Quantum kernels for unattributed graphs using discrete-time quantum walks

Lu Bai, Luca Rossi, Lixin Cui, Zhihong Zhang, Peng Ren, Xiao Bai, Edwin Hancock

Research output: Journal article publicationJournal articleAcademic researchpeer-review

22 Citations (Scopus)

Abstract

In this paper, we develop a new family of graph kernels where the graph structure is probed by means of a discrete-time quantum walk. Given a pair of graphs, we let a quantum walk evolve on each graph and compute a density matrix with each walk. With the density matrices for the pair of graphs to hand, the kernel between the graphs is defined as the negative exponential of the quantum Jensen–Shannon divergence between their density matrices. In order to cope with large graph structures, we propose to construct a sparser version of the original graphs using the simplification method introduced in Qiu and Hancock (2007). To this end, we compute the minimum spanning tree over the commute time matrix of a graph. This spanning tree representation minimizes the number of edges of the original graph while preserving most of its structural information. The kernel between two graphs is then computed on their respective minimum spanning trees. We evaluate the performance of the proposed kernels on several standard graph datasets and we demonstrate their effectiveness and efficiency.

Original languageEnglish
Pages (from-to)96-103
Number of pages8
JournalPattern Recognition Letters
Volume87
DOIs
Publication statusPublished - 1 Feb 2017
Externally publishedYes

Keywords

  • Discrete-time quantum walks
  • Graph kernels
  • Quantum Jensen–Shannon divergence

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence

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