Abstract:
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Independent component analysis (ICA) is a popular approach for finding a suitable representation of multivariate data. The independent component model is generalized to a linear latent variable model with both non-Gaussian components (signals) and Gaussian components (noise), where observed components are linear combinations of independent components. Generalized independent component analysis (GICA) estimates the transformation matrix from observed components to independent components. We propose an optimization method to improve the estimation in which non-Gaussian components and Gaussian components are estimated simultaneously. We measure the divergence of estimated components from the Gaussian distribution via a general class of statistics, maximizing the divergence of each non-Gaussian component, while minimizing the divergence of each Gaussian component. We introduce a statistical test to decide the number of non-Gaussian components based on the divergence of all components. Throughout a variety of simulations, our method is competitive with other existing methods, in both estimating the transformation matrix and determining the number of non-Gaussian components accurately.
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