Approximate and Spectral Clustering for Network and Affinity Data

This chapter is devoted to clustering similarity, graph and network data – these are represented by square matrices rather than rectangular ones. This chapter describes methods for finding a cluster or two-cluster split combining three types of approaches from both old and recent developments: (a)combinatorial approach that is oriented at clustering as optimization of some reasonable measure of cluster homogeneity, (b)additive clustering approach that is based on a data recovery model at which the data is decoded from a cluster structure to be found by minimizing the discrepancy between them and observed similarities, and (c)spectral clustering approach exploiting the machinery of matrix eigenvalues and eigenvectors as a relaxation of combinatorial problems for similarity clustering.