Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models

Neil D. Lawrence
Journal of Machine Learning Research, 6:1783-1816, 2005.

Abstract

Summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure. In this paper we provide an overview of some existing techniques for discovering such embeddings. We then introduce a novel probabilistic interpretation of principal component analysis (PCA) that we term dual probabilistic PCA (DPPCA). The DPPCA model has the additional advantage that the linear mappings from the embedded space can easily be non-linearised through Gaussian processes. We refer to this model as a Gaussian process latent variable model (GP-LVM). Through analysis of the GP-LVM objective function, we relate the model to popular spectral techniques such as kernel PCA and multidimensional scaling. We then review a practical algorithm for GP-LVMs in the context of large data sets and develop it to also handle discrete valued data and missing attributes. We demonstrate the model on a range of real-world and artificially generated data sets.

Cite this Paper

BibTeX
@Article{Lawrence-pnpca05, title = {Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models}, author = {Lawrence, Neil D.}, journal = {Journal of Machine Learning Research}, pages = {1783--1816}, year = {2005}, volume = {6}, url = {http://inverseprobability.com/publications/lawrence-pnpca05.html}, abstract = {Summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure. In this paper we provide an overview of some existing techniques for discovering such embeddings. We then introduce a novel probabilistic interpretation of principal component analysis (PCA) that we term dual probabilistic PCA (DPPCA). The DPPCA model has the additional advantage that the linear mappings from the embedded space can easily be non-linearised through Gaussian processes. We refer to this model as a Gaussian process latent variable model (GP-LVM). Through analysis of the GP-LVM objective function, we relate the model to popular spectral techniques such as kernel PCA and multidimensional scaling. We then review a practical algorithm for GP-LVMs in the context of large data sets and develop it to also handle discrete valued data and missing attributes. We demonstrate the model on a range of real-world and artificially generated data sets.} }
Endnote
%0 Journal Article %T Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models %A Neil D. Lawrence %J Journal of Machine Learning Research %D 2005 %F Lawrence-pnpca05 %P 1783--1816 %U http://inverseprobability.com/publications/lawrence-pnpca05.html %V 6 %X Summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure. In this paper we provide an overview of some existing techniques for discovering such embeddings. We then introduce a novel probabilistic interpretation of principal component analysis (PCA) that we term dual probabilistic PCA (DPPCA). The DPPCA model has the additional advantage that the linear mappings from the embedded space can easily be non-linearised through Gaussian processes. We refer to this model as a Gaussian process latent variable model (GP-LVM). Through analysis of the GP-LVM objective function, we relate the model to popular spectral techniques such as kernel PCA and multidimensional scaling. We then review a practical algorithm for GP-LVMs in the context of large data sets and develop it to also handle discrete valued data and missing attributes. We demonstrate the model on a range of real-world and artificially generated data sets.
RIS
TY - JOUR TI - Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models AU - Neil D. Lawrence DA - 2005/11/01 ID - Lawrence-pnpca05 VL - 6 SP - 1783 EP - 1816 UR - http://inverseprobability.com/publications/lawrence-pnpca05.html AB - Summarising a high dimensional data set with a low dimensional embedding is a standard approach for exploring its structure. In this paper we provide an overview of some existing techniques for discovering such embeddings. We then introduce a novel probabilistic interpretation of principal component analysis (PCA) that we term dual probabilistic PCA (DPPCA). The DPPCA model has the additional advantage that the linear mappings from the embedded space can easily be non-linearised through Gaussian processes. We refer to this model as a Gaussian process latent variable model (GP-LVM). Through analysis of the GP-LVM objective function, we relate the model to popular spectral techniques such as kernel PCA and multidimensional scaling. We then review a practical algorithm for GP-LVMs in the context of large data sets and develop it to also handle discrete valued data and missing attributes. We demonstrate the model on a range of real-world and artificially generated data sets. ER -
APA
Lawrence, N.D.. (2005). Probabilistic Non-linear Principal Component Analysis with Gaussian Process Latent Variable Models. Journal of Machine Learning Research 6:1783-1816 Available from http://inverseprobability.com/publications/lawrence-pnpca05.html.

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