A quantum Jensen-Shannon graph kernel for unattributed graphs

PATTERN RECOGNITION

卷:48

Article; Proceedings Paper

Bai, Lu¹  Rossi, Luca²  Torsello, Andrea³  Hancock, Edwin R.¹ 

[1] Univ York, Dept Comp Sci, York YO10 5DD, N Yorkshire, England

[2] Univ Birmingham, Sch Comp Sci, Birmingham B15 2TT, W Midlands, England

[3] Ca Foscari Univ Venice, Dept Environm Sci Informat & Stat, Venice, VE, Italy

关键词: Graph kernels;    Continuous-time quantum walk;    Quantum state;    Quantum Jensen-Shannon divergence;   

DOI  :  10.1016/j.patcog.2014.03.028

来源: Elsevier

【 摘 要 】

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. (C) 2014 Elsevier Ltd. All rights reserved.

【 授权许可】

Free