Unsupervised Learning of Graph Matching With Mixture of Modes via Discrepancy Minimization

Graph matching (GM) has been a long-standing combinatorial problem due to its NP-hard nature. Recently (deep) learning-based approaches have shown their superiority over the traditional solvers while the methods are almost based on supervised learning which can be expensive or even impractical. We develop a unified unsupervised framework from matching two graphs to multiple graphs, without correspondence ground truth for training. Specifically, a Siamese-style unsupervised learning framework is devised and trained by minimizing the discrepancy of a second-order classic solver and a first-order (differentiable) Sinkhorn net as two branches for matching prediction. The two branches share the same CNN backbone for visual graph matching. Our framework further allows unsupervised learning with graphs from a mixture of modes which is ubiquitous in reality. Specifically, we develop and unify the graduated assignment (GA) strategy for matching two-graph, multi-graph, and graphs from a mixture of modes, whereby two-way constraint and clustering confidence (for mixture case) are modulated by two separate annealing parameters, respectively. Moreover, for partial and outlier matching, an adaptive reweighting technique is developed to suppress the overmatching issue. Experimental results on real-world benchmarks including natural image matching show our unsupervised method performs comparatively and even better against two-graph based supervised approaches.