Refereed full papers (journals, book chapters, international conferences)

2000

This paper is an introduction to the concept of independent component analysis (ICA) which has recently been developed in the area of signal processing. ICA is a variant of principal component analysis (PCA) in which the components are assumed to be mutually statistically independent instead of merely uncorrelated. The stronger condition allows one to remove the rotational invariance of PCA, i.e. ICA provides a meaningful unique bilinear decomposition of two-way data that can be considered as a linear mixture of a number of independent source signals. The discipline of multilinear algebra offers some means to solve the ICA problem. In this paper we briefly discuss four orthogonal tensor decompositions that can be interpreted in terms of higher-order generalizations of the symmetric eigenvalue decomposition.