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Laplacian Eigenmaps for dimensionality reduction and data representation
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Journal of Computer and System Sciences - Special issue on FOCS 2002
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Diffusion Kernels on Statistical Manifolds
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Characteristic Polynomial Analysis on Matrix Representations of Graphs
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Graph embedding using an edge-based wave Kernel
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Computer Vision and Image Understanding
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Graph descriptors from B-matrix representation
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Characterizing graphs using approximate von Neumann entropy
IbPRIA'11 Proceedings of the 5th Iberian conference on Pattern recognition and image analysis
Graph clustering using the Jensen-Shannon Kernel
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
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Pattern Recognition Letters
Pattern analysis with graphs: Parallel work at Bern and York
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Invariants of distance k-graphs for graph embedding
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Laplacian eigenimages in discrete scale space
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SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Information-theoretic selection of high-dimensional spectral features for structural recognition
Computer Vision and Image Understanding
Graph Kernels from the Jensen-Shannon Divergence
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Entropy and heterogeneity measures for directed graphs
SIMBAD'13 Proceedings of the Second international conference on Similarity-Based Pattern Recognition
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Graph structures have been proved important in high level-vision since they can be used to represent structural and relational arrangements of objects in a scene. One of the problems that arises in the analysis of structural abstractions of objects is graph clustering. In this paper, we explore 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. The heat kernel is the solution of the heat equation and is a compact representation of the path-length distribution on a graph. The trace of the heat kernel is given by the sum of the Laplacian eigenvalues exponentiated with time. We explore three different approaches to characterizing the heat kernel trace as a function of time. Our first characterization is based on the zeta function, which from the Mellin transform is the moment generating function of the heat kernel trace. Our second characterization is unary and is found by computing the derivative of the zeta function at the origin. The third characterization is derived from the heat content, i.e. the sum of the elements of the heat kernel. We show how the heat content can be expanded as a power series in time, and the coefficients of the series can be computed using the Laplacian spectrum. We explore the use of these characterizations as a means of representing graph structure for the purposes of clustering, and compare them with the use of the Laplacian spectrum. Experiments with the synthetic and real-world databases reveal that each of the three proposed invariants is effective and outperforms the traditional Laplacian spectrum. Moreover, the heat-content invariants appear to consistently give the best results in both synthetic sensitivity studies and on real-world object recognition problems.