Optimization using fourier expansion over a geodesic for non-negative ICA

Abstract

We propose a new algorithm for the non-negative ICA problem, based on the rotational nature of optimization over a set of square orthogonal (orthonormal) matrices W, i.e. where WTW = WWT = In. Using a truncated Fourier expansion of J(t), we obtain a Newton-like update step along the steepest-descent geodesic, which automatically approximates to a usual (Taylor expansion) Newton update step near to a minimum. Experiments confirm that this algorithm is effective, and it compares favourably with existing non-negative ICA algorithms. We suggest that this approach could modified for other algorithms, such as the normal ICA task. © Springer-Verlag 2004.