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Open AccessFeature PaperArticle

First Order and Second Order Learning Algorithms on the Special Orthogonal Group to Compute the SVD of Data Matrices

1
Department of Information Engineering, Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy
2
Graduate School of Computer Engineering, Università di Modena e Reggio Emilia, Via Università 4, 41121 Modena, Italy
3
Graduate School of Computer Science and Automation Engineering, Università Politecnica delle Marche, Via Brecce Bianche, 60131 Ancona, Italy
4
Graduate School of Computer Science, Università di Parma, Via Università 12, 43121 Parma, Italy
*
Author to whom correspondence should be addressed.
Electronics 2020, 9(2), 334; https://doi.org/10.3390/electronics9020334
Received: 16 December 2019 / Revised: 10 February 2020 / Accepted: 11 February 2020 / Published: 15 February 2020
(This article belongs to the Special Issue Recent Machine Learning Applications to Internet of Things (IoT))
The present paper deals with neural algorithms to learn the singular value decomposition (SVD) of data matrices. The neural algorithms utilized in the present research endeavor were developed by Helmke and Moore (HM) and appear under the form of two continuous-time differential equations over the special orthogonal group of matrices. The purpose of the present paper is to develop and compare different numerical schemes, under the form of two alternating learning rules, to learn the singular value decomposition of large matrices on the basis of the HM learning paradigm. The numerical schemes developed here are both first-order (Euler-like) and second-order (Runge-like). Moreover, a reduced Euler scheme is presented that consists of a single learning rule for one of the factors involved in the SVD. Numerical experiments performed to estimate the optical-flow (which is a component of modern IoT technologies) in real-world video sequences illustrate the features of the novel learning schemes. View Full-Text
Keywords: singular value decomposition; initial value problem; first-order numerical method; second-order numerical method; manifold calculus and Lie groups; learning system; Internet of Things singular value decomposition; initial value problem; first-order numerical method; second-order numerical method; manifold calculus and Lie groups; learning system; Internet of Things
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MDPI and ACS Style

Fiori, S.; Del Rossi, L.; Gigli, M.; Saccuti, A. First Order and Second Order Learning Algorithms on the Special Orthogonal Group to Compute the SVD of Data Matrices. Electronics 2020, 9, 334.

AMA Style

Fiori S, Del Rossi L, Gigli M, Saccuti A. First Order and Second Order Learning Algorithms on the Special Orthogonal Group to Compute the SVD of Data Matrices. Electronics. 2020; 9(2):334.

Chicago/Turabian Style

Fiori, Simone; Del Rossi, Lorenzo; Gigli, Michele; Saccuti, Alessio. 2020. "First Order and Second Order Learning Algorithms on the Special Orthogonal Group to Compute the SVD of Data Matrices" Electronics 9, no. 2: 334.

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