Predicting the correctness of node assignments in bipartite graph matching

Abstract

Due to their high representational power and flexibility, graphs have emerged as a widely used data structure for complex pattern representation. The advantages of graphs are, however, at the expense of a substantial increase of the computational complexity of the associated algorithms. For instance, exact graph similarity or distance can be computed in exponential time only. An algorithmic framework based on bipartite graph matching (allowing graph dissimilarity computation in cubic time) has been presented recently. However, this fast computation leads in general to some incorrect node assignments with respect to a globally optimal graph matching. In this paper we present a novel methodology for predicting which of the node assignments are actually incorrectly assigned by this approximation. To this end, a comprehensive set of features – which numerically characterize the assignments – is defined and extracted from the underlying graphs. These features are in turn used for training a statistical classifier, which can eventually be employed for predicting unseen assignments. The power and applicability of our novel approach is empirically verified on eight real world data sets.