Topologically-Constrained Latent Variable Models

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

Cite this Paper


BibTeX
@InProceedings{pmlr-v-urtasun-topology08, title = {Topologically-Constrained Latent Variable Models}, author = {Raquel Urtasun and David J. Fleet and Andreas Geiger and Jovan Popović and Trevor J. Darrell and Neil D. Lawrence}, pages = {1080--1087}, year = {}, editor = {}, volume = {25}, url = {http://inverseprobability.com/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 %C Proceedings of Machine Learning Research %D %E %F pmlr-v-urtasun-topology08 %I PMLR %J Proceedings of Machine Learning Research %P 1080--1087 %R 10.1145/1390156.1390292 %U http://inverseprobability.com %V %W PMLR %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 - PY - DA - ED - ID - pmlr-v-urtasun-topology08 PB - PMLR SP - 1080 DP - PMLR EP - 1087 DO - 10.1145/1390156.1390292 L1 - UR - http://inverseprobability.com/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.. (). Topologically-Constrained Latent Variable Models. , in PMLR :1080-1087

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