Multivariate Density Factorization for Independent Component Analysis: An Unsupervised Artificial Neural Network Approach

Mark Girolami, Colin Fyfe
Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics, PMLR R1:223-230, 1997.

Abstract

We propose a novel homogenous nonlinear self-organising network which employs solely computationally simple hebbian and anti-hebbian learning, in approximating a linear independent component analysis (ICA). The learning algorithms diagonalise the transformed data covariance matrix and approximate an orthogonal rotation which maximises the sum offourth order cumulants. This provides factorisation of the input multivariate density into the individual independent latent marginal densities. We apply this network to linear mixtures of data, which are inherently non-gaussian and have both Laplacian and bi-modal probability densities. We show that the proposed network is capable of factorising multivariate densities which are linear mixtures of independent latent playkurtic, leptokurtic and uniform distributions.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR1-girolami97a, title = {Multivariate Density Factorization for Independent Component Analysis: An Unsupervised Artificial Neural Network Approach}, author = {Girolami, Mark and Fyfe, Colin}, booktitle = {Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics}, pages = {223--230}, year = {1997}, editor = {Madigan, David and Smyth, Padhraic}, volume = {R1}, series = {Proceedings of Machine Learning Research}, month = {04--07 Jan}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/r1/girolami97a/girolami97a.pdf}, url = {https://proceedings.mlr.press/r1/girolami97a.html}, abstract = {We propose a novel homogenous nonlinear self-organising network which employs solely computationally simple hebbian and anti-hebbian learning, in approximating a linear independent component analysis (ICA). The learning algorithms diagonalise the transformed data covariance matrix and approximate an orthogonal rotation which maximises the sum offourth order cumulants. This provides factorisation of the input multivariate density into the individual independent latent marginal densities. We apply this network to linear mixtures of data, which are inherently non-gaussian and have both Laplacian and bi-modal probability densities. We show that the proposed network is capable of factorising multivariate densities which are linear mixtures of independent latent playkurtic, leptokurtic and uniform distributions.}, note = {Reissued by PMLR on 30 March 2021.} }
Endnote
%0 Conference Paper %T Multivariate Density Factorization for Independent Component Analysis: An Unsupervised Artificial Neural Network Approach %A Mark Girolami %A Colin Fyfe %B Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 1997 %E David Madigan %E Padhraic Smyth %F pmlr-vR1-girolami97a %I PMLR %P 223--230 %U https://proceedings.mlr.press/r1/girolami97a.html %V R1 %X We propose a novel homogenous nonlinear self-organising network which employs solely computationally simple hebbian and anti-hebbian learning, in approximating a linear independent component analysis (ICA). The learning algorithms diagonalise the transformed data covariance matrix and approximate an orthogonal rotation which maximises the sum offourth order cumulants. This provides factorisation of the input multivariate density into the individual independent latent marginal densities. We apply this network to linear mixtures of data, which are inherently non-gaussian and have both Laplacian and bi-modal probability densities. We show that the proposed network is capable of factorising multivariate densities which are linear mixtures of independent latent playkurtic, leptokurtic and uniform distributions. %Z Reissued by PMLR on 30 March 2021.
APA
Girolami, M. & Fyfe, C.. (1997). Multivariate Density Factorization for Independent Component Analysis: An Unsupervised Artificial Neural Network Approach. Proceedings of the Sixth International Workshop on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research R1:223-230 Available from https://proceedings.mlr.press/r1/girolami97a.html. Reissued by PMLR on 30 March 2021.

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