# 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.

## Files

@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}, }