Nonnegative compression for Semi-Nonnegative Independent Component Analysis

In 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.