Florian T. Pokorny
Assistant Professor, School of Computer Science and Communication, KTH Royal Institute of TechnologyPersistent Homology for Learning Densities with Bounded Support
In Advances in Neural Information Processing Systems 25, 2012, pp. 1826--1834
Abstract
We present a novel method for learning densities with bounded support
which enables us to incorporate `hard' topological constraints.
In particular, we show how emerging techniques from computational algebraic topology
and the notion of persistent homology can be combined with kernel-based
methods from machine learning for the purpose of density estimation.
The proposed formalism facilitates learning of models with bounded support in a principled
way, and -- by incorporating persistent homology techniques in our
approach -- we are able to encode algebraic-topological constraints which are not
addressed in current state of the art probabilistic models. We study the
behaviour of our method on two synthetic examples for various sample
sizes and exemplify the benefits of the proposed approach on a
real-world dataset by learning a motion model for a race car. We
show how to learn a model which respects the underlying topological
structure of the racetrack, constraining the trajectories of the
car.
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Download this publicationBibtex
@incollection{pokorny2012a,
title = {Persistent Homology for Learning Densities with Bounded Support},
author = {Pokorny, Florian T. and Ek, Carl Henrik and Kjellstr{\"o}m, Hedvig and Kragic, Danica},
booktitle = {Advances in Neural Information Processing Systems 25},
editor = {P. Bartlett and F.C.N. Pereira and C.J.C. Burges and L. Bottou and K.Q. Weinberger},
pages = {1826--1834},
year = {2012},
url = {http://www.csc.kth.se/~fpokorny/static/publications/pokorny2012a.pdf},
}