Adaptive Softassign via Hadamard-Equipped Sinkhorn

Softassign is a pivotal method in graph matching and other learning tasks. Many softassign-based algorithms ex-hibit performance sensitivity to a parameter in the softas-sign. However, tuning the parameter is challenging and al-most done empirically. This paper proposes an adaptive softassign method for graph matching by analyzing the re-lationship between the objective score and the parameter. This method can automatically tune the parameter based on a given error bound to guarantee accuracy. The Hadamard-Equipped Sinkhorn formulas introduced in this study signif-icantly enhance the efficiency and stability of the adaptive softassign. Moreover, these formulas can also be used in optimal transport problems. The resulting adaptive softas-sign graph matching algorithm enjoys significantly higher accuracy than previous state-of-the-art large graph matching algorithms while maintaining comparable efficiency.