Funded by

Launch Day: Abstracts

[Up to: Launch Day 13 April 2005]

Solving the blind separation problem with FastICA

Prof Erkki Oja
Helsinki University of Technology, Finland

Independent Component Analysis (ICA) is a computational technique for revealing hidden factors that underlie sets of measurements or signals. ICA assumes a statistical model whereby the observed multivariate data, typically given as a large database of samples, are assumed to be linear or nonlinear mixtures of some unknown latent variables. The mixing coefficients are also unknown. The latent variables are nongaussian and mutually independent, and they are called the independent components of the observed data. By ICA, these independent components, also called sources or factors, can be found. Thus ICA can be seen as an extension to Principal Component Analysis and Factor Analysis. ICA is a much richer technique, however, capable of finding the sources when these classical methods fail completely.

In many cases, the measurements are given as a set of parallel signals or images. Typical examples are mixtures of simultaneous sounds or human voices that have been picked up by several microphones, brain images obtained by MRI, or several radio signals arriving at a portable phone. The term blind source separation is used to characterize this problem.

The lecture will cover some of the basic principles and approaches to independent component analysis, concentrating on the FastICA algorithm for separating a number of source signals or images from their linear instantaneous mixtures. Performance of the algorithm will be discussed. Some applications will be briefly covered: extraction of meaningful components of brain activity from biomedical images, finding topical factors from text documents, and finding hidden factors in climate patterns.

Source separation with Gaussian models

Prof Jean-François Cardoso
ENST, France

The "historical" approach to Independent Component Analysis (ICA) and to Blind Source Separation (BSS) has been to use express statistical independence using simple non Gaussian models. Here, "simple" means ignoring the temporal dependence of the signals to be separated (or ignoring spatial dependence in the case of images). It is possible, however, to build models with simple time (or space) dependence which allow for the blind separation of sources in the Gaussian framework.

The talk will describe such models and discuss some of their properties: the benefit of sufficient statistics (tanks to the Gaussian framework), the existence of fast algorithms, the connection with the notion of sparseness (as in the non Gaussian case), the ability to deal with noise in a straightforward manner.