Pattern Vectors from Algebraic Graph Theory
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spherical embedding and classification
SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
The dissimilarity representation for structural pattern recognition
CIARP'11 Proceedings of the 16th Iberoamerican Congress conference on Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
SemaFor: semantic document indexing using semantic forests
Proceedings of the 21st ACM international conference on Information and knowledge management
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In this paper, we explore whether the geometric properties of the point distribution obtained by embedding the nodes of a graph on a manifold can be used for the purposes of graph clustering. The embedding is performed using the heat-kernel of the graph, computed by exponentiating the Laplacian eigen-system. By equating the spectral heat kernel and its Gaussian form we are able to approximate the Euclidean distance between nodes on the manifold. The difference between the geodesic and Euclidean distances can be used to compute the sectional curvatures associated with the edges of the graph. To characterise the manifold on which the graph resides, we use the normalised histogram of sectional curvatures. By performing PCA on long-vectors representing the histogram bin-contents, we construct a pattern space for sets of graphs. We apply the technique to images from the COIL database, and demonstrate that it leads to well defined graph clusters.