co-citations, market-basket analysis, and collaborative filtering. Our goal is to monitor (i) the centrality of an individual node (e.g., who are the most important authors?); and (ii) the proximity of two nodes or sets of nodes (e.g., who are the most important authors with respect to a particular conference?) Moreover, we want to do this efficiently and incrementally, and to provide “any-time ” answers. We propose pTrack and cTrack, which are based on random walk with restart, and use powerful matrix tools. Experiments on real data show that our methods are effective and efficient: the mining results agree with intuition; and we achieve up to 15∼176 times speed-up, without any quality loss. 1

Clustering is an important data mining task for exploration and visualization of different data types like news stories, scientific publications, weblogs, etc. Due to the evolving nature of these data, evolutionary clustering, also known as dynamic clustering, has recently emerged to cope with the challenges of mining temporally smooth clusters over time. A good evolutionary clustering algorithm should be able to fit the data well at each time epoch, and at the same time results in a smooth cluster evolution that provides the data analyst with a coherent and easily interpretable model. In this paper we introduce the temporal Dirichlet process mixture model (TDPM) as a framework for evolutionary clustering. TDPM is a generalization of the DPM framework for clustering that automatically grows the number of clusters with the data. In our framework, the data is divided into epochs; all data points inside the same epoch are assumed to be fully exchangeable, whereas the temporal order is maintained across epochs. Moreover, The number of clusters in each epoch is unbounded: the clusters can retain, die out or emerge over time, and the actual parameterization of each cluster can also evolve over time in a Markovian fashion. We give a detailed and intuitive construction of this framework using the recurrent Chinese restaurant process (RCRP) metaphor, as well as a Gibbs sampling algorithm to carry out posterior inference in order to determine the optimal cluster evolution. We demonstrate our model over simulated data by using it to build an infinite dynamic mixture of Gaussian factors, and over real dataset by using it to build a simple non-parametric dynamic clustering-topic model and apply it to analyze the NIPS12 document collection.

Low-rank approximations of the adjacency matrix of a graph are essential in finding patterns (such as communities) and detecting anomalies. Additionally, it is desirable to track the low-rank structure as the graph evolves over time, efficiently and within limited storage. Real graphs typically have thousands or millions of nodes, but are usually very sparse. However, standard decompositions such as SVD do not preserve sparsity. This has led to the development of methods such as CUR and CMD, which seek a nonorthogonal basis by sampling the columns and/or rows of the sparse matrix. However, these approaches will typically produce overcomplete bases, which wastes both space and time. In this paper we propose the family of Colibri methods to deal with these challenges. Our version for static graphs, Colibri-S, iteratively finds a nonredundant basis and we prove that it has no loss of accuracy compared to the best competitors (CUR and CMD), while achieving significant savings in space and time: on real data, Colibri-S requires much less space and is orders of magnitude faster (in proportion to the square of the number of non-redundant columns). Additionally, we propose an efficient update algorithm for dynamic, time-evolving graphs, Colibri-D. Our evaluation on a large, real network traffic dataset shows that Colibri-D is over 100 times faster than the best published competitor (CMD).

Recently, dynamic networks are attracting increasing interest due to their high potential in capturing natural and social phenomena over time. Discovery of evolutionary communities in dynamic networks has become a critical task. The previous evolutionary clustering methods usually adopt the temporal smoothness framework, which has a desirable feature of controlling the balance between temporal noise and true concept drift of communities. They, however, have some major drawbacks: (1) assuming only a fixed number of communities over time; and (2) not allowing arbitrary start/stop of community over time. The forming of new communities and dissolving of existing communities are very common phenomena in real dynamic networks. In this paper, we propose a new particle-and-density based evolutionary clustering method that efficiently discovers a variable number of communities of arbitrary forming and dissolving. We first model a dynamic network as a collection of lots of particles called nano-communities, and a community as a densely connected subset of particles, called a quasi l-clique-by-clique (shortly, l-KK). Each particle contains a small amount of information about the evolution of data or patterns, and the quasi l-KK s inherent in a given dynamic network provide us with guidance on how to find a variable number of communities of arbitrary forming and dissolving. We propose a density-based clustering method that efficiently finds temporally smoothed local clusters of high quality by using a cost embedding technique and optimal modularity. We also propose a mapping method based on information theory that makes sequences of smoothed local clusters as close as possible to data-inherent quasi l-KKs. The result of the mapping method allows us to easily identify the stage of each community among the three stages: evolving, forming, and dissolving. Experimental studies, by using various data sets, demonstrate that our method improves the clustering accuracy, and at the same time, the time performance by an order of magnitude compared with the current state-of-the art method.

Multiple view data, which have multiple representations from different feature spaces or graph spaces, arise in various data mining applications such as information retrieval, bioinformatics and social network analysis. Since different representations could have very different statistical properties, how to learn a consensus pattern from multiple representations is a challenging problem. In this paper, we propose a general model for multiple view unsupervised learning. The proposed model introduces the concept of mapping function to make the different patterns from different pattern spaces comparable and hence an optimal pattern can be learned from the multiple patterns of multiple representations. Under this model, we formulate two specific models for

Abstract. Spectral clustering algorithm has been shown to be more effective in finding clusters than most traditional algorithms. However, spectral clustering suffers from a scalability problem in both memory use and computational time when a dataset size is large. To perform clustering on large datasets, we propose to parallelize both memory use and computation on distributed computers. Through an empirical study on a large document dataset of 193, 844 data instances and a large photo dataset of 637, 137, we demonstrate that our parallel algorithm can effectively alleviate the scalability problem. Key words: Parallel spectral clustering, distributed computing 1