Fast Computation of Moore-Penrose Inverse Matrices

Number of pages: 5. Typo page 26 line 3: one must read W=G^+F (instead of W=G^+W, which does not make sense!)International audienceMany 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