Graph Nodes Clustering Based on the Commute-Time Kernel

Abstract

This work presents a kernel method for clustering the nodes of a weighted, undirected, graph. The algorithm is based on a two-step procedure. First, the sigmoid commute-time kernel ( $\mathbf{K}_{\text{CT}}$ ), providing a similarity measure between any couple of nodes by taking the indirect links into account, is computed from the adjacency matrix of the graph. Then, the nodes of the graph are clustered by performing a kernel k-means or fuzzy k-means on this CT kernel matrix. For this purpose, a new, simple, version of the kernel k-means and the kernel fuzzy k-means is introduced. The joint use of the CT kernel matrix and kernel clustering appears to be quite successful. Indeed, it provides good results on a document clustering problem involving the newsgroups database.