Regularized Gradient algorithm for Non-Negative Independent Component Analysis

Independent Component Analysis (ICA) is a well-known technique for solving blind source separation (BSS) problem. However “classical” ICA algorithms seem not suited for non-negative sources. This paper proposes a gradient descent approach for solving the Non-Negative Independent Component Analysis problem (NNICA). NNICA original separation criterion contains the discontinuous sign function whose minimization may lead to ill convergence (local minima) especially for sparse sources. Replacing the discontinuous function by a continuous one tanh, we propose a more accurate regularized Gradient algorithm called “Exact” Regularized Gradient (ERG) for NNICA. Experiments on synthetic data with different sparsity degrees illustrate the efficiency of the proposed method and a comparison shows that the proposed ERG outperforms existing methods.