PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Graph matching using the interference of continuous-time quantum walks
David Emms, Richard Wilson and Edwin Hancock
Pattern Recognition Volume 42, Number 5, pp. 985-1002, 2009. ISSN 0031-3203

Abstract

We consider how continuous-time quantum walks can be used for graph matching. We focus in detail on both exact and inexact graph matching, and consider in depth the problem of measuring graph similarity. We commence by constructing an auxiliary graph, in which the two graphs to be matched are co-joined by a layer of indicator vertices (one for each potential correspondence between a pair of vertices). We simulate a continuous-time quantum walk in parallel on the two graphs. The layer of connecting indicator vertices in the auxiliary graph allow quantum interference to take place between the two walks. The interference amplitudes on the indicator vertices are determined by differences in the two walks, and can be used to calculate probabilities for matches between pairs of vertices from the graphs. By applying the Hungarian (Kuhn–Munkres) algorithm to these probabilities, we recover a correspondence mapping between the graphs. To calculate graph similarity, we combine these probabilities with edge-consistency information to give a consistency measure. Based on the consistency measure, we define two graph similarity measures, one of which requires correspondence matches while the second does not. We analyse our approach experimentally using synthetic and real-world graphs. This reveals that our method gives results that are intermediate between the most sophisticated iterative techniques available, and simpler less complex ones.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Machine Vision
Theory & Algorithms
ID Code:6841
Deposited By:Edwin Hancock
Deposited On:08 March 2010