Gaussian Process Models for Visualisation of High Dimensional Data

Neil D. Lawrence

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Gaussian Process Models for Visualisation of High Dimensional Data

Neil D. Lawrence

Advances in Neural Information Processing Systems, MIT Press 16:329-336, 2004.

Abstract

In this paper we introduce a new underlying probabilistic model for principal component analysis (PCA). Our formulation interprets PCA as a particular Gaussian process prior on a mapping from a latent space to the observed data-space. We show that if the prior’s covariance function constrains the mappings to be linear the model is equivalent to PCA, we then extend the model by considering less restrictive covariance functions which allow non-linear mappings. This more general Gaussian process latent variable model (GPLVM) is then evaluated as an approach to the visualisation of high dimensional data for three different data-sets. Additionally our non-linear algorithm can be further kernelised leading to ‘twin kernel PCA’ in which a mapping between feature spaces occurs.

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Cite this Paper

BibTeX


@InProceedings{Lawrence:gplvm03,
  title = 	 {{G}aussian Process Models for Visualisation of High Dimensional Data},
  author = 	 {Lawrence, Neil D.},
  booktitle = 	 {Advances in Neural Information Processing Systems},
  pages = 	 {329--336},
  year = 	 {2004},
  editor = 	 {Thrun, Sebastian and Saul, Lawrence and Schölkopf, Bernhard},
  volume = 	 {16},
  address = 	 {Cambridge, MA},
  publisher =    {MIT Press},
  pdf = 	 {https://proceedings.neurips.cc/paper/2003/file/9657c1fffd38824e5ab0472e022e577e-Paper.pdf},
  url = 	 {/publications/lawrence-gplvm03.html},
  abstract = 	 {In this paper we introduce a new underlying probabilistic model for
principal component analysis (PCA). Our formulation interprets PCA
as a particular Gaussian process prior on a mapping from a latent
space to the observed data-space. We show that if the prior's
covariance function constrains the mappings to be linear the model
is equivalent to PCA, we then extend the model by considering less
restrictive covariance functions which allow non-linear
mappings. This more general Gaussian process latent variable model
(GPLVM) is then evaluated as an approach to the visualisation of
high dimensional data for three different data-sets. Additionally
our non-linear algorithm can be *further* kernelised leading to
'twin kernel PCA' in which a *mapping between feature spaces*
occurs.
}
}

Endnote

%0 Conference Paper
%T Gaussian Process Models for Visualisation of High Dimensional Data
%A Neil D. Lawrence
%B Advances in Neural Information Processing Systems
%D 2004
%E Sebastian Thrun
%E Lawrence Saul
%E Bernhard Schölkopf	
%F Lawrence:gplvm03
%I MIT Press
%P 329--336
%U /publications/lawrence-gplvm03.html
%V 16
%X In this paper we introduce a new underlying probabilistic model for
principal component analysis (PCA). Our formulation interprets PCA
as a particular Gaussian process prior on a mapping from a latent
space to the observed data-space. We show that if the prior's
covariance function constrains the mappings to be linear the model
is equivalent to PCA, we then extend the model by considering less
restrictive covariance functions which allow non-linear
mappings. This more general Gaussian process latent variable model
(GPLVM) is then evaluated as an approach to the visualisation of
high dimensional data for three different data-sets. Additionally
our non-linear algorithm can be *further* kernelised leading to
'twin kernel PCA' in which a *mapping between feature spaces*
occurs.

RIS


TY  - CPAPER
TI  - Gaussian Process Models for Visualisation of High Dimensional Data
AU  - Neil D. Lawrence
BT  - Advances in Neural Information Processing Systems
DA  - 2004/01/01
ED  - Sebastian Thrun
ED  - Lawrence Saul
ED  - Bernhard Schölkopf	
ID  - Lawrence:gplvm03
PB  - MIT Press
VL  - 16
SP  - 329
EP  - 336
L1  - https://proceedings.neurips.cc/paper/2003/file/9657c1fffd38824e5ab0472e022e577e-Paper.pdf
UR  - /publications/lawrence-gplvm03.html
AB  - In this paper we introduce a new underlying probabilistic model for
principal component analysis (PCA). Our formulation interprets PCA
as a particular Gaussian process prior on a mapping from a latent
space to the observed data-space. We show that if the prior's
covariance function constrains the mappings to be linear the model
is equivalent to PCA, we then extend the model by considering less
restrictive covariance functions which allow non-linear
mappings. This more general Gaussian process latent variable model
(GPLVM) is then evaluated as an approach to the visualisation of
high dimensional data for three different data-sets. Additionally
our non-linear algorithm can be *further* kernelised leading to
'twin kernel PCA' in which a *mapping between feature spaces*
occurs.

ER  -

APA


Lawrence, N.D.. (2004). Gaussian Process Models for Visualisation of High Dimensional Data. Advances in Neural Information Processing Systems 16:329-336 Available from /publications/lawrence-gplvm03.html.