PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Local distance preservation in the GP-LVM through back constraints
Neil Lawrence and Joaquin Quinonero Candela
In: ICML 2006, 25-29th June 2006, Pittsburgh, U.S.A..

Abstract

The Gaussian process latent variable model (GP-LVM) is a generative approach to non-linear low dimensional embedding, that provides a smooth probabilistic mapping from latent to data space. It is also a non-linear generalization of probabilistic PCA (PPCA) [Tipping:probpca99]. While most approaches to non-linear dimensionality methods focus on preserving local distances in data space, the GP-LVM focusses on exactly the opposite. Being a smooth mapping from latent to data space, it focusses on keeping things apart in latent space that are far apart in data space. In this paper we first provide an overview of dimensionality reduction techniques, placing the emphasis on the kind of distance relation preserved. We then show how the GP-LVM can be generalized, through back constraints, to additionally preserve local distances. We give illustrative experiments on common data sets.

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EPrint Type:Conference or Workshop Item (Paper)
Additional Information:Software available from http://www.dcs.shef.ac.uk/~neil/fgplvm/
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:2607
Deposited By:Neil Lawrence
Deposited On:22 November 2006