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Abstract

The singular value decomposition (SVD) allows to write a matrix as a product of a left singular vectors matrix, a nonnegative singular values diagonal matrix and a right singular vectors matrix. Among the applications of the SVD are the principal component analysis, the low-rank matrix approximation and the solving of a linear system of equations. The methods used for computing this decomposition allow to get the complete or partial result. For very large size matrix, the probabilistic methods allow to get partial result by using less computational load. A power method is proposed in this paper for computing all or the $k$ first largest SVD subspaces for a real-valued matrix. The $k$ first right singular vectors of this method are the $k$ columns of a neural network encoder weight matrix. The accuracy of this iterative search method depends on the behavior of the singular values and the settings of the gradient search optimizer used. A R package implementing the proposed method is available at https://cran.r-project.org/web/packages/psvd/index.html.