An introduction to independent component analysis

This paper is an introduction to the concept of independent component analy sis (ICA) which has recently been developed in the area of signal processin g. ICA is a variant of principal component analysis (PCA) in which the comp onents are assumed to be mutually statistically independent instead of mere ly uncorrelated. The stronger condition allows one to remove the rotational invariance of PCA, i.e. ICA provides a meaningful unique bilinear decompos ition of two-way data that can be considered as a linear mixture of a numbe r of independent source signals. The discipline of multilinear algebra offe rs some means to solve the ICA problem. In this paper we briefly discuss fo ur orthogonal tensor decompositions that can be interpreted in terms of hig her-order generalizations of the symmetric eigenvalue decomposition. Copyri ght (C) 2000 John Wiley & Sons, Ltd.