  Softassign is a pivotal method in graph matching and other learning tasks.
Many softassign-based algorithms exhibit performance sensitivity to a parameter
in the softassign. However, tuning the parameter is challenging and almost done
empirically. This paper proposes an adaptive softassign method for graph
matching by analyzing the relationship 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 significantly enhance the efficiency and stability of
the adaptive softassign. Moreover, these formulas can also be used in optimal
transport problems. The resulting adaptive softassign graph matching algorithm
enjoys significantly higher accuracy than previous state-of-the-art large graph
matching algorithms while maintaining comparable efficiency.
