A quantum Jensen-Shannon graph kernel for unattributed graphs


In this paper, we use the quantum Jensen-Shannon divergence as a means of measuring the information theoretic dissimilarity of graphs and thus develop a novel graph kernel. In quantum mechanics, the quantum Jensen-Shannon divergence can be used to measure the dissimilarity of quantum systems specified in terms of their density matrices. We commence by computing the density matrix associated with a continuous-time quantum walk over each graph being compared. In particular, we adopt the closed form solution of the density matrix introduced in Rossi et al. (2013) [27,28] to reduce the computational complexity and to avoid the cumbersome task of simulating the quantum walk evolution explicitly. Next, we compare the mixed states represented by the density matrices using the quantum Jensen-Shannon divergence. With the quantum states for a pair of graphs described by their density matrices to hand, the quantum graph kernel between the pair of graphs is defined using the quantum Jensen-Shannon divergence between the graph density matrices. We evaluate the performance of our kernel on several standard graph datasets from both bioinformatics and computer vision. The experimental results demonstrate the effectiveness of the proposed quantum graph kernel.

Publication DOI: https://doi.org/10.1016/j.patcog.2014.03.028
Divisions: College of Engineering & Physical Sciences
College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: © 2015, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/
Uncontrolled Keywords: continuous-time quantum walk,graph kernels,quantum Jensen-Shannon divergence,quantum state,Software,Artificial Intelligence,Computer Vision and Pattern Recognition,Signal Processing
Publication ISSN: 1873-5142
Last Modified: 05 Jan 2024 08:16
Date Deposited: 17 Sep 2015 13:00
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Related URLs: http://www.scop ... tnerID=8YFLogxK (Scopus URL)
PURE Output Type: Article
Published Date: 2015-02
Published Online Date: 2014-04-04
Authors: Bai, Lu
Rossi, Luca (ORCID Profile 0000-0002-6116-9761)
Torsello, Andrea
Hancock, Edwin R.

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