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-entropy-based 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.