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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Given a large time-evolving graph, how can we model and characterize the temporal behaviors of individual nodes (and network states)? How can we model the behavioral transition patterns of nodes? We propose a temporal behavior model that captures the "roles" of nodes in the graph and how they evolve over time. The proposed dynamic behavioral mixed-membership model (DBMM) is scalable, fully automatic (no user-defined parameters), non-parametric data-driven (no specific functional form or parameterization), interpretable (identifies explainable patterns), and flexible (applicable to dynamic and streaming networks). Moreover, the interpretable behavioral roles are generalizable and computationally efficient. We applied our model for (a) identifying patterns and trends of nodes and network states based on the temporal behavior, (b) predicting future structural changes, and (c) detecting unusual temporal behavior transitions. The experiments demonstrate the scalability, flexibility, and effectiveness of our model for identifying interesting patterns, detecting unusual structural transitions, and predicting the future structural changes of the network and individual nodes. We explore scalable and accurate dynamic pattern detection methods in graph-based data sets. We apply our proposed Dynamic Subset Scan method to the task of detecting, tracking, and source-tracing contaminant plumes spreading through a water distribution system equipped with noisy, binary sensors. While static patterns affect the same subset of data over a period of time, dynamic patterns may affect different subsets of the data at each time step. These dynamic patterns require a new approach to define and optimize penalized likelihood ratio statistics in the subset scan framework, as well as new computational techniques that scale to large, real-world networks. To address the first concern, we develop new subset scan methods that allow the detected subset of nodes to change over time, while incorporating temporal consistency constraints to reward patterns that do not dramatically change between adjacent time steps. Second, our Additive Graph Scan algorithm allows our novel scan statistic to process small graphs (500 nodes) in 4.1 seconds on average while maintaining an approximation ratio over 99 compared to an exact optimization method, and to scale to large graphs with over 12,000 nodes in 30 minutes on average. Evaluation results across multiple detection, tracking, and source-tracing tasks demonstrate substantial performance gains achieved by the Dynamic Subset Scan approach. Learning the network structure of a large graph is computationally demanding, and dynamically monitoring the network over time for any changes in structure threatens to be more challenging still. This paper presents a two-stage method for anomaly detection in dynamic graphs: the first stage uses simple, conjugate Bayesian models for discrete time counting processes to track the pairwise links of all nodes in the graph to assess normality of behavior; the second stage applies standard network inference tools on a greatly reduced subset of potentially anomalous nodes. The utility of the method is demonstrated on simulated and real data sets. How can we describe a large, dynamic graph over time? Is it random? If not, what are the most apparent deviations from randomness -- a dense block of actors that persists over time, or perhaps a star with many satellite nodes that appears with some fixed periodicity? In practice, these deviations indicate patterns -- for example, botnet attackers forming a bipartite core with their victims over the duration of an attack, family members bonding in a clique-like fashion over a difficult period of time, or research collaborations forming and fading away over the years. Which patterns exist in real-world dynamic graphs, and how can we find and rank them in terms of importance? These are exactly the problems we focus on in this work. Our main contributions are (a) formulation: we show how to formalize this problem as minimizing the encoding cost in a data compression paradigm, (b) algorithm: we propose TIMECRUNCH, an effective, scalable and parameter-free method for finding coherent, temporal patterns in dynamic graphs and (c) practicality: we apply our method to several large, diverse real-world datasets with up to 36 million edges and 6.3 million nodes. We show that TIMECRUNCH is able to compress these graphs by summarizing important temporal structures and finds patterns that agree with intuition.