Clustering shapes using heat content invariants

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 coefficients of the polynomial are known to be permutation invariants. We demonstrate how the polynomial coefficients can be computed from the Laplacian eigen-system. Graph-clustering is performed by applying principal components analysis to vectors constructed from the polynomial coefficients. We experiment with the resulting algorithm on the COIL database, where it is demonstrated to outperform the use of Laplacian eigenvalues.