An edge-based matching kernel through discrete-time quantum walks


In this paper, we propose a new edge-based matching kernel for graphs by using discrete-time quantum walks. To this end, we commence by transforming a graph into a directed line graph. The reasons of using the line graph structure are twofold. First, for a graph, its directed line graph is a dual representation and each vertex of the line graph represents a corresponding edge in the original graph. Second, we show that the discrete-time quantum walk can be seen as a walk on the line graph and the state space of the walk is the vertex set of the line graph, i.e., the state space of the walk is the edges of the original graph. As a result, the directed line graph provides an elegant way of developing new edge-based matching kernel based on discrete-time quantum walks. For a pair of graphs, we compute the h-layer depth-based representation for each vertex of their directed line graphs by computing entropic signatures (computed from discrete-time quantum walks on the line graphs) on the family of K-layer expansion subgraphs rooted at the vertex, i.e., we compute the depth-based representations for edges of the original graphs through their directed line graphs. Based on the new representations, we define an edge-based matching method for the pair of graphs by aligning the h-layer depth-based representations computed through the directed line graphs. The new edge-based matching kernel is thus computed by counting the number of matched vertices identified by the matching method on the directed line graphs. Experiments on standard graph datasets demonstrate the effectiveness of our new kernel.

Publication DOI:
Divisions: College of Engineering & Physical Sciences
College of Engineering & Physical Sciences > Systems analytics research institute (SARI)
Additional Information: The final publication is available at Springer via
Event Title: 18th International Conference on Image Analysis and Processing
Event Type: Other
Event Dates: 2015-09-07 - 2015-09-11
ISBN: 978-3-319-23230-0, 978-3-319-23231-7
Last Modified: 05 Jan 2024 08:28
Date Deposited: 17 Sep 2015 11:30
Full Text Link: http://link.spr ... 3-319-23231-7_3
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PURE Output Type: Conference contribution
Published Date: 2015-08-21
Authors: Bai, Lu
Zhang, Zhihong
Ren, Peng
Rossi, Luca (ORCID Profile 0000-0002-6116-9761)
Hancock, Edwin R.



Version: Accepted Version

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