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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