Stable and Informative Spectral Signatures for Graph Matching

TL;DR

This paper develops stable spectral signatures based on the graph Laplacian for improved approximate weighted graph matching, demonstrating superior performance on synthetic and real datasets.

Contribution

It introduces a new spectral node signature and a pairwise heat kernel distance for stable, informative graph matching compatibility terms.

Findings

Spectral signatures improve matching stability and accuracy.

Heat kernel distance converges to classical adjacency-based measures.

Experimental results outperform existing compatibility functions.

Abstract

In this paper, we consider the approximate weighted graph matching problem and introduce stable and informative first and second order compatibility terms suitable for inclusion into the popular integer quadratic program formulation. Our approach relies on a rigorous analysis of stability of spectral signatures based on the graph Laplacian. In the case of the first order term, we derive an objective function that measures both the stability and informativeness of a given spectral signature. By optimizing this objective, we design new spectral node signatures tuned to a specific graph to be matched. We also introduce the pairwise heat kernel distance as a stable second order compatibility term; we justify its plausibility by showing that in a certain limiting case it converges to the classical adjacency matrix-based second order compatibility function. We have tested our approach on a set of synthetic graphs, the widely-used CMU house sequence, and a set of real images. These experiments show the superior performance of our first and second order compatibility terms as compared with the commonly used ones.