We derive coupled on-line learning rules for the singular value decomposition (SVD) of a cross-covariance matrix. In coupled SVD rules, the singular value is estimated alongside the singular vectors, and the effective learning rates for the singular vector rules are influenced by the singular value estimates. In addition, we use a first-order approximation of Gram-Schmidt orthonormalization as ...

The null vectors of an arbitrary highest weight representation of the WA2 algebra are constructed. Using an extension of the enveloping algebra by allowing complex powers of one of the generators, analysed by Kent for the Virasoro theory, we generate all the singular vectors indicated by the Kac determinant. We prove that the singular vectors with given weights are unique up to normalisation an...

We use recently derived explicit formulae for the Virasoro algebra’s singular vectors to give constructive proofs of three results due to Feigin and Fuchs. The main result, which is needed for a rigorous treatment of fusion, describes the action of the singular vectors on conformal fields.

This paper discusses the computation and utilization of singular values and singular vectors in the solution of very large inverse problems that arise in the study of physical models for the internal structure of the Earth. In this study, the Earth is discretized into layers and the layers into cells, and travel times of sound waves generated by earthquakes are used to construct the models. The...

This paper discusses the use of singular values and singular vectors in the solution of large inverse problems that arise in the study of physical models for the internal structure of the Earth. In this study, the Earth is discretized into layers and the layers into cells, and travel times of sound waves generated by earthquakes are used to construct the corresponding physical models. The under...

Abstract : A new algorithm for noise filtering, based on non-linear processing of image in blocks, using singular value decomposition (SVD) is presented in this paper. Noise filtering is performed in the domain of singular values and singular vectors. A priori noise variance knowledge is not required, because a singular value-based noise variance estimation is performed in the first phase of th...

We study the behavior of stochastic gradient descent applied to $\|Ax -b \|_2^2 \rightarrow \min$ for invertible $A \in \mathbb{R}^{n \times n}$. show that there is an explicit constant $c_{A}$ depending (mildly) on $A$ such $$ \mathbb{E} ~\left\| Ax_{k+1}-b\right\|^2_{2} \leq \left(1 + \frac{c_{A}}{\|A\|_F^2}\right) \left\|A x_k \right\|^2_{2} - \frac{2}{\|A\|_F^2} \left\|A^T A (x_k x)\right\|...

In this paper, we develop a new image quality assessment scheme with the use of Singular Value Decomposition (SVD). In a previous work [1], only the singular values out of SVD were used for quality assessment. We show that singular vectors are even more important than singular values for quality assessment. Hence, we use both singular vectors and values for comprehensive image quality evaluatio...

This paper presents a novel approach for power system dynamic voltage stability analysis based on the multi-input multi-output (MIMO) transfer function. The MIMO system is defined taking into account the critical nodal voltages as outputs and possible control variables as the input. Based on the modal analysis and singular value analysis, the dynamic voltage stability analysis is carried out. T...