A unified neural bigradient algorithm for robust PCA and MCA

A new instantaneous-gradient search algorithm for computing a principal component or minor component type solution is proposed. The algorithm can use normalized Hebbian or anti-Hebbian learning in a unified formula. Starting from one-unit rule, a multi-unit algorithm is developed which can simultaneously extract several robust counterparts of the principal or minor eigenvectors of the data covariance matrix. Standard principal or minor components emerge as special cases from the general non-quadratic criterion. The learning rule is analyzed mathematically, and the theoretical results are verified by simulations. The proposed bigradient approach can be applied to blind separation of independent source signals from their linear mixtures.