Singular value thresholding (SVT) is a basic subroutine in many popular numerical schemes for solving nuclear norm minimization that arises from low-rank matrix recovery problems such as matrix completion. The conventional approach for SVT is first to find the singular value decomposition (SVD) and then to shrink the singular values. However, such an approach is time-consuming under some circum...

The speech enhancement techniques are often employed to improve the quality and intelligibility of the noisy speech signals. This paper discusses a novel technique for speech enhancement which is based on Singular Value Decomposition. This implementation utilizes a Genetic Algorithm based optimization method for reducing the effects of environmental noises from the singular vectors as well as t...

The singular value decomposition SVD is a powerful technique in many matrix computa tions and analyses Using the SVD of a matrix in computations rather than the original matrix has the advantage of being more robust to numerical error Additionally the SVD exposes the geometric structure of a matrix an important aspect of many matrix calcula tions A matrix can be described as a tranformation fro...

The speech enhancement techniques are often employed to improve the quality and intelligibility of the noisy speech signals. This paper discusses a novel technique for speech enhancement which is based on Singular Value Decomposition. This implementation utilizes a Genetic Algorithm based optimization method for reducing the effects of environmental noises from the singular vectors as well as t...

The Analytic Hierarchy Process (AHP) (Saaty, 1990) has been accepted as a leading multiattribute decision model both by practitioners and academics. AHP can solve decision problems in various fields by the prioritization of alternatives. The heart of the most familiar version of the AHP is the Saaty’s eigenvector method (EM) which approximates an positive reciprocal matrix n n× ) ( ij a A = , ,...

Abstract: In this note, we introduce the singular value decomposition Geršgorin set, Γ (A), of an N ×N complex matrix A, where N ≤ ∞. For N finite, the set Γ (A) is similar to the standard Geršgorin set, Γ(A), in that it is a union of N closed disks in the complex plane and it contains the spectrum, σ(A), of A. However, Γ (A) is constructed using column sums of singular value decomposition matr...

∀ ` σ` ∈ R, σ` ≥ 0 (2) ∀ `, `′ 〈u`, u`′〉 = 〈v`, v`′〉 = δ(`, `′) (3) To prove this consider the matrix AA ∈ Rm×m. Set u` to be the `’th eigenvector of AA . By definition we have that AAu` = λ`u`. Since AA T is positive semidefinite we have λ` ≥ 0. Since AA is symmetric we have that ∀ `, `′ 〈u`, u`′〉 = δ(`, `′). Set σ` = √ λ` and v` = 1 σ` Au`. Now we can compute the following: 〈v`, v`′〉 = 1 σ2 `...

We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generaliz...

In this paper, a steganography technique for JPEG2000 compressed images using singular value decomposition in wavelet transform domain is proposed. In this technique, DWT is applied on the cover image to get wavelet coefficients and SVD is applied on these wavelet coefficients to get the singular values. Then secret data is embedded into these singular values using scaling factor. Different com...