Geometric algorithms for the non-whitened one-unit linear Independent Component Analysis problem

In this paper, we study the problem of one-unit linear independent component analysis (ICA) without whitening. The FastICA algorithm is arguably the most popular algorithm for solving the whitened one-unit linear ICA problem. Although a modified FastICA has been already proposed to solve the non-whitened one-unit linear ICA problem, there is unfortunately no known analysis regarding its effectiveness and efficiency. In this work, the non-whitened FastICA algorithm is revisited and analyzed in the framework of geometric optimization algorithms. In this paper, a conjugate gradient (CG) algorithm for the non-whitened one-unit linear ICA problem is developed as well. Local convergence properties of both algorithms are discussed. Finally, local convergence performance of the algorithms is investigated by several numerical experiments.