PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Gaussian process models for visualisation of high dimensional data
Neil Lawrence
In: NIPS 2003, 9-11 Dec 2003, Vancouver, Canada.

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.

Other (gzipped postscript)
EPrint Type:Conference or Workshop Item (Paper)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:912
Deposited By:Neil Lawrence
Deposited On:06 January 2005