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.