An MM Estimation Algorithm for Independent Component Analysis

Estimating the unmixing matrix in independent component analysis (ICA) by maximizing the statistical independence of the sources has been a central problem over the past few decades. This paper exploits the minorization-maximization (MM) principle by constructing a quadratic lower-bound surrogate for its log-likelihood. We derive an explicit update that satisfies the surrogate's first-order stationarity condition using the Fan-von Neumann inequality. Its cost per iteration is dominated by two matrix-matrix multiplications and a singular value decomposition of a small square matrix, resulting in low computational overhead and making the method amenable to GPU acceleration. Across three real datasets, the proposed MM method consistently runs faster than three Newton-type algorithms, including Picard's method, while attaining comparable or higher loglikelihood values. Particularly, the GPU version of MM is faster by an order of magnitude.