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
Unsupervised Learning of Finite Mixture Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognition of Shapes by Editing Their Shock Graphs
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pattern Vectors from Algebraic Graph Theory
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Shape Matching Using Shape Contexts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discovering Shape Classes using Tree Edit-Distance and Pairwise Clustering
International Journal of Computer Vision
Trace formula analysis of graphs
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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The Laplacian spectrum has proved useful for pattern analysis tasks, and one of its important properties is its close relationship with the heat equation. In this paper, we first show how permutation invariants computed from the trace of the heat kernel can be used to characterize graphs for the purposes of measuring similarity and clustering. We explore three different approaches to characterize the heat kernel trace as a function of time. These are the heat kernel trace moments, heat content invariants and symmetric polynomials with Laplacian eigenvalues as inputs. We then use synthetic and real world datasets to give a quantitative evaluation of these feature invariants deduced from heat kernel analysis. We compare their performance with traditional spectrum invariants.