Graph nodes clustering with the sigmoid commute-time kernel: A comparative study

This work addresses the problem of detecting clusters 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 proposed algorithms are based on a two-step procedure. First, a kernel or similarity matrix, 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 similarity matrix. Besides the introduction of a prototype-based kernel version of the gaussian mixtures model and Ward's hierarchical clustering, in addition to the already known kernel k-means and fuzzy k-means, a new kernel, called the sigmoid commute-time kernel (K"C"T^S) is presented. The joint use of the K"C"T^S kernel matrix and kernel clustering appears to be quite effective. Indeed, this methodology provides the best results on a systematic comparison with a selection of graph clustering and communities detection algorithms on three real-world databases. Finally, some links between the proposed hierarchical kernel clustering and spectral clustering are examined.