Link-based Community Detection with the Commute-Time Kernel

The main purpose of this work is to find communities in a weighted, undirected, graph by using kernel-based clustering methods, directly partitioning the graph according to a well-defined similarity measure between the nodes (a kernel on a graph). The algorithm is based on a two-step procedure. First, the sigmoid commute-time kernel (KCT), providing a meaningful similarity measure between any couple of nodes, is computed from the adjacency matrix of the graph. Then, the nodes of the graph are clustered by performing a kernel clustering on this CT kernel matrix. For this purpose, simple, prototype-based, kernel versions of the k-means, the fuzzy k-means, the entropy-based fuzzy k-means, the gaussian mixtures model, as well as Ward’s hierarchical clustering, are introduced. The joint use of the CT kernel matrix and kernel clustering appears to be quite effective. Indeed, this methodology provides good results, outperforming the spherical k-means and spectral clustering, on a document clustering problem involving the newsgroups database, where the set of documents is viewed as a graph. Finally, the links between the proposed hierarchical kernel clustering and spectral clustering are examined.