A quantum Jensen–Shannon graph kernel for unattributed graphs

• Published in: Pattern recognition Vol. 48; no. 2; pp. 344 - 355
• Main Authors: Bai, Lu, Rossi, Luca, Torsello, Andrea, Hancock, Edwin R.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Kidlington Elsevier Ltd 01.02.2015; Elsevier
• Subjects: Applied sciences; Artificial intelligence; Computer science; control theory; systems; Continuous-time quantum walk; Exact sciences and technology; Graph kernels; Information theory; Information, signal and communications theory; Pattern recognition. Digital image processing. Computational geometry; Quantum Jensen–Shannon divergence; Quantum state; Telecommunications and information theory; Quantum Jensen–Shannon divergence; Graph kernels; Continuous-time quantum walk; Quantum state; Performance evaluation; Quantum system; Computer vision; Mixed state; Similarity; Continuous time; Closed form equation; Computational complexity; Kernel method; Quantum mechanics; Quantum Jensen-Shannon divergence; Bioinformatics; Information theory
• ISSN: 0031-3203; 1873-5142
• DOI: 10.1016/j.patcog.2014.03.028

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. •We compute a density matrix for a graph using the continuous-time quantum walk.•We compute the quantum Jensen–Shannon divergence between graph density matrixes.•We define a quantum Jensen–Shannon graph kernel using the quantum divergence.•We evaluate the performance of our quantum kernel on standard graph datasets.•We demonstrate the effectiveness of the proposed quantum kernel.