An Eigendecomposition Approach to Weighted Graph Matching Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Spectral Algorithm for Seriation and the Consecutive Ones Problem
SIAM Journal on Computing
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Properties of Embedding Methods for Similarity Searching in Metric Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
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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.