#### AN ITERATIVE NONLINEAR GAUSSIANIZATION ALGORITHM FOR RESAMPING DEPENDENT COMPONENTS

Jen-Jen Lin

emails: jjlin@mcu.edu.tw, saito@math.ucdavis.edu, levine@wald.ucdavis.edu

We propose an Iterative Nonlinear Gaussianization Algo-
rithm (INGA), which seeks a nonlinear map from a set of
dependent random variables to independent Gaussian ran-
dom 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 (inde-
pendent up to second order) random variables. An obvious
advantage of deriving independent components is that we
can simulate a stochastic process of dependent multivari-
ate variables by sampling univariate independent variables.
The quality of the transformation is evaluated by statis-
tical 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.