"An iterative nonlinear Gaussianization algorithm for resampling dependent components," (with J.-J. Lin and R. A. Levine), Proc. 2nd International Workshop on Independent Component Analysis and Blind Signal Separation, pp.245-250, 2000.

Abstract

We propose an Iterative Nonlinear Gaussianization Algorithm (INGA), which seeks a nonlinear map from a set of dependent random variables to independent Gaussian random variables. A direct motivation of the INGA is to extend the principal component analysis (PCA) which transforms a set of correlated random variables into uncorrelated (independent up to second order) random variables. An obvious advantage of deriving independent components is that we can simulate a stochastic process of dependent multivariate variables by sampling univariate independent variables. The quality of the transformation is evaluated by statistical tests on the Kullback-Leibler (KL) distance between the distribution of the transformed variables the standard multivariate Gaussian distribution N(0,I). The quality of the simulations is evaluated quantitatively by the statistics of the KL distances between the sample mean distribution of the original samples and that of the simulated samples. Several numerical examples including synthetic and real-life image databases show the capabilities and limitations of INGA.

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