A graph distance metric based on the maximal common subgraph
Pattern Recognition Letters
Shock Graphs and Shape Matching
International Journal of Computer Vision
Shortest-Path Kernels on Graphs
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
Graph embedding using quantum commute times
GbRPR'07 Proceedings of the 6th IAPR-TC-15 international conference on Graph-based representations in pattern recognition
Quantum Computation and Quantum Information: 10th Anniversary Edition
Quantum Computation and Quantum Information: 10th Anniversary Edition
Supervised learning of graph structure
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
Structural Descriptions and Inexact Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximate axial symmetries from continuous time quantum walks
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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One of the most fundamental problem that we face in the graph domain is that of establishing the similarity, or alternatively the distance, between graphs. In this paper, we address the problem of measuring the similarity between attributed graphs. In particular, we propose a novel way to measure the similarity through the evolution of a continuous-time quantum walk. Given a pair of graphs, we create a derived structure whose degree of symmetry is maximum when the original graphs are isomorphic, and where a subset of the edges is labeled with the similarity between the respective nodes. With this compositional structure to hand, we compute the density operators of the quantum systems representing the evolution of two suitably defined quantum walks. We define the similarity between the two original graphs as the quantum Jensen-Shannon divergence between these two density operators, and then we show how to build a novel kernel on attributed graphs based on the proposed similarity measure. We perform an extensive experimental evaluation both on synthetic and real-world data, which shows the effectiveness the proposed approach.