Graph embedding using quantum commute times

Authors:
David Emms;Richard C. Wilson;Edwin Hancock
Affiliations:
Department of Computer Science, University of York, UK;Department of Computer Science, University of York, UK;Department of Computer Science, University of York, UK
Venue:
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Year:
2007

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Abstract

In this paper, we explore analytically and experimentally the commute time of the continuous-time quantum walk. For the classical random walk, the commute time has been shown to be robust to errors in edge weight structure and to lead to spectral clustering algorithms with improved performance. Our analysis shows that the commute time of the continuous-time quantum walk can be determined via integrals of the Laplacian spectrum, calculated using Gauss-Laguerre quadrature. We analyse the quantum commute times with reference to their classical counterpart. Experimentally, we show that the quantum commute times can be used to emphasise cluster-structure.