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.
One-unit algorithms for ICA estimate the independent components (or projection pursuit directions) of the data one-by-one, which is in contrast to most conventional ICA algorithms, which try to estimate all the independent components at the same time. One-unit (or deflation) algorithms generally fall into one of the two categories: (ordinary) gradient algorithms, and fixed-point algorithms.
The FastICA algorithm is a computationally highly
efficient method for performing the estimation of ICA.
In independent experiments
it has been found to be 10-100 times faster than conventional gradient
descent methods for ICA. Another advantage of the fixed-point algorithm
is that since it is based on one-by-one estimation, it can be used to perform
projection pursuit as well. Thus it provides a general-purpose data
analysis method that can be used both in an exploratory fashion and for
estimation of independent components (or sources). It can be used, however,
to implement classical maximum likelihood ICA estimation as well.
Here you can
find publications on the fixed-point algorithm (and other one-unit
algorithms).
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.
Home page of the ICA group at Helsinki University of Technology