Monte Carlo algorithm for least dependent non-negative mixture decomposition

We propose a simulated annealing algorithm (stochastic non-negative independent component analysis, SNICA) for blind decomposition of linear mixtures of non-negative sources with non-negative coefficients. The demixing is based on a Metropolis-type Monte Carlo search for least dependent components, with the mutual information between recovered components as a cost function and their non-negativity as a hard constraint. Elementary moves are shears in two-dimensional subspaces and rotations in three-dimensional subspaces. The algorithm is geared at decomposing signals whose probability densities peak at zero, the case typical in analytical spectroscopy and multivariate curve resolution. The decomposition performance on large samples of synthetic mixtures and experimental data is much better than that of traditional blind source separation methods based on principal component analysis (MILCA, FastICA, RADICAL) and chemometrics techniques (SIMPLISMA, ALS, BTEM).