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Pattern vectors from algebraic graph theory

Wilson, R C (orcid.org/0000-0001-7265-3033), Hancock, E R (orcid.org/0000-0003-4496-2028) and Luo, B (2005) Pattern vectors from algebraic graph theory. IEEE Transactions on Pattern Analysis and Machine Intelligence. pp. 1112-1124. ISSN 0162-8828

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Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: graph matching,graph features,spectral methods,SEGMENTATION,EIGENVALUES,FRAMEWORK,ALGORITHM,SHAPE
Institution: The University of York
Academic Units: The University of York > Computer Science (York)
Depositing User: Repository Officer
Date Deposited: 21 Feb 2007
Last Modified: 10 Apr 2016 22:40
Published Version: http://dx.doi.org/10.1109/TPAMI.2005.145
Status: Published
Refereed: Yes
URI: http://eprints.whiterose.ac.uk/id/eprint/1994

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