On Large Scale near Independent Blind Source Separation

Abstract

The thesis addresses Blind Source Separation (BSS) in Large Scale (LS) and near-Independent newline(nI) sources scenario. The large scale in BSS imply number of unknown sources ranging from 15 to 140, so that the corresponding number of unknowns to be optimized range from 100 to 10000. The real world sources producing either an added spurious local optima or a shift of global optima or both are defined to be near-independent with respect to the used BSS contrast as an optimization criteria. The exponentially increasing solution space with linearly increasing dimensions for optimization and added complexity in the optimization landscape due to the near-independent sources make the Large Scale near-Independent BSS (LSnIBSS) to be a more difficult problem than the BSS. As a solution to the LSnIBSS problem, the thesis derives suitable optimization criteria and a Large Scale Global Optimization (LSGO) technique. Looking Probability Density Function (PDF) as a generalized multivariate differentiable function, there is derived L2-Norm of Gradient of Function Difference (GFD) as a BSS contrast, where, GFD is the difference between gradient of product of marginal PDFs and gradient of joint PDF. A nonparametric estimation of the derived contrast is achieved through least squares based kernel method in a single stage directly, instead of a two stages indirect estimation method. The contrast estimation is a particular demonstration of a derived more general method for information field analysis through a newly introduced concept of Reference Information Potential (RIP). The performance of kernel methods depend upon the choice of kernel bandwidth parameter. There is derived Extended Rule-of-thumb (ExROT) for bandwidth parameter selection in Kernel Density Estimation (KDE). The method is based on Gram-Charlier A-Series expansion as an approximation to the unknown PDF, assuming it being near Gaussian. The ExROT is better, in terms of Integrated Mean Square Error (IMSE) criteria of performance, compare to the Silverman s Rule-of-thum