The FastICA algorithm for independent component analysis and projection pursuit

Independent component analysis, or ICA, is a statistical technique that represents a multidimensional random vector as a linear combination of nongaussian random variables ('independent components') that are as independent as possible. ICA is a nongaussian version of factor analysis, and somewhat similar to principal component analysis. ICA has many applications in data analysis, source separation, and feature extraction.

Projection pursuit is a technique for exploratory data analysis with emphasis on visualization. It is  based on finding low-dimensional projections of multivariate data that show highly nongaussian distributions. Projection pursuit is technically very closely related to ICA.

The FastICA algorithm is a computationally highly efficient method for performing the estimation of ICA. It uses a fixed-point iteration scheme that has been found in independent experiments to be 10-100 times faster than conventional gradient descent methods for ICA. Another advantage of the FastICA algorithm is that it can be used to perform projection pursuit as well, thus providing a general-purpose data analysis method that can be used both in an exploratory fashion and for estimation of independent components (or sources). Here are some publications on the algorithm.

The FastICA package for MATLAB (versions 5 or 4) is  program package with graphical user interface that implements the fixed-point algorithm for ICA. See the FastICA home page.

More information on ICA

ICA research at Helsinki University of Technology