Generalised Component Analysis

Neil D. Lawrence, Michael E. Tipping
, 2003.

Abstract

Principal component analysis is a well known approach for determining the principal sub-space of a data-set. Independent component analysis is a widely utilised technique for recovering the linearly embedded independent components of a data-set. In this paper we develop an algorithm that, for super-Gaussian sources, extracts the direction and number of independent components of a data-set and determines the principal sub-space of the remaining components. This is achieved through the use of a latent variable model. We refer to the approach as Generalised Component Analysis and demonstrate its ability to both extract independent and principal components, as well as to determine the number of independent components, on toy and real word data-sets.

Cite this Paper

BibTeX
@Misc{Lawrence:GCA01, title = {Generalised Component Analysis}, author = {Lawrence, Neil D. and Tipping, Michael E.}, year = {2003}, number = {CS-03-10}, pdf = {https://lawrennd.github.io/publications/files/gca.pdf}, url = {http://inverseprobability.com/publications/lawrence-gca01.html}, abstract = {Principal component analysis is a well known approach for determining the principal sub-space of a data-set. Independent component analysis is a widely utilised technique for recovering the linearly embedded independent components of a data-set. In this paper we develop an algorithm that, for super-Gaussian sources, extracts the direction and number of independent components of a data-set and determines the principal sub-space of the remaining components. This is achieved through the use of a latent variable model. We refer to the approach as Generalised Component Analysis and demonstrate its ability to both extract independent and principal components, as well as to determine the number of independent components, on toy and real word data-sets.}, note = {} }
Endnote
%0 Generic %T Generalised Component Analysis %A Neil D. Lawrence %A Michael E. Tipping %D 2003 %F Lawrence:GCA01 %U http://inverseprobability.com/publications/lawrence-gca01.html %N CS-03-10 %X Principal component analysis is a well known approach for determining the principal sub-space of a data-set. Independent component analysis is a widely utilised technique for recovering the linearly embedded independent components of a data-set. In this paper we develop an algorithm that, for super-Gaussian sources, extracts the direction and number of independent components of a data-set and determines the principal sub-space of the remaining components. This is achieved through the use of a latent variable model. We refer to the approach as Generalised Component Analysis and demonstrate its ability to both extract independent and principal components, as well as to determine the number of independent components, on toy and real word data-sets. %Z
RIS
TY - GEN TI - Generalised Component Analysis AU - Neil D. Lawrence AU - Michael E. Tipping DA - 2003/05/23 ID - Lawrence:GCA01 IS - CS-03-10 L1 - https://lawrennd.github.io/publications/files/gca.pdf UR - http://inverseprobability.com/publications/lawrence-gca01.html AB - Principal component analysis is a well known approach for determining the principal sub-space of a data-set. Independent component analysis is a widely utilised technique for recovering the linearly embedded independent components of a data-set. In this paper we develop an algorithm that, for super-Gaussian sources, extracts the direction and number of independent components of a data-set and determines the principal sub-space of the remaining components. This is achieved through the use of a latent variable model. We refer to the approach as Generalised Component Analysis and demonstrate its ability to both extract independent and principal components, as well as to determine the number of independent components, on toy and real word data-sets. N1 - ER -
APA
Lawrence, N.D. & Tipping, M.E.. (2003). Generalised Component Analysis. (CS-03-10) Available from http://inverseprobability.com/publications/lawrence-gca01.html.

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