Fast Computation of Moore-Penrose Inverse Matrices

authors

• Courrieu Pierre

keywords

• Rank Deficient Least Square Systems
• Moore-Penrose Inverse
• Pseudoinverse
• Generalized Inverse
• Neural Learning
• Minimum-norm Synaptic Weight Vectors
• Regularization

document type

abstract

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.

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