Fast Computation of Moore-Penrose Inverse Matrices

TL;DR

This paper introduces a fast algorithm based on Cholesky factorization for computing Moore-Penrose inverse matrices, significantly reducing computation time for large systems in neural learning applications.

Contribution

The paper presents a novel, efficient algorithm for Moore-Penrose inverse computation using full rank Cholesky factorization, improving speed over existing methods.

Findings

Substantially shorter computation times for large systems.

Comparable accuracy to existing algorithms.

Effective in neural learning contexts.

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.