Lagrange constraint neural network for audio varying BSS

Harold H. Szu; Charles C. Hsu

doi:10.1117/12.458767

8 March 2002 Lagrange constraint neural network for audio varying BSS

Harold H. Szu, Charles C. Hsu

Proceedings Volume 4738, Wavelet and Independent Component Analysis Applications IX; (2002) https://doi.org/10.1117/12.458767
Event: AeroSense 2002, 2002, Orlando, FL, United States

Abstract

Lagrange Constraint Neural Network (LCNN) is a statistical-mechanical ab-initio model without assuming the artificial neural network (ANN) model at all but derived it from the first principle of Hamilton and Lagrange Methodology: H(S,A)= f(S)- (lambda) C(s,A(x,t)) that incorporates measurement constraint C(S,A(x,t))= (lambda) ([A]S-X)+((lambda) ₀-1)((Sigma) _is_i -1) using the vector Lagrange multiplier-(lambda) and a- priori Shannon Entropy f(S) = -(Sigma) _i s_i log s_i as the Contrast function of unknown number of independent sources s_i. Szu et al. have first solved in 1997 the general Blind Source Separation (BSS) problem for spatial-temporal varying mixing matrix for the real world remote sensing where a large pixel footprint implies the mixing matrix [A(x,t)] necessarily fill with diurnal and seasonal variations. Because the ground truth is difficult to be ascertained in the remote sensing, we have thus illustrated in this paper, each step of the LCNN algorithm for the simulated spatial-temporal varying BSS in speech, music audio mixing. We review and compare LCNN with other popular a-posteriori Maximum Entropy methodologies defined by ANN weight matrix-[W] sigmoid-(sigma) post processing H(Y=(sigma) ([W]X)) by Bell-Sejnowski, Amari and Oja (BSAO) called Independent Component Analysis (ICA). Both are mirror symmetric of the MaxEnt methodologies and work for a constant unknown mixing matrix [A], but the major difference is whether the ensemble average is taken at neighborhood pixel data X's in BASO or at the a priori sources S variables in LCNN that dictates which method works for spatial-temporal varying [A(x,t)] that would not allow the neighborhood pixel average. We expected the success of sharper de-mixing by the LCNN method in terms of a controlled ground truth experiment in the simulation of variant mixture of two music of similar Kurtosis (15 seconds composed of Saint-Saens Swan and Rachmaninov cello concerto).

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Harold H. Szu and Charles C. Hsu "Lagrange constraint neural network for audio varying BSS", Proc. SPIE 4738, Wavelet and Independent Component Analysis Applications IX, (8 March 2002); https://doi.org/10.1117/12.458767

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