Laplace eigenvalues of graphs—a survey
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Quantitative measures of change based on feature organization: eigenvalues and eigenvectors
Computer Vision and Image Understanding
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
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
From graphs to manifolds – weak and strong pointwise consistency of graph laplacians
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Quantitative Evaluation on Heat Kernel Permutation Invariants
SSPR & SPR '08 Proceedings of the 2008 Joint IAPR International Workshop on Structural, Syntactic, and Statistical Pattern Recognition
A generative model for graph matching and embedding
Computer Vision and Image Understanding
Geometric Characterizations of Graphs Using Heat Kernel Embeddings
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
Geometric characterization and clustering of graphs using heat kernel embeddings
Image and Vision Computing
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In this paper, we explore how the trace of the heat kernel can be used to characterise graphs for the purposes of measuring similarity and clustering. The heat-kernel is the solution of the heat-equation and may be computed by exponentiating the Laplacian eigensystem with time. To characterise the shape of the heat-kernel trace we use the zeta-function, which is found by exponentiating and summing the reciprocals of the Laplacian eigenvalues. From the Mellin transform, it follows that the zeta-function is the moment generating function of the heat-kernel trace. We explore the use of the heat-kernel moments as a means of characterising graph structure for the purposes of clustering. Experiments with the COIL and Oxford-Caltech databases reveal the effectiveness of the representation.