Detecting Smooth Cluster Changes in Evolving Graph Structures

Abstract

Graph mining is a set of techniques for finding useful patterns in various types of structured data. Many effective algorithms for mining static graphs have been proposed. However, graphs of human relationships and evolving genes change over time, and such evolving graphs require different algorithms for analysis. In this chapter, we explain a method called O2I for clustering in evolving graphs that can detect changes in clusters over time. O2I partitions the graph sequence into smooth clusters, even when the numbers of clusters and vertices vary. It first constructs a graph from the graph sequence, then uses spectral clustering and the RatioCut to apply k partitioning to this graph. O2I is compared in detail with the preserving clustering membership (PCM) algorithm, which is a conventional online graph-sequence clustering algorithm in which the numbers of clusters and vertices must remain constant. We further show that, in contrast to PCM, the performance of O2I is not dependent on the clustering of the initial graph in the graph sequence. Experiments on synthetic evolving graphs show that O2I is practical to calculate and addresses the main disadvantages of PCM. Further tests on real-world data show that O2I can obtain reasonable clusters. This method is hence a flexible clustering solution and will be useful on a wide range of graph-mining applications in which the connections, number of clusters, and number of vertices of the graphs evolve over time.