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

#### Cite this Paper

BibTeX

```
@InProceedings{pmlr-v-lawrence-gca01,
title = {Generalised Component Analysis},
author = {Neil D. Lawrence and Michael E. Tipping},
year = {},
editor = {},
number = {CS-03-10},
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.}
}
```

Endnote

```
%0 Conference Paper
%T Generalised Component Analysis
%A Neil D. Lawrence
%A Michael E. Tipping
%B
%C Proceedings of Machine Learning Research
%D
%E
%F pmlr-v-lawrence-gca01
%I PMLR
%J Proceedings of Machine Learning Research
%P --
%U http://inverseprobability.com
%V
%N CS-03-10
%W PMLR
%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.
```

RIS

```
TY - CPAPER
TI - Generalised Component Analysis
AU - Neil D. Lawrence
AU - Michael E. Tipping
BT -
PY -
DA -
ED -
ID - pmlr-v-lawrence-gca01
PB - PMLR
SP -
DP - PMLR
EP -
L1 -
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 -
```

APA

`Lawrence, N.D. & Tipping, M.E.. (). Generalised Component Analysis. `*, in PMLR* (CS-03-10):-

#### Related Material

BibTeX

```
@InProceedings{/lawrence-gca01,
title = {Generalised Component Analysis},
author = {Neil D. Lawrence and Michael E. Tipping},
year = {},
editor = {},
number = {CS-03-10},
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.}
}
```

Endnote

```
%0 Conference Paper
%T Generalised Component Analysis
%A Neil D. Lawrence
%A Michael E. Tipping
%B
%C Proceedings of Machine Learning Research
%D
%E
%F /lawrence-gca01
%I PMLR
%J Proceedings of Machine Learning Research
%P --
%U http://inverseprobability.com
%V
%N CS-03-10
%W PMLR
%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.
```

RIS

```
TY - CPAPER
TI - Generalised Component Analysis
AU - Neil D. Lawrence
AU - Michael E. Tipping
BT -
PY -
DA -
ED -
ID - /lawrence-gca01
PB - PMLR
SP -
DP - PMLR
EP -
L1 -
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 -
```

APA

`Lawrence, N.D. & Tipping, M.E.. (). Generalised Component Analysis. `*, in PMLR* (CS-03-10):-