Post factor analysis as a post-processing for ICA and new optimization algorithm as para-quantum dynamics

Optimization problems on the general Lie group GL(N, |R) are naturally considered as those on the coset R^x(N)/GL(N, R) when the optimum is scale invariant. In this paper, we propose a new algorithm for optimization problems on this coset, named nested Newton´s method, where we decompose the flow of optimization into quantum-like dynamics of N-particles under two-body interactions. Next, we propose a post-processing for independent component analysis (ICA) without pre-whitening, which we name the “post factor analysis” (post-FA). By post-FA we can estimate the noise variance beyond the known bound for the FA