KerGM: Kernelized Graph Matching

Graph matching plays a central role in such fields as computer vision, pattern recognition, and bioinformatics. Graph matching problems can be cast as two types of quadratic assignment problems (QAPs): Koopmans-Beckmann's QAP or Lawler's QAP. In our paper, we provide a unifying view for these two problems by introducing new rules for array operations in Hilbert spaces. Consequently, Lawler's QAP can be considered as the Koopmans-Beckmann's alignment between two arrays in reproducing kernel Hilbert spaces (RKHS), making it possible to efficiently solve the problem without computing a huge affinity matrix. Furthermore, we develop the entropy-regularized Frank-Wolfe (EnFW) algorithm for optimizing QAPs, which has the same convergence rate as the original FW algorithm while dramatically reducing the computational burden for each outer iteration.