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.
Code (1)
Similar Papers 제목 키워드 기반
Differentiable SVD based on Moore-Penrose Pseudoinverse for Inverse Imaging Problems
Low-rank regularization-based deep unrolling networks have achieved remarkable success in various inverse imaging problems (IIPs). However, the singular value decomposition (SVD) is non-differentiable when duplicated sin…
compressed sensingImage Compressed SensingMRI ReconstructionSpectral Stability of Pseudoinverse-Based Extreme Learning Machine
Extreme Learning Machine (ELM) computes output weights analytically using the Moore-Penrose pseudoinverse. Although this leads to fast training, its numerical stability depends strongly on the conditioning of the hidden …
Comparing the Moore-Penrose Pseudoinverse and Gradient Descent for Solving Linear Regression Problems: A Performance Analysis
This paper investigates the comparative performance of two fundamental approaches to solving linear regression problems: the closed-form Moore-Penrose pseudoinverse and the iterative gradient descent method. Linear regre…
regressionGeneralized Inversion of Nonlinear Operators
Inversion of operators is a fundamental concept in data processing. Inversion of linear operators is well studied, supported by established theory. When an inverse either does not exist or is not unique, generalized inve…
Non-iterative recomputation of dense layers for performance improvement of DCNN
An iterative method of learning has become a paradigm for training deep convolutional neural networks (DCNN). However, utilizing a non-iterative learning strategy can accelerate the training process of the DCNN and surpr…
Object Recognition