then σ is a singular value of A and u and v are corresponding left and right singular vectors, respectively. (For generality it is assumed that the matrices here are complex, although given these results, the analogs for real matrices are obvious.) If, for a given positive singular value, there are exactly t linearly independent corresponding right singular vectors and t linearly independent co...

Position-specific scoring matrices (PSSMs) are useful for detecting weak homology in protein sequence analysis, and they are thought to contain some essential signatures of the protein families. In order to elucidate what kind of ingredients constitute such family-specific signatures, we apply singular value decomposition to a set of PSSMs and examine the properties of dominant right and left s...

In this paper we propose new blur identi cation algorithm based on singular value decomposition (SVD) of degraded image. An unknown space-invariant point-spread function (PSF) is also decomposed using SVD. Magnitude functions of PSF singular vectors (left and right) are identi ed using averaged spectra of corresponding singular vectors of degraded image. Phase functions of PSF singular vectors ...

In this paper, a semi-blind biometric watermarking scheme is proposed for fingerprinting application. Watermark is derived from face image using Principal Component Analysis. These face features are then embedded in host image using block-based watermarking scheme, which uses Singular Value Decomposition transform. This watermarking scheme works by initially dividing the original image into non...

Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...

Consider the SVD X = UDV >, where U is n× n, V is p× p and D is an n× p “diagonal” matrix with entries d1 < . . . < dn. Define two groups of left and right singular vectors associated with the q smallest and n − q largest singular values. Let the groups be defined by Uq, Un−q and Vq, Vn−q . Suppose HJ chooses as its row-basis the n−q largest right singular vectors, Vn−q . Then, from Table 1 of ...

Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row-column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse...

A variational formulation for the generalized singular value decomposition GSVD of a pair of matrices A R n and B R n is presented In particular a duality theory analogous to that of the SVD provides new understanding of left and right generalized singular vectors It is shown that the intersection of row spaces of A and B plays a key role in the GSVD duality theory The main result that characte...

This article presents a new subspace-based technique for reducing the noise of signals in time-series. In the proposed approach, the signal is initially represented as a data matrix. Then using Singular Value Decomposition (SVD), noisy data matrix is divided into signal subspace and noise subspace. In this subspace division, each derivative of the singular values with respect to rank order is u...

this article presents a new subspace-based technique for reducing the noise ofsignals in time-series. in the proposed approach, the signal is initially representedas a data matrix. then using singular value decomposition (svd), noisy datamatrix is divided into signal subspace and noise subspace. in this subspace division,each derivative of the singular values with respect to rank order is used ...