A Parallel Computing Method for the Computation of the Moore-Penrose Generalized Inverse for Shared-Memory Architectures

The computation of the Moore-Penrose generalized inverse is a commonly used operation in various fields such as the training of neural networks based on random weights. Therefore, a fast computation of this inverse is important for problems where such neural networks provide a solution. However, due...

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Bibliographic Details
Published in:IEEE access Vol. 11; p. 1
Main Authors: Gelvez-Almeida, Elkin, Barrientos, Ricardo J., Vilches-Ponce, Karina, Mora, Marco
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.01.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Computational efficiency
Computer architecture
Computer memory
Computing time
Generalized inverse
High-performance computing
Matrix decomposition
Moore–Penrose generalized inverse matrix
Neural networks
neural networks with random weights
parallel computing
Parallel processing
Partitioning algorithms
Sparse matrices
Strassen algorithm
Symmetric matrices
ISSN:2169-3536, 2169-3536
Online Access:Get full text
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Summary:The computation of the Moore-Penrose generalized inverse is a commonly used operation in various fields such as the training of neural networks based on random weights. Therefore, a fast computation of this inverse is important for problems where such neural networks provide a solution. However, due to the growth of databases, the matrices involved have large dimensions, thus requiring a significant amount of processing and execution time. In this paper, we propose a parallel computing method for the computation of the Moore-Penrose generalized inverse of large-size full-rank rectangular matrices. The proposed method employs the Strassen algorithm to compute the inverse of a nonsingular matrix and is implemented on a shared-memory architecture. The results show a significant reduction in computation time, especially for high-rank matrices. Furthermore, in a sequential computing scenario (using a single execution thread), our method achieves a reduced computation time compared with other previously reported algorithms. Consequently, our approach provides a promising solution for the efficient computation of the Moore-Penrose generalized inverse of large-size matrices employed in practical scenarios.
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ISSN:2169-3536
2169-3536
DOI:10.1109/ACCESS.2023.3338544