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Frequent pattern mining is a key area of study that gives insights into thestructure and dynamics of evolving networks, such as social or road networks.However, not only does a network evolve, but often the way that it evolves,itself evolves. Thus, knowing, in addition to patterns' frequencies, for howlong and how regularly they have occurred---i.e., their persistence---can addto our understanding of evolving networks. In this work, we propose the problemof mining activity that persists through time in continually evolvingnetworks---i.e., activity that repeatedly and consistently occurs. We extendthe notion of temporal motifs to capture activity among specific nodes, in whatwe call activity snippets, which are small sequences of edge-updates thatreoccur. We propose axioms and properties that a measure of persistence shouldsatisfy, and develop such a persistence measure. We also propose PENminer, anefficient framework for mining activity snippets' Persistence in EvolvingNetworks, and design both offline and streaming algorithms. We apply PENminerto numerous real, large-scale evolving networks and edge streams, and findactivity that is surprisingly regular over a long period of time, but tooinfrequent to be discovered by aggregate count alone, and bursts of activityexposed by their lack of persistence. Our findings with PENminer includeneighborhoods in NYC where taxi traffic persisted through Hurricane Sandy, theopening of new bike-stations, characteristics of social network users, andmore. Moreover, we use PENminer towards identifying anomalies in multiplenetworks, outperforming baselines at identifying subtle anomalies by 9.8-48% inAUC.

Mining Persistent Activity in Continually Evolving Networks