Scalable and Axiomatic Ranking of Network Role Similarity.

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 equivalent 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 similarity 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.

A Sparsification Approach for Temporal Graphical Model Decomposition.

Temporal causal modeling can be used to recover the causal structure among a group of relevant time series variables. Several methods have been developed to explicitly construct temporal causal graphical models. However, how to best understand and conceptualize these complicated causal relationships is still an open problem. In this paper, we propose a decomposition approach to simplify the temporal graphical model. Our method clusters time series variables into groups such that strong interactions appear among the variables within each group and weak (or no) interactions exist for cross-group variable pairs. Specifically, we formulate the clustering problem for temporal graphical models as a regression-coefficient sparsification problem and define an interesting objective function which balances the model prediction power and its cluster structure. We introduce an iterative optimization approach utilizing the Quasi-Newton method and generalized ridge regression to minimize the objective function and to produce a clustered temporal graphical model. We also present a novel optimization procedure utilizing a graph theoretical tool based on the maximum weight independent set problem to speed up the Quasi-Newton method for a large number of variables. Finally, our detailed experimental study on both synthetic and real datasets demonstrates the effectiveness of our methods.