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 reduced order representation of a large data set is often realized through a principal component analysis based upon a singular value decomposition (SVD) of the data. The left singular vectors of a truncated SVD provide the reduced basis. In several applications such as facial analysis and protein dynamics, structural symmetry is inherent in the data. Typically, reflective or rotational symme...

The singular value decomposition (SVD) technique is extended to incorporate the additive components for approximation of a rectangular matrix by the outer products of vectors. While dual vectors of the regular SVD can be expressed one via linear transformation of the other, the modified SVD corresponds to the general linear transformation with the additive part. The method obtained can be relat...

This paper presents an alternative algorithm based on the singular value decomposition (SVD) that creates vector representation for linguistic units with reduced dimensionality. The work was motivated by an application aimed to represent text segments for further processing in a multi-document summarization system. The algorithm tries to compensate for SVD’s bias towards dominant-topic document...

Abstract—Image or document encryption is needed through egovernment data base. Really in this paper we introduce two matrices images, one is the public, and the second is the secret (original). The analyses of each matrix is achieved using the transformation of singular values decomposition. So each matrix is transformed or analyzed to three matrices say row orthogonal basis, column orthogonal ...

We present a new, statistically consistent algorithm for phylogenetic tree construction that uses the algebraic theory of statistical models (as developed in [5]). Our basic tool is the Singular Value Decomposition (SVD) from numerical linear algebra (see [3]). Starting with a multiple alignment of n species, we show that the SVD allows us to decide whether a split of the species occurs in thei...

image analysis, feature correspondence, stereo, singular value, decomposition This paper presents a new simple method for achieving feature correspondence across a pair of images which requires no calibration information and draws from the method proposed by Scott and Longuet Higgins [8]. Despite the well-known combinatorial complexity of the problem, this work shows that an acceptably good sol...

In this paper, we explore the application of SVD for collaborative filtering. We employ the incremental SVD method for predicting movie ratings based on previous user preferences using the dataset provided by Netflix. Various experiments are performed to see the effect of different parameters on the performance of the algorithm. The results show that the method has potential, although it is pro...

− The steady state data reconciliation problem is approached via a geometrical picture of its model and measurement abstract spaces. By completely utilizing the structure of the problem constraint matrix, via its singular value decomposition (SVD), data adjustment is accomplished and redundancy and observability conditions are formulated. As an example, the method is applied to a small network ...

An explicit procedure is presented for computing both model and data resolution matrices within a Paige-Saunders LSQR algorithm for iterative inversion in seismic tomography. These methods are designed to avoid the need for an additional singular value decomposition of the ray-path matrix. The techniques discussed are completely general since they are based on the multiplicity of equivalent exa...