To understand the structural dynamics of a large-scale social, biological or technological network, it may be useful to discover behavioral roles representing the main connectivity patterns present over time. In this paper, we propose a scalable non-parametric approach to automatically learn the structural dynamics of the network and individual nodes. Roles may represent structural or behavioral patterns such as the center of a star, peripheral nodes, or bridge nodes that connect different communities. Our novel approach learns the appropriate structural role dynamics for any arbitrary network and tracks the changes over time. In particular, we uncover the specific global network dynamics and the local node dynamics of a technological, communication, and social network. We identify interesting node and network patterns such as stationary and non-stationary roles, spikes steps in role-memberships (perhaps indicating anomalies), increasing decreasing role trends, among many others. Our results indicate that the nodes in each of these networks have distinct connectivity patterns that are non-stationary and evolve considerably over time. Overall, the experiments demonstrate the effectiveness of our approach for fast mining and tracking of the dynamics in large networks. Furthermore, the dynamic structural representation provides a basis for building more sophisticated models and tools that are fast for exploring large dynamic networks.
While there is a lot of work on dynamic graph patterns @cite_7 @cite_3 @cite_9 @cite_17 @cite_8 , temporal link prediction @cite_18 , anomaly detection @cite_4 , dynamic communities @cite_19 @cite_0 @cite_15 , and many others @cite_23 @cite_16 @cite_14 . No one has yet to propose a scalable role-based analysis framework for large time-varying networks. The closest work is that of @cite_2 @cite_24 where they develop the dMMSB model (based on a completely different process) for small graphs. Their model is capable of handling 1,000 nodes in approximately 1 day while our approach is linear in the number of edges and capable of handling 1,000 nodes in only a few minutes (practical for large real-world networks).
@cite_18 @cite_14 @cite_4 @cite_7 @cite_8 @cite_9 @cite_3 @cite_0 @cite_19 @cite_24 @cite_23 @cite_2 @cite_15 @cite_16 @cite_17
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The data in many disciplines such as social networks, Web analysis, etc. is link-based, and the link structure can be exploited for many different data mining tasks. In this article, we consider the problem of temporal link prediction: Given link data for times 1 through T, can we predict the links at time T + 1? If our data has underlying periodic structure, can we predict out even further in time, i.e., links at time T + 2, T + 3, etc.? In this article, we consider bipartite graphs that evolve over time and consider matrix- and tensor-based methods for predicting future links. We present a weight-based method for collapsing multiyear data into a single matrix. We show how the well-known Katz method for link prediction can be extended to bipartite graphs and, moreover, approximated in a scalable way using a truncated singular value decomposition. Using a CANDECOMP PARAFAC tensor decomposition of the data, we illustrate the usefulness of exploiting the natural three-dimensional structure of temporal link data. Through several numerical experiments, we demonstrate that both matrix- and tensor-based techniques are effective for temporal link prediction despite the inherent difficulty of the problem. Additionally, we show that tensor-based techniques are particularly effective for temporal data with varying periodic patterns. Event-based network data consists of sets of events over time, each of which may involve multiple entities. Examples include email traffic, telephone calls, and research publications (interpreted as co-authorship events). Traditional network analysis techniques, such as social network models, often aggregate the relational information from each event into a single static network. In contrast, in this paper we focus on the temporal nature of such data. In particular, we look at the problems of temporal link prediction and node ranking, and describe new methods that illustrate opportunities for data mining and machine learning techniques in this context. Experimental results are discussed for a large set of co-authorship events measured over multiple years, and a large corporate email data set spanning 21 months. We address the problem of detecting characteristic patterns in communication networks. We introduce a scalable approach based on set-system discrepancy. By implicitly labeling each network edge with the sequence of times in which its two endpoints communicate, we view an entire communication network as a set-system. This view allows us to use combinatorial discrepancy as a mechanism to "observe" system behavior at different time scales. We illustrate our approach, called Discrepancy-based Novelty Detector (DND), on networks obtained from emails, blue tooth connections, IP traffic, and tweets. DND has almost linear runtime complexity and linear storage complexity in the number of