Spherical mesh adaptive direct search for separating quasi-uncorrelated sources by range-based independent component analysis

A Derivative-Free Riemannian Powell's Method, Minimizing Hartley-Entropy-Based ICA Contrast

Even though the Hartley-entropy-based contrast function guarantees an unmixing local minimum, the reported nonsmooth optimization techniques that minimize this nondifferentiable function encounter computational bottlenecks. Toward this, Powell's derivative-free optimization method has been extended to a Riemannian manifold, namely, oblique manifold, for the recovery of quasi-correlated sources by minimizing this contrast function. The proposed scheme has been demonstrated to converge faster than the related algorithms in the literature, besides the impressive source separation results in simulations involving synthetic sources having finite-support distributions and correlated images.

Range-based ICA using a nonsmooth quasi-newton optimizer for electroencephalographic source localization in focal epilepsy

Independent component analysis (ICA) aims at separating a multivariate signal into independent nongaussian signals by optimizing a contrast function with no knowledge on the mixing mechanism. Despite the availability of a constellation of contrast functions, a Hartley-entropy-based ICA contrast endowed with the discriminacy property makes it an appealing choice as it guarantees the absence of mixing local optima. Fueled by an outstanding source separation performance of this contrast function in practical instances, a succession of optimization techniques has recently been adopted to solve the ICA problem. Nevertheless, the nondifferentiability of the considered contrast restricts the choice of the optimizer to the class of derivative-free methods. On the contrary, this letter concerns a Riemannian quasi-Newton scheme involving an explicit expression for the gradient to optimize the contrast function that is differentiable almost everywhere. Furthermore, the inexact line search insisting on the weak Wolfe condition and a terminating criterion befitting the partly smooth function optimization have been generalized to manifold settings, leaving the previous results intact. The investigations with diversified images and the electroencephalographic (EEG) data acquired from 45 focal epileptic subjects demonstrate the efficacy of our approach in terms of computational savings and reliable EEG source localization, respectively. Additional experimental results are available in the online supplement.

Nonsmooth ICA contrast minimization using a Riemannian Nelder-Mead method

This brief concerns the design and application of a Riemannian Nelder-Mead algorithm to minimize a Hartley-entropybased contrast function to reliably estimate the sources from their mixtures. Despite its nondifferentiability, the contrast function is endowed with attractive properties such as discriminacy, and hence warrants an effort to be effectively handled by a derivative-free optimizer. Aside from tailoring the Nelder-Mead technique to the constraint set, namely, oblique manifold, the source separation results attained in an empirical study with quasi-correlated synthetic signals and digital images are presented, which favor the proposed method on a comparative basis.