Robust Multimodal Graph Matching: Sparse Coding Meets Graph Matching
This work addresses graph matching for applications in fields such as image analysis and biomedicine, presenting an incremental improvement with integration into collaborative inference.
The paper tackles the challenging problem of graph matching by proposing a robust algorithm based on sparsity-related techniques, which is tested on synthetic and real graphs and applied to multimodal data like fMRI for brain connectivity inference.
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.