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Persistent Homology for Learning Densities with Bounded Support
KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.ORCID iD: 0000-0003-1114-6040
KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.
KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.ORCID iD: 0000-0002-5750-9655
KTH, School of Computer Science and Communication (CSC), Computer Vision and Active Perception, CVAP.ORCID iD: 0000-0003-2965-2953
2012 (English)In: Advances in Neural Information Processing Systems 25: 26th Annual Conference on Neural Information Processing Systems 2012 / [ed] P. Bartlett, F.C.N. Pereira, C.J.C. Burges, L. Bottou and K.Q. Weinberger, Curran Associates, Inc., 2012, 1817-1825 p.Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Curran Associates, Inc., 2012. 1817-1825 p.
Series
Advances in Neural Information Processing Systems, ISSN 1049-5258 ; 3
Keyword [en]
persistent homology, density estimation, topological constraints
National Category
Probability Theory and Statistics Computer Vision and Robotics (Autonomous Systems)
Research subject
SRA - ICT
Identifiers
URN: urn:nbn:se:kth:diva-104754Scopus ID: 2-s2.0-84877777095ISBN: 978-162748003-1 (print)OAI: oai:DiVA.org:kth-104754DiVA: diva2:579082
Conference
26th Annual Conference on Neural Information Processing Systems 2012, NIPS 2012; Lake Tahoe, NV; United States; 3 December 2012 through 6 December 2012
Funder
EU, FP7, Seventh Framework Programme, 270436EU, European Research Council, 279933Swedish Foundation for Strategic Research
Note

QC 20120115

Available from: 2012-12-19 Created: 2012-11-12 Last updated: 2014-05-12Bibliographically approved

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Pokorny, Florian T.Kjellström, HedvigKragic, Danica

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