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arXiv · 0806.2890

Learning Graph Matching

Tiberio S. Caetano·Julian J. McAuley·Li Cheng·Quoc V. Le·Alex J. Smola
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Abstract

As a fundamental problem in pattern recognition, graph matching has applications in a variety of fields, from computer vision to computational biology. In graph matching, patterns are modeled as graphs and pattern recognition amounts to finding a correspondence between the nodes of different graphs. Many formulations of this problem can be cast in general as a quadratic assignment problem, where a linear term in the objective function encodes node compatibility and a quadratic term encodes edge compatibility. The main research focus in this theme is about designing efficient algorithms for approximately solving the quadratic assignment problem, since it is NP-hard. In this paper we turn our attention to a different question: how to estimate compatibility functions such that the solution of the resulting graph matching problem best matches the expected solution that a human would manually provide. We present a method for learning graph matching: the training examples are pairs of graphs and the `labels' are matches between them. Our experimental results reveal that learning can substantially improve the performance of standard graph matching algorithms. In particular, we find that simple linear assignment with such a learning scheme outperforms Graduated Assignment with bistochastic normalisation, a state-of-the-art quadratic assignment relaxation algorithm.

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Tiberio S. Caetano, Julian J. McAuley, Li Cheng, Quoc V. Le, Alex J. Smola. 2008-06-17. Learning Graph Matching. https://arxiv.org/abs/0806.2890

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