Topological Constraints and Kernel-Based Density Estimation

Florian T. Pokorny, Carl Henrik Ek, Hedvig Kjellström, Danica Kragic
In Advances in Neural Information Processing Systems 25, Workshop on Algebraic Topology and Machine Learning, 2012

Abstract

This extended abstract 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 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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Bibtex

@incollection{pokorny2012b, title = {Topological Constraints and Kernel-Based Density Estimation}, author = {Pokorny, Florian T. and Ek, Carl Henrik and Kjellstr{\"o}m, Hedvig and Kragic, Danica}, booktitle = {Advances in Neural Information Processing Systems 25, Workshop on Algebraic Topology and Machine Learning}, year = {2012}, url = {http://www.csc.kth.se/~fpokorny/static/publications/pokorny2012b.pdf}, }