communications. Examples of novel discrepancies that it detects are (i) asynchronous communications and (ii) disagreements in the firing rates of nodes and edges relative to the communication network as a whole. How do blogs produce posts? What local, underlying mechanisms lead to the bursty temporal behaviors observed in blog networks? Earlier work analyzed network patterns of blogs and found that blog behavior is bursty and often follows power laws in both topological and temporal characteristics. However, no intuitive and realistic model has yet been introduced, that can lead to such patterns. This is exactly the focus of this work. We propose a generative model that uses simple and intuitive principles for each individual blog, and yet it is able to produce the temporal characteristics of the blogosphere together with global topological network patterns, like power-laws for degree distributions, for inter-posting times, and several more. Our model ZC uses a novel ‘zero-crossing’ approach based on a random walk, combined with other powerful ideas like exploration and exploitation. This makes it the first model to simultaneously model the topology and temporal dynamics of the blogosphere. We validate our model with experiments on a large collection of 45,000 blogs and 2.2 million posts. How can we find communities in dynamic networks of socialinteractions, such as who calls whom, who emails whom, or who sells to whom? How can we spot discontinuity time-points in such streams of graphs, in an on-line, any-time fashion? We propose GraphScope, that addresses both problems, using information theoretic principles. Contrary to the majority of earlier methods, it needs no user-defined parameters. Moreover, it is designed to operate on large graphs, in a streaming fashion. We demonstrate the efficiency and effectiveness of our GraphScope on real datasets from several diverse domains. In all cases it produces meaningful time-evolving patterns that agree with human intuition. We present an analysis of a person-to-person recommendation network, consisting of 4 million people who made 16 million recommendations on half a million products. We observe the propagation of recommendations and the cascade sizes, which we explain by a simple stochastic model. We analyze how user behavior varies within user communities defined by a recommendation network. Product purchases follow a ‘long tail’ where a significant share of purchases belongs to rarely sold items. We establish how the recommendation network grows over time and how effective it is from the viewpoint of the sender and receiver of the recommendations. While on average recommendations are not very effective at inducing purchases and do not spread very far, we present a model that successfully identifies communities, product, and pricing categories for which viral marketing seems to be very effective. 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. 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 process. This novel framework will discover communities and capture their evolution with temporal smoothness given by historic community structures. Our approach relies on formulating the problem in terms of maximum a posteriori (MAP) estimation, where the community structure is estimated both by the observed networked data and by the prior distribution given by historic community structures. Then we develop an iterative algorithm, with proven low time complexity, which is guaranteed to converge to an optimal solution. We perform extensive experimental studies, on both synthetic datasets and real datasets, to demonstrate that our method discovers meaningful communities and provides additional insights not directly obtainable from traditional methods. In a dynamic social or biological environment, the interactions between the actors can undergo large and systematic changes. In this paper we propose a model-based approach to analyze what we will refer to as the dynamic tomography of such time-evolving networks. Our approach offers an intuitive but powerful tool to infer the semantic underpinnings of each actor, such as its social roles or biological functions, underlying the observed network topologies. Our model builds on earlier work on a mixed membership stochastic blockmodel for static networks, and the state-space model for tracking object trajectory. It overcomes a major limitation of many current network inference techniques, which assume that each actor plays a unique and invariant role that accounts for all its interactions with other actors; instead, our method models the role of each actor as a time-evolving mixed membership vector that allows actors to behave differently over time and carry out different roles functions when interacting with different peers, which is closer to reality. We present an efficient algorithm for approximate inference and learning using our model; and we applied our model to analyze a social network between monks (i.e., the Sampson's network), a dynamic email communication network between the Enron employees, and a rewiring gene interaction network of fruit fly collected during its full life cycle. In all cases, our model reveals interesting patterns of