Regularization Kernels and Softassign

In this paper we analyze the use of regularization kernels on graphs to weight the quadratic cost function used in the Softassign graph-matching algorithm. In a previous work, we have showed that when using diffusion kernels on graphs such a weighting improves significantly the matching performance yielding a slow decay with increasing noise. Weights, relying on the entropies of the probability distributions associated to the vertices after diffusion kernel computation, transform the original unweighted matching problem into a weighted one. In this regard, as diffusion kernels are a particular case of regularization kernels it is interesting to study the utility of this family of kernels for matching purposes. We have designed an experimental set for discovering the optimal performance for each regularization kernel. Our results suggest that kernel combination could be a key point to address in the future.

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