A High Order Cumulants Based Multivariate Nonlinear Blind Source Separation Method |
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Authors: | Feng Zhang |
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Affiliation: | (1) Fairchild Semiconductor, 82 Running Hill Road, South Portland, ME 04106, USA |
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Abstract: | This article addresses the problem of identifying multiple linear and nonlinear patterns from multivariate noisy data represented
by an additive model. Following the proposed nonlinear model, the blind source separation (BSS) criterion, as a function of
high-order cumulants, is shown to produce a block-structured joint cumulant matrix by an orthogonal rotation. An intuitive
interpretation of this criterion is to rotate the elements of whitened principal component analysis (PCA) scores such that
they are as independent as possible. The resulting optimal joint cumulant matrix contains diagonal “blocks” that correspond
to the linear and nonlinear patterns caused by independent sources, from which linear patterns are recognized as in linear
BSS. The nonlinear patterns are identified by extracting their lower-dimensional manifolds via the principal curves method
and then transforming back to the original data space. As illustrated in the experimental study, the estimated linear and
nonlinear patterns will provide more accurate diagnosing of the root causes that contribute to the observed variability in
multivariate manufacturing.
Editor: Dale Schuurmans |
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Keywords: | blind source separation cumulant cumulant matrix principal component analysis |
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