We show that a set of real-valued word vectors formed by right singular vectors of a transformed co-occurrence matrix are meaningful for determining different types of dependency relations between words. Our experimental results on the task of dependency parsing confirm the superiority of the word vectors to the other sets of word vectors generated by popular methods of word embedding. We also ...

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 ...

We write down one-to-one mappings between the singular vectors of the Neveu-Schwarz N=2 superconformal algebra and 16 + 16 types of singular vectors of the Topological and of the Ramond N=2 superconformal algebras. As a result one obtains construction formulae for the latter using the construction formulae for the Neveu-Schwarz singular vectors due to Dörrzapf. The indecomposable singular vecto...

The authors explore the use of the ‘‘neutral vectors’’ of a linearized version of a global quasigeostrophic atmospheric model with realistic mean flow in the study of the nonlinear model’s low-frequency variability. Neutral vectors are the (right) singular vectors of the linearized model’s tendency matrix that have the smallest eigenvalues; they are also the patterns that exhibit the largest re...

In this paper, we consider the singular values and singular vectors of finite, low rank perturbations of large rectangular random matrices. Specifically, we prove almost sure convergence of the extreme singular values and appropriate projections of the corresponding singular vectors of the perturbed matrix. As in the prequel, where we considered the eigenvalues of Hermitian matrices, the non-ra...

Identification of the channel matrix is of main concern in wireless MIMO (Multiple Input Multiple Output) systems. To maximize the SNR, the best way to utilize a MIMO system is to communicate on the top singular vectors of the channel matrix. Here, we present a new approach for direct blind identification of the main independent singular modes, without first estimating the channel matrix itself...

2 has nonzero entries only on its diagonal and first superdiagonal ) Compute orthogonal matrices P and Q such that Σ = P BQ is diagonal and nonnegat i 2 2 2 T 2 ive. The diagonal entries σ of Σ are the singular values of A . We will take them to be sorted in decreasing order: σ ≥ σ . The columns of Q= Q Q are the right singular vec i i + 1 1 2 t 1 2 ors, and the columns of P= P P are the left s...

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...

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...

carries important information about the structure of the data set, especially when the rank k of X is small. In particular, the columns of U (known as the left singular vectors of X) span the principal directions of the data set and can be used as basis vectors for building up typical signals, and the diagonal entries of Σ (known as the singular values of X) reflect the energy of the data set i...