Kernelized multi-graph matching

TL;DR

This paper introduces a kernelized multigraph matching method that incorporates vertex and edge attributes, solving a complex quadratic assignment problem efficiently and with improved stability, demonstrating competitive performance.

Contribution

It presents a novel kernelized approach for multigraph matching that handles attribute vectors and enhances stability through new projection techniques.

Findings

Method is competitive against other unsupervised approaches.

Handles attribute vectors on vertices and edges efficiently.

Improves stability with new projection methods.

Abstract

Multigraph matching is a recent variant of the graph matching problem. In this framework, the optimization procedure considers several graphs and enforces the consistency of the matches along the graphs. This constraint can be formalized as a cycle consistency across the pairwise permutation matrices, which implies the definition of a universe of vertex~\citep{pachauri2013solving}. The label of each vertex is encoded by a sparse vector and the dimension of this space corresponds to the rank of the bulk permutation matrix, the matrix built from the aggregation of all the pairwise permutation matrices. The matching problem can then be formulated as a non-convex quadratic optimization problem (QAP) under constraints imposed on the rank and the permutations. In this paper, we introduce a novel kernelized multigraph matching technique that handles vectors of attributes on both the vertices and edges of the graphs, while maintaining a low memory usage. We solve the QAP problem using a projected power optimization approach and propose several projectors leading to improved stability of the results. We provide several experiments showing that our method is competitive against other unsupervised methods.