Topological constraints and kernel-based density estimation

This extended abstract1 explores the question of how to estimate a probability distribution from a finite number of samples when information about the topology of the support region of an underlying density is known. This workshop contribution is a continuation of our recent work [1] combining persistent homology and kernel-based density estimation for the first time and in which we explored an approach capable of incorporating topological constraints in bandwidth selection. We report on some recent experiments with high-dimensional motion capture data which show that our method is applicable even in high dimensions and develop our ideas for potential future applications of this framework.

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