Journal ArticleDOI
The Fixed-Point Algorithm and Maximum Likelihood Estimation forIndependent Component Analysis
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TLDR
It is shown that the fast fixed-point algorithm is closely connected to maximum likelihood estimation as well, and modifications of the algorithm maximize the likelihood without constraints.Abstract:
The author previously introduced a fast fixed-point algorithm for independent component analysis. The algorithm was derived from objective functions motivated by projection pursuit. In this paper, it is shown that the algorithm is closely connected to maximum likelihood estimation as well. The basic fixed-point algorithm maximizes the likelihood under the constraint of decorrelation, if the score function is used as the nonlinearity. Modifications of the algorithm maximize the likelihood without constraints.read more
Citations
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Journal ArticleDOI
Independent component analysis: algorithms and applications
Aapo Hyvärinen,Erkki Oja +1 more
TL;DR: The basic theory and applications of ICA are presented, and the goal is to find a linear representation of non-Gaussian data so that the components are statistically independent, or as independent as possible.
Journal ArticleDOI
Fast and robust fixed-point algorithms for independent component analysis
TL;DR: Using maximum entropy approximations of differential entropy, a family of new contrast (objective) functions for ICA enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions.
Journal ArticleDOI
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
TL;DR: This work suggests a two-stage separation process: a priori selection of a possibly overcomplete signal dictionary in which the sources are assumed to be sparsely representable, followed by unmixing the sources by exploiting the their sparse representability.
Book
Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning
TL;DR: Techniques covered range from traditional multivariate methods, such as multiple regression, principal components, canonical variates, linear discriminant analysis, factor analysis, clustering, multidimensional scaling, and correspondence analysis, to the newer methods of density estimation, projection pursuit, neural networks, and classification and regression trees.
Journal ArticleDOI
Recognizing faces with PCA and ICA
TL;DR: It is able to show that the FastICA algorithm configured according to ICA architecture II yields the highest performance for identifying faces, while the InfoMax algorithm configurations is better for recognizing facial actions.
References
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Journal ArticleDOI
An information-maximization approach to blind separation and blind deconvolution
TL;DR: It is suggested that information maximization provides a unifying framework for problems in "blind" signal processing and dependencies of information transfer on time delays are derived.
Journal ArticleDOI
Independent component analysis, a new concept?
TL;DR: An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time and may actually be seen as an extension of the principal component analysis (PCA).
Journal ArticleDOI
Fast and robust fixed-point algorithms for independent component analysis
TL;DR: Using maximum entropy approximations of differential entropy, a family of new contrast (objective) functions for ICA enable both the estimation of the whole decomposition by minimizing mutual information, and estimation of individual independent components as projection pursuit directions.
Book
Optimization by Vector Space Methods
TL;DR: This book shows engineers how to use optimization theory to solve complex problems with a minimum of mathematics and unifies the large field of optimization with a few geometric principles.
Journal ArticleDOI
A fast fixed-point algorithm for independent component analysis
Aapo Hyvärinen,Erkki Oja +1 more
TL;DR: A novel fast algorithm for independent component analysis is introduced, which can be used for blind source separation and feature extraction, and the convergence speed is shown to be cubic.