Independent Component Analysis

Independent component analysis is a useful extension of the principal component analysis (PCA). It has been developed some years ago in context with blind source separation applications jutten,comon. In PCA, the eigenvectors of the signal covariance matrix ${\bf C} = E\{ {\bf xx}^T\}$ give the directions of largest variance on the input data ${\bf x}$. The principal components found by projecting ${\bf x}$ onto those perpendicular basis vectors are uncorrelated, and their directions orthogonal.

However, standard PCA is not suited for dealing with non-Gaussian data. Several authors, from the signal processing to the artificial neural network communities, have shown that information obtained from a second-order method such as PCA is not enough and higher-order statistics are needed when dealing with the more demanding restriction of independence jutten,comon. A good tutorial on neural ICA implementations is available by kar+. The particular algorithm used in this study was presented and derived by Hyvärinen and Oja hyvar,hyvar_b.