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An introduction to independent component analysis
Author(s) -
De Lathauwer Lieven,
De Moor Bart,
Vandewalle Joos
Publication year - 2000
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/1099-128x(200005/06)14:3<123::aid-cem589>3.0.co;2-1
Subject(s) - independent component analysis , multilinear algebra , principal component analysis , multilinear map , eigenvalues and eigenvectors , bilinear interpolation , tensor (intrinsic definition) , uncorrelated , mathematics , rotational invariance , component (thermodynamics) , component analysis , decomposition , computer science , pattern recognition (psychology) , algorithm , algebra over a field , artificial intelligence , pure mathematics , statistics , physics , quantum mechanics , division algebra , thermodynamics , ecology , biology , filtered algebra
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. Copyright © 2000 John Wiley & Sons, Ltd.