the dynamic roles of the actors. Online content exhibits rich temporal dynamics, and diverse realtime user generated content further intensifies this process. However, temporal patterns by which online content grows and fades over time, and by which different pieces of content compete for attention remain largely unexplored. We study temporal patterns associated with online content and how the content's popularity grows and fades over time. The attention that content receives on the Web varies depending on many factors and occurs on very different time scales and at different resolutions. In order to uncover the temporal dynamics of online content we formulate a time series clustering problem using a similarity metric that is invariant to scaling and shifting. We develop the K-Spectral Centroid (K-SC) clustering algorithm that effectively finds cluster centroids with our similarity measure. By applying an adaptive wavelet-based incremental approach to clustering, we scale K-SC to large data sets. We demonstrate our approach on two massive datasets: a set of 580 million Tweets, and a set of 170 million blog posts and news media articles. We find that K-SC outperforms the K-means clustering algorithm in finding distinct shapes of time series. Our analysis shows that there are six main temporal shapes of attention of online content. We also present a simple model that reliably predicts the shape of attention by using information about only a small number of participants. Our analyses offer insight into common temporal patterns of the content on theWeb and broaden the understanding of the dynamics of human attention. In a dynamic social or biological environment, interactions between the underlying actors can undergo large and systematic changes. Each actor can assume multiple roles and their degrees of affiliation to these roles can also exhibit rich temporal phenomena. We propose a state space mixed membership stochastic blockmodel which can track across time the evolving roles of the actors. We also derive an efficient variational inference procedure for our model, and apply it to the Enron email networks, and rewiring gene regulatory networks of yeast. In both cases, our model reveals interesting dynamical roles of the actors. Real-world social networks from a variety of domains can naturally be modelled as dynamic graphs. However, approaches to detecting communities have largely focused on identifying communities in static graphs. Recently, researchers have begun to consider the problem of tracking the evolution of groups of users in dynamic scenarios. Here we describe a model for tracking the progress of communities over time in a dynamic network, where each community is characterised by a series of significant evolutionary events. This model is used to motivate a community-matching strategy for efficiently identifying and tracking dynamic communities. Evaluations on synthetic graphs containing embedded events demonstrate that this strategy can successfully track communities over time in volatile networks. In addition, we describe experiments exploring the dynamic communities detected in a real mobile operator network containing millions of users. Social interactions are conduits for various processes spreading through a population, from rumors and opinions to behaviors and diseases. In the context of the spread of a disease or undesirable behavior, it is important to identify blockers: individuals that are most effective in stopping or slowing down the spread of a process through the population. This problem has so far resisted systematic algorithmic solutions. In an effort to formulate practical solutions, in this paper we ask: Are there structural network measures that are indicative of the best blockers in dynamic social networks? Our contribution is two-fold. First, we extend standard structural network measures to dynamic networks. Second, we compare the blocking ability of individuals in the order of ranking by the new dynamic measures. We found that overall, simple ranking according to a node's static degree, or the dynamic version of a node's degree, performed consistently well. Surprisingly the dynamic clustering coefficient seems to be a good indicator, while its static version performs worse than the random ranking. This provides simple practical and locally computable algorithms for identifying key blockers in a network. In this paper, we introduce SPIRIT (Streaming Pattern dIscoveRy in multIple Time-series). Given n numerical data streams, all of whose values we observe at each time tick t, SPIRIT can incrementally find correlations and hidden variables, which summarise the key trends in the entire stream collection. It can do this quickly, with no buffering of stream values and without comparing pairs of streams. Moreover, it is any-time, single pass, and it dynamically detects changes. The discovered trends can also be used to immediately spot potential anomalies, to do efficient forecasting and, more generally, to dramatically simplify further data processing. Our experimental evaluation and case studies show that SPIRIT can incrementally capture correlations and discover trends, efficiently and effectively.