Summarizing Network Processes with Network-Constrained Boolean Matrix Factorization

Abstract

Understanding and modeling complex network processes is an important task in many real-world applications. The first challenge is to discover patterns in such complex data. In this work, our goal is to summarize different processes in a network by a small yet interpretable set of network patterns, each of which represents a local community of connected nodes frequently participating in the same network processes. We formulate this problem as a Boolean Matrix Factorization with a network constraint, which we prove to be NP-hard. We then propose an efficient algorithm that incrementally adds the best patterns and achieve scalability with two further improvements. First, to decide which network processes contain which network patterns, we introduce two mapping algorithms with linear costs. Second, to systematically mine the exponential subgraph search space for good patterns, we devise two sampling algorithms based on Monte Carlo Markov Chain. Experimental results on both synthetic and real-world datasets show that our solutions are scalable and find network patterns that effectively summarize network processes.