Singular Value Decomposition update and its application to (Inc)-OP-ELM

In this paper, we consider the theory and the practical implementation of Singular Value Decomposition (SVD) update algorithm. By updating, we mean using previously computed SVD to compute the SVD of a matrix augmented by one column (or row). We compare it with the standard SVD algorithm in terms of...

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Bibliographic Details
Published inNeurocomputing (Amsterdam) Vol. 174; pp. 99 - 108
Main Authors Grigorievskiy, Alexander, Miche, Yoan, Käpylä, Maarit, Lendasse, Amaury
Format Journal Article
LanguageEnglish
Published Elsevier B.V 22.01.2016
Subjects
Extreme Learning Machine, ELM
Incremental ELM
Leave-one-out, LOO
OP-ELM
PRESS statistics
Singular Value Decomposition, SVD
Incremental ELM
OP-ELM
Singular Value Decomposition, SVD
PRESS statistics
Leave-one-out, LOO
Extreme Learning Machine, ELM
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Summary:In this paper, we consider the theory and the practical implementation of Singular Value Decomposition (SVD) update algorithm. By updating, we mean using previously computed SVD to compute the SVD of a matrix augmented by one column (or row). We compare it with the standard SVD algorithm in terms of computational complexity and accuracy. We show that SVD update algorithm scales better and works faster than SVD computed from scratch. In addition, we analyze errors in singular values after many consecutive updates and verify that they are within reasonable bounds. Finally, we apply SVD update to speed up OP-ELM algorithm and propose new algorithm (Inc)-OP-LEM. In conclusion, we believe that SVD update can be applied to other computational intelligence methods to improve their computational time and scaling.
ISSN:0925-2312
1872-8286
DOI:10.1016/j.neucom.2015.03.107