Nonnegative Compression for Semi-Nonnegative Independent Component Analysis

International audienceIn many Independent Component Analysis (ICA) problems the mixing matrix is nonnegative while the sources are unconstrained, giving rise to what we call hereafter the Semi-Nonnegative ICA (SN-ICA) problems. Exploiting the nonnegativity property can improve the ICA result. Besides, in some practical applications, the dimension of the observation space must be reduced. However, the classical dimension compression procedure, such as prewhitening, breaks the nonnegativity property of the compressed mixing matrix. In this paper, we introduce a new nonnegative compression method, which guarantees the nonnegativity of the compressed mixing matrix. Simulation results show its fast convergence property. An illustration of Blind Source Separation (BSS) of Magnetic Resonance Spectroscopy (MRS) data confirms the validity of the proposed method

Nonnegative Joint Diagonalization by Congruence Based on LU Matrix Factorization

International audienceIn this letter, a new algorithm for joint diagonalization of a set of matrices by congruence is proposed to compute the nonnegative joint diagonalizer. The nonnegativity constraint is imposed by means of a square change of variables. Then we formulate the high-dimensional optimization problem into several sequential polynomial subproblems using LU matrix factorization. Numerical experiments on simulated matrices emphasize the advantages of the proposed method, especially in the case of degeneracies such as for low SNR values and a small number of matrices. An illustration of blind separation of nuclear magnetic resonance spectroscopy confirms the validity and improvement of the proposed method