A new perspective on independent component analysis. (October 2015)

• Record Type: Journal Article
• Authors: Zhao, H.; Grigoriu, M.
• Is Part Of: Probabilistic engineering mechanics. Volume 42(2015:Oct.)
• Page Start: 64
• Page End: 70
• Publication Date: 2015-10
• Subjects: Independent component analysis -- Gaussian and non-Gaussian vectors -- Translation vectors -- Tail independent vectors -- Wind engineering; Engineering -- Statistical methods -- Periodicals; Mechanics, Applied -- Statistical methods -- Periodicals; Probabilities -- Periodicals; Ingénierie -- Méthodes statistiques -- Périodiques; Mécanique appliquée -- Méthodes statistiques -- Périodiques; Probabilités -- Périodiques; 620.100727
• DOI: 10.1016/j.probengmech.2015.09.011
• Languages: English
• ISSNs: 0266-8920

Abstract

Abstract: The paper examines the performance of the independent component analysis (ICA) which represents random vectors X by vectors X ˜ whose components are linear forms of independent random variables. The representation holds exactly or asymptotically in tails for Gaussian and non-Gaussian vectors with special characteristic functions or Gaussian, translation, and non-Gaussian vectors with independent tails. However, the distributions of X ˜ and its target vector X differ for a board range of non-Gaussian vectors. This statement is supported by numerical examples and theoretical arguments. It is also shown that the ICA representation X ˜ is approximately Gaussian for high dimensional vectors. Abstract : Highlights: ICA may or may not provide accurate representations for non-Gaussian vectors. ICA representations hold exactly or asymptotically in tails for some random vectors. ICA representations are approximately Gaussian for large dimensional random vectors.