Learning Graph Matching

TL;DR

This paper introduces a learning-based approach to optimize compatibility functions in graph matching, significantly improving matching accuracy over traditional algorithms by training on example graph pairs and their human-provided matches.

Contribution

It proposes a novel method for learning compatibility functions in graph matching, enhancing existing algorithms' performance through training on labeled graph pairs.

Findings

Learning improves graph matching accuracy

Simple linear assignment outperforms advanced algorithms

Training on human-labeled matches enhances results

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.