Topologically-Constrained Latent Variable Models

Raquel Urtasun; David J. Fleet; Andreas Geiger; Jovan Popović; Trevor J. Darrell; Neil D. Lawrence

doi:10.1145/1390156.1390292

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Topologically-Constrained Latent Variable Models

Raquel Urtasun, David J. Fleet, Andreas Geiger, Jovan Popović, Trevor J. Darrell, Neil D. Lawrence

Proceedings of the International Conference in Machine Learning, Omnipress 25:1080-1087, 2008.

Abstract

In dimensionality reduction approaches, the data are typically embedded in a Euclidean latent space. However for some data sets this is inappropriate. For example, in human motion data we expect latent spaces that are cylindrical or a toroidal, that are poorly captured with a Euclidean space. In this paper, we present a range of approaches for embedding data in a non-Euclidean latent space. Our focus is the Gaussian Process latent variable model. In the context of human motion modeling this allows us to (a) learn models with interpretable latent directions enabling, for example, style/content separation, and (b) generalise beyond the data set enabling us to learn transitions between motion styles even though such transitions are not present in the data.

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BibTeX


@InProceedings{Urtasun:topology08,
  title = 	 {Topologically-Constrained Latent Variable Models},
  author = 	 {Urtasun, Raquel and Fleet, David J. and Geiger, Andreas and Popović, Jovan and Darrell, Trevor J. and Lawrence, Neil D.},
  booktitle = 	 {Proceedings of the International Conference in Machine Learning},
  pages = 	 {1080--1087},
  year = 	 {2008},
  editor = 	 {Roweis, Sam and McCallum, Andrew},
  volume = 	 {25},
  publisher =    {Omnipress},
  doi = 	 {10.1145/1390156.1390292},
  pdf = 	 {https://lawrennd.github.io/publications/files/topology.pdf},
  url = 	 {/publications/urtasun-topology08.html},
  abstract = 	 {In dimensionality reduction approaches, the data are typically embedded in a Euclidean latent space. However for some data sets this is inappropriate. For example, in human motion data we expect latent spaces that are cylindrical or a toroidal, that are poorly captured with a Euclidean space. In this paper, we present a range of approaches for embedding data in a non-Euclidean latent space. Our focus is the Gaussian Process latent variable model. In the context of human motion modeling this allows us to (a) learn models with interpretable latent directions enabling, for example, style/content separation, and (b) generalise beyond the data set enabling us to learn transitions between motion styles even though such transitions are not present in the data.}
}

Endnote

%0 Conference Paper
%T Topologically-Constrained Latent Variable Models
%A Raquel Urtasun
%A David J. Fleet
%A Andreas Geiger
%A Jovan Popović
%A Trevor J. Darrell
%A Neil D. Lawrence
%B Proceedings of the International Conference in Machine Learning
%D 2008
%E Sam Roweis
%E Andrew McCallum	
%F Urtasun:topology08
%I Omnipress
%P 1080--1087
%R 10.1145/1390156.1390292
%U /publications/urtasun-topology08.html
%V 25
%X In dimensionality reduction approaches, the data are typically embedded in a Euclidean latent space. However for some data sets this is inappropriate. For example, in human motion data we expect latent spaces that are cylindrical or a toroidal, that are poorly captured with a Euclidean space. In this paper, we present a range of approaches for embedding data in a non-Euclidean latent space. Our focus is the Gaussian Process latent variable model. In the context of human motion modeling this allows us to (a) learn models with interpretable latent directions enabling, for example, style/content separation, and (b) generalise beyond the data set enabling us to learn transitions between motion styles even though such transitions are not present in the data.

RIS


TY  - CPAPER
TI  - Topologically-Constrained Latent Variable Models
AU  - Raquel Urtasun
AU  - David J. Fleet
AU  - Andreas Geiger
AU  - Jovan Popović
AU  - Trevor J. Darrell
AU  - Neil D. Lawrence
BT  - Proceedings of the International Conference in Machine Learning
DA  - 2008/07/05
ED  - Sam Roweis
ED  - Andrew McCallum	
ID  - Urtasun:topology08
PB  - Omnipress
VL  - 25
SP  - 1080
EP  - 1087
DO  - 10.1145/1390156.1390292
L1  - https://lawrennd.github.io/publications/files/topology.pdf
UR  - /publications/urtasun-topology08.html
AB  - In dimensionality reduction approaches, the data are typically embedded in a Euclidean latent space. However for some data sets this is inappropriate. For example, in human motion data we expect latent spaces that are cylindrical or a toroidal, that are poorly captured with a Euclidean space. In this paper, we present a range of approaches for embedding data in a non-Euclidean latent space. Our focus is the Gaussian Process latent variable model. In the context of human motion modeling this allows us to (a) learn models with interpretable latent directions enabling, for example, style/content separation, and (b) generalise beyond the data set enabling us to learn transitions between motion styles even though such transitions are not present in the data.
ER  -

APA


Urtasun, R., Fleet, D.J., Geiger, A., Popović, J., Darrell, T.J. & Lawrence, N.D.. (2008). Topologically-Constrained Latent Variable Models. Proceedings of the International Conference in Machine Learning 25:1080-1087 doi:10.1145/1390156.1390292 Available from /publications/urtasun-topology08.html.