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.
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Xiao, B., Hancock, E.R. (2005). Graph Clustering Using Heat Content Invariants. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds) Pattern Recognition and Image Analysis. IbPRIA 2005. Lecture Notes in Computer Science, vol 3523. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11492542_16
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DOI: https://doi.org/10.1007/11492542_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26154-4
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