M3C: A Framework towards Convergent, Flexible, and Unsupervised Learning of Mixture Graph Matching and Clustering

• URL: http://arxiv.org/abs/2310.18444v1
• Date: Fri, 27 Oct 2023 19:40:34 GMT
• Title: M3C: A Framework towards Convergent, Flexible, and Unsupervised Learning of Mixture Graph Matching and Clustering
• Authors: Jiaxin Lu, Zetian Jiang, Tianzhe Wang, Junchi Yan
• Abstract summary: We introduce Minorize-Maximization Matching and Clustering (M3C), a learning-free algorithm that guarantees theoretical convergence. We develop UM3C, an unsupervised model that incorporates novel edge-wise affinity learning and pseudo label selection. Our method outperforms state-of-the-art graph matching and mixture graph matching and clustering approaches in both accuracy and efficiency.
• Score: 57.947071423091415
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Existing graph matching methods typically assume that there are similar structures between graphs and they are matchable. However, these assumptions do not align with real-world applications. This work addresses a more realistic scenario where graphs exhibit diverse modes, requiring graph grouping before or along with matching, a task termed mixture graph matching and clustering. We introduce Minorize-Maximization Matching and Clustering (M3C), a learning-free algorithm that guarantees theoretical convergence through the Minorize-Maximization framework and offers enhanced flexibility via relaxed clustering. Building on M3C, we develop UM3C, an unsupervised model that incorporates novel edge-wise affinity learning and pseudo label selection. Extensive experimental results on public benchmarks demonstrate that our method outperforms state-of-the-art graph matching and mixture graph matching and clustering approaches in both accuracy and efficiency. Source code will be made publicly available.

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