We propose new algorithms for singular value decomposition (SVD) of very large-scale matrices based on a low-rank tensor approximation technique called the tensor train (TT) format. The proposed algorithms can compute several dominant singular values and corresponding singular vectors for large-scale structured matrices given in a TT format. The computational complexity of the proposed methods ...

Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose tangled evolution is not consistent with the structure of the underlying random process. The solution to this problem is developed as follows: (i) a SVD with re...

BACKGROUND AND PURPOSE It is unknown whether changes in cerebral small vessel disease (SVD) are limited to the brain or part of a generalized vascular disorder. METHODS We examined the sublingual microcirculation of 10 healthy controls, 10 patients with large vessel disease, and 8 with SVD, with side-stream dark field imaging. We analyzed 146 video fragments masked to the origin of the videos...

Spectral embedding based on the Singular Value Decomposition (SVD) is a widely used “preprocessing” step in many learning tasks, typically leading to dimensionality reduction by projecting onto a number of dominant singular vectors and rescaling the coordinate axes (by a predefined function of the singular value). However, the number of such vectors required to capture problem structure grows w...

In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensorSingular Value Decomposition (t-SVD)[1], which is a group theoretic framework for tensor decomposition. In contrast to popular existing tensor decomposition techniques such as higher-order SVD (HOSVD), t-SVD has optimality properties similar to t...

With the development of data mining technologies, privacy protection has become a challenge for data mining applications in many fields. To solve this problem, many privacy-preserving data mining methods have been proposed. One important type of such methods is based on Singular Value Decomposition (SVD). The SVD-based method provides perturbed data instead of original data, and users extract o...

In this paper a parallel implementation of the SVD{updating algorithm using approximate rotations is presented. In its original form the SVD{updating algorithm had numerical problems if no reorthogonalization steps were applied. Representing the orthogonal matrix V (right singular vectors) using its parameterization in terms of the rotation angles of n(n?1)=2 plane rotations these reorthogonali...

In this paper the implementation of the SVD{updating algorithm using orthonormal { rotations is presented. An orthonormal {rotation is a rotation by an angle of a given set of {rotation angles (e.g. the angles i = arctan2 ?i) which are choosen such that the rotation can be implemented by a small amount of shift{add operations. A version of the SVD{updating algorithm is used where all computatio...

This paper presents an image compression using singular value decomposition (SVD) by extracting the red, green, and blue (RGB) channel colors. Image is needed in development of various multimedia computer services applications for example telecommunications storage technologies. Now a days, video technology, digital broadcast codec teleconferencing become popular always requires high process di...

Singular Value Decomposition (SVD) is considered to be the holy grail of matrix factorizations. Here an SVD method is used to classify handwritten digits and to aid in the recovery of marred facial images from an ensemble of similar images.