It is shown that an innnite Hankel matrix of a nite rank (or a nite Hankel matrix) admits a generalized Vandermonde decomposition H = V T DV , where V is a generalized Vandermonde matrix, and D is a block diagonal matrix. The full structure of this decomposition was rst fully discussed by Vandevoorde 9], but the development here is based solely on linear algebra considerations, speciically the ...

We present a probabilistic model for tensor decomposition where one or more tensor modes may have sideinformation about the mode entities in form of their features and/or their adjacency network. We consider a Bayesian approach based on the Canonical PARAFAC (CP) decomposition and enrich this single-layer decomposition approach with a two-layer decomposition. The second layer fits a factor mode...

The problem of polynomial regression in which the usual monomial basis is replaced by the Bernstein basis is considered. The coefficient matrix A of the overdetermined system to be solved in the least squares sense is then a rectangular Bernstein-Vandermonde matrix. In order to use the method based on the QR decomposition of A, the first stage consists of computing the bidiagonal decomposition ...

A new method is described for computing the singular value decomposition (SVD). It begins by computing the polar decomposition and then computes the spectral decomposition of the Hermitian polar factor. The method is particularly attractive for shared memory parallel computers with a relatively small number of processors, because the polar decomposition can be computed efficiently on such machi...

The estimation of mixing matrix is a key step to solve the problem of blind source separation. The existing algorithm can only estimate the matrix of well-determined, over-determined and under-determined in condition of sparse source. Scaling and permutation ambiguities lie in both factor matrix of tensor Canonical Decomposition and mixing matrix in blind source separation. With this property, ...

This paper presents a robust matrix decomposition approach that automatically segments a binary image to foreground regions and background regions under high observation noise levels and uneven background intensities. The work is motivated by the need of identifying foreground objects in a noisy electron microscopic image, but the method can be extended for a general binary classification probl...

In this paper, a 2kb/s Waveform Interpolation speech coder is proposed based on non-negative matrix factorization (NMF). In characteristic waveforms (CWs) decomposition, band-partitioning initialization constraints were set to basis vectors before NMF was carried out. This decomposition method only requires speech signal from the current frame, and can yield high decomposition quality with low ...

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 ...

This paper presents a Σ-unitary analogue to the CS decomposition of a partitioned unitary matrix. The hyperbolic rotations revealed by the decomposition are shown to be optimal in that, among a broader class of decompositions of Σ-unitary matrices into elementary hyperbolic rotations, they are the smallest possible in a sum-of-squares sense. A similar optimality property is shown to hold for th...

Hessenberg decomposition is the basic tool used in computational linear algebra to approximate the eigenvalues of a matrix. In this article, we generalize Hessenberg decomposition to continuous matrix fields over topological spaces. This works in great generality: the space is only required to be normal and to have finite covering dimension. As applications, we derive some new structure results...