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.

@InProceedings{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},
booktitle = {Proceedings of the International Conference in Machine Learning},
pages = {1080},
year = {2008},
editor = {Sam Roweis and Andrew McCallum},
volume = {25},
month = {00},
publisher = {Omnipress},
edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2008-01-01-urtasun-topology08.md},
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.},
crossref = {Roweis:icml08},
key = {Urtasun:topology08},
doi = {10.1145/1390156.1390292},
linkpdf = {ftp://ftp.dcs.shef.ac.uk/home/neil/topology.pdf},
group = {}
}

%T Topologically-Constrained Latent Variable Models
%A Raquel Urtasun and David J. Fleet and Andreas Geiger and Jovan Popović and Trevor J. Darrell and Neil D. Lawrence
%B
%C Proceedings of the International Conference in Machine Learning
%D
%E Sam Roweis and Andrew McCallum
%F urtasun-topology08
%I Omnipress
%P 1080--1087
%R 10.1145/1390156.1390292
%U http://inverseprobability.com/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.

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
PY - 2008/01/01
DA - 2008/01/01
ED - Sam Roweis
ED - Andrew McCallum
ID - urtasun-topology08
PB - Omnipress
SP - 1080
EP - 1087
DO - 10.1145/1390156.1390292
L1 - ftp://ftp.dcs.shef.ac.uk/home/neil/topology.pdf
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 -

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