Robust Multimodal Graph Matching: Sparse Coding Meets Graph Matching

TL;DR

This paper introduces a robust graph matching algorithm based on sparsity techniques that effectively handles multimodal data and can be applied to various network inference problems, including brain connectivity analysis.

Contribution

It presents a novel sparsity-inspired convex optimization approach for multimodal graph matching and collaborative network inference, with efficient solution methods and broad applicability.

Findings

Outperforms state-of-the-art in synthetic and real graph matching tasks

Effectively handles multimodal and weighted graphs

Successfully applied to brain connectivity inference from fMRI data

Abstract

Graph matching is a challenging problem with very important applications in a wide range of fields, from image and video analysis to biological and biomedical problems. We propose a robust graph matching algorithm inspired in sparsity-related techniques. We cast the problem, resembling group or collaborative sparsity formulations, as a non-smooth convex optimization problem that can be efficiently solved using augmented Lagrangian techniques. The method can deal with weighted or unweighted graphs, as well as multimodal data, where different graphs represent different types of data. The proposed approach is also naturally integrated with collaborative graph inference techniques, solving general network inference problems where the observed variables, possibly coming from different modalities, are not in correspondence. The algorithm is tested and compared with state-of-the-art graph matching techniques in both synthetic and real graphs. We also present results on multimodal graphs and applications to collaborative inference of brain connectivity from alignment-free functional magnetic resonance imaging (fMRI) data. The code is publicly available.