Fast Computation of Moore-Penrose Inverse Matrices

Many neural learning algorithms require to solve large least square systems in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for solving such systems, even with rank deficiency, and they provide minimum-norm vectors of synaptic weights, which contribute to the regularization of the input-output mapping. It is thus of interest to develop fast and accurate algorithms for computing Moore-Penrose inverse matrices. In this paper, an algorithm based on a full rank Cholesky factorization is proposed. The resulting pseudoinverse matrices are similar to those provided by other algorithms. However the computation time is substantially shorter, particularly for large systems. KeywordsRank Deficient Least Square Systems, Moore-Penrose Inverse, Pseudoinverse, Generalized Inverse, Neural Learning, Minimum-norm Synaptic Weight Vectors, Regularization.