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Graph edit distance from spectral seriation

Robles-Kelly, A and Hancock, E R (2005) Graph edit distance from spectral seriation. IEEE Transactions on Pattern Analysis and Machine Intelligence. pp. 365-378. ISSN 0162-8828

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Abstract

This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graph-matching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems.

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 edit distance, graph seriation, maximum a posteriori probability (MAP), graph-spectral methods, OBJECT RECOGNITION, ALGORITHM, SHAPE, RELAXATION
Academic Units: The University of York > Computer Science (York)
Depositing User: Repository Officer
Date Deposited: 21 Feb 2007
Last Modified: 17 Oct 2013 14:23
Published Version: http://dx.doi.org/10.1109/TPAMI.2005.56
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1993

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