title: How many separable sources? Model selection in independent components analysis.
abstract: Unlike mixtures consisting solely of non-Gaussian sources, mixtures including two or more Gaussian components cannot be separated using standard independent components analysis methods that are based on higher order statistics and independent observations. The mixed Independent Components Analysis/Principal Components Analysis (mixed ICA/PCA) model described here accommodates one or more Gaussian components in the independent components analysis model and uses principal components analysis to characterize contributions from this inseparable Gaussian subspace. Information theory can then be used to select from among potential model categories with differing numbers of Gaussian components. Based on simulation studies, the assumptions and approximations underlying the Akaike Information Criterion do not hold in this setting, even with a very large number of observations. Cross-validation is a suitable, though computationally intensive alternative for model selection. Application of the algorithm is illustrated using Fisher's iris data set and Howells' craniometric data set. Mixed ICA/PCA is of potential interest in any field of scientific investigation where the authenticity of blindly separated non-Gaussian sources might otherwise be questionable. Failure of the Akaike Information Criterion in model selection also has relevance in traditional independent components analysis where all sources are assumed non-Gaussian.
authors: Departments of Neurology and of Psychiatry and Biobehavioral Sciences, David Geffen School of Medicine at the University of California Los Angeles, Los Angeles, California, United States of America.
authors: Roger P
authors: RP
authors: Woods
authors: Department of Applied Mathematics and Computer Science, Technical University of Denmark, Lyngby, Denmark.
authors: Lars Kai
authors: LK
authors: Hansen
authors: Rotman Research Institute, Baycrest, and Department of Medical Biophysics, University of Toronto, Toronto, Canada.
authors: Stephen
authors: S
authors: Strother
mesh_terms: D000465:Algorithms; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D016011:Normal Distribution; D025341:Principal Component Analysis; D012886:Skull / Q000033:anatomy & histology