Graph clustering using heat content invariants

Abstract

In this paper, we investigate the use of invariants derived from the heat kernel as a means of clustering graphs. We turn to the heat-content, i.e. the sum of the elements of the heat kernel. The heat content can be expanded as a polynomial in time, and the co-efficients of the polynomial are known to be permutation invariants. We demonstrate how the polynomial co-efficients can be computed from the Laplacian eigensystem. Graph-clustering is performed by applying principal components analysis to vectors constructed from the polynomial co-efficients. We experiment with the resulting algorithm on the COIL database, where it is demonstrated to outperform the use of Laplacian eigenvalues. © Springer-Verlag Berlin Heidelberg 2005.