Matrix decomposition methods are extensively used for Collaborative Filtering in Recommender Systems. This research work investigates the effectiveness of various Matrix decomposition methods for Collaborative Filtering (CF) to predict recommendations. There is a tradeoff between the scalability and quality of predictions; Recommendations made by Singular Value Decomposition (SVD) based algorit...

We explore a connection between the singular value decomposition (SVD) and functional principal component analysis (FPCA) models in high-dimensional brain imaging applications. We formally link right singular vectors to principal scores of FPCA. This, combined with the fact that left singular vectors estimate principal components, allows us to deploy the numerical efficiency of SVD to fully est...

A reduced order modeling method based on a system description in terms of orthonormal Laguerre functions, together with a Krylov subspace decomposition technique is presented. The link with Padé approximation, the block Arnoldi process and singular value decomposition (SVD) leads to a simple and stable implementation of the algorithm. Novel features of the approach include the determination of ...

A recent image quality measure, M-SVD, can express the quality of distorted images either numerically or graphically. Based on the Singular Value Decomposition (SVD), it consistently measures the distortion across different distortion types and within a given distortion type at different distortion levels. The SVD decomposes every real matrix into a product of three matrices A = USV, where U an...

As it is known, groups of correlated 2D images of various kind could be represented as 3D images, which are mathematically described as 3 rd order tensors. Various generalizations of the Singular Value Decomposition (SVD) exist, aimed at the tensor description reduction. In this work, new approach is presented for 3 rd order tensor decomposition, where unlike the famous methods for decompositio...

In this paper, we present a GPU-accelerated implementation of randomized Singular Value Decomposition (SVD) algorithm on a large matrix to rapidly approximate the top-k dominating singular values and correspondent singular vectors. The fundamental idea of randomized SVD is to condense a large matrix into a small dense matrix by random sampling while keeping the important information. Then perfo...

Singular value decomposition (SVD) is one of the most useful matrix decompositions in linear algebra. Here, a novel application SVD recovering ripped photos was exploited. Recovery done by applying truncated iteratively. Performance evaluated using Frobenius norm. Results from few experimental were decent.

Singular Value Decomposition (SVD) is of great significance in theory development of mathematics and statistics. In this paper we propose the SVD for 3-dimensional (3-D) matrices and extend it to the general Multidimensional Matrices (MM). We use the basic operations associated with MM introduced by Solo to define some additional aspects of MM. We achieve SVD for 3-D matrix through these MM ope...

A new algorithm of Demmel et al. for computing the singular value decomposition (SVD) to high relative accuracy begins by computing a rank-revealing decomposition (RRD). Demmel et al. analyse the use of Gaussian elimination with complete pivoting (GECP) for computing the RRD. We investigate the use of QR factorization with complete pivoting (that is, column pivoting together with row sorting or...

The algorithm of Mathias and Stewart [A block QR algorithm and the singular value decomposition, Linear Algebra and Its Applications, 182:91-100, 1993] is examined as a tool for constructing regularized solutions to rank-deficient and ill-posed linear equations. The algorithm is based on a sequence of QR factorizations. If it is stopped after the first step it produces that same solution as the...