# Generalised Component Analysis

Neil D. Lawrence, University of Sheffield
Michael E. Tipping

#### 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 indpendent and principal components, as well as to determine the number of independent components, on toy and real word data-sets.

  @TechReport{lawrence-gca01, title = {Generalised Component Analysis}, author = {Neil D. Lawrence and Michael E. Tipping}, year = {2003}, institution = {The University of Sheffield, Department of Computer Science}, number = {CS-03-10}, month = {00}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2003-01-01-lawrence-gca01.md}, 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 indpendent and principal components, as well as to determine the number of independent components, on toy and real word data-sets.}, key = {Lawrence:GCA01}, note = {}, linkpsgz = {ftp://ftp.dcs.shef.ac.uk/home/neil/gca.ps.gz}, linksoftware = {http://inverseprobability.com/gca/}, group = {shefml} }
 %T Generalised Component Analysis %A Neil D. Lawrence and Michael E. Tipping %B %D %F lawrence-gca01 %P -- %R %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 indpendent and principal components, as well as to determine the number of independent components, on toy and real word data-sets. 
 TY - CPAPER TI - Generalised Component Analysis AU - Neil D. Lawrence AU - Michael E. Tipping PY - 2003/01/01 DA - 2003/01/01 ID - lawrence-gca01 SP - EP - 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 indpendent and principal components, as well as to determine the number of independent components, on toy and real word data-sets. ER - 
 Lawrence, N.D. & Tipping, M.E.. (2003). Generalised Component Analysis.(CS-03-10):-