Showing papers on "Matrix analysis published in 2019"

Fast Multichannel Source Separation Based on Jointly Diagonalizable Spatial Covariance Matrices

Abstract: This paper describes a versatile method that accelerates multichannel source separation methods based on full-rank spatial modeling. A popular approach to multichannel source separation is to integrate a spatial model with a source model for estimating the spatial covariance matrices (SCMs) and power spectral densities (PSDs) of each sound source in the time-frequency domain. One of the most successful examples of this approach is multichannel nonnegative matrix factorization (MNMF) based on a full-rank spatial model and a low-rank source model. MNMF, however, is computationally expensive and often works poorly due to the difficulty of estimating the unconstrained full-rank SCMs. Instead of restricting the SCMs to rank -1 matrices with the severe loss of the spatial modeling ability as in independent low-rank matrix analysis (ILRMA), we restrict the SCMs of each frequency bin to jointly-diagonalizable but still full-rank matrices. For such a fast version of MNMF, we propose a computationally-efficient and convergence-guaranteed algorithm that is similar in form to that of ILRMA. Similarly, we propose a fast version of a state of-the-art speech enhancement method based on a deep speech model and a low-rank noise model. Experimental results showed that the fast versions of MNMF and the deep speech enhancement method were several times faster and performed even better than the original versions of those methods, respectively.

Independent Low-Rank Matrix Analysis with Decorrelation Learning

Abstract: This paper addresses the determined convolutive blind source separation (BSS) problem. The state-of-the-art independent low-rank matrix analysis (ILRMA), unifying independent component analysis (ICA) and nonnegative matrix factorization, has the disadvantage of ignoring inter-frame and inter-frequency spectral correlation of source signals. We here propose a new BSS method that estimates a linear transformation for spectral decorrelation and performs ILRMA in the transformed domain. A newly introduced optimization problem is an extension of that for ICA based on maximum likelihood. For this problem, we provide a necessary and sufficient condition for the existence of optimal solutions, and develop algorithms based on block coordinate descent methods with closed-form solutions. Experimental results show the improved separation performance of the proposed method compared to ILRMA.

Measuring Linear Correlation Between Random Vectors

Abstract: We introduce a new scalar coefficient to measure linear correlation between random vectors which preserves all the relevant properties of Pearson’s correlation in arbitrary dimensions. The new measure and its bounds are derived from a mass transportation approach in which the expected inner product of two random vectors is taken as a measure of their covariance and then standardized by the maximal attainable value given their marginal covariance matrices. In several simulative studies we show the limiting distribution of the empirical estimator of the newly defined index and of the corresponding rank correlation. A comparative study shows that our proposed correlation, though derived from a novel approach, behaves similarly to some of the multivariate dependence notions recently introduced in the literature. Throughout the paper, we also give some auxiliary results of independent interest in matrix analysis and mass transportation theory, including an improvement to the Cauchy-Schwarz inequality for positive definite covariance matrices.

Single-phase-to-ground Fault Diagnosis Based on Waveform Feature Extraction and Matrix Analysis

Abstract: A large proportion of the distribution network operates under neutral point ungrounded mode or arc suppression coil grounded mode. The single-phase-to-ground fault current is small, which brings difficulties to fault diagnosis. A single-phase-to-ground fault section identification method is proposed based on synchronous waveform feature extraction and matrix analysis. Firstly, the proper features are extracted from the current waveforms of grounding phase obtained with fault recorders, which are used to construct topology matrix. Then, random matrix theory is used to get the random matrix eigenvalues. Using the distribution of the eigenvalues, K-means clustering algorithm is utilized in clustering the fault cases and get the final classification center point. Through finding the central point which has the smallest distance with new faulty data set, the fault section can be automatically identified. The effectiveness of proposed method is verified by IEEE 34 nodes test system.

Fast Multichannel Source Separation Based on Jointly Diagonalizable Spatial Covariance Matrices

Abstract: This paper describes a versatile method that accelerates multichannel source separation methods based on full-rank spatial modeling. A popular approach to multichannel source separation is to integrate a spatial model with a source model for estimating the spatial covariance matrices (SCMs) and power spectral densities (PSDs) of each sound source in the time-frequency domain. One of the most successful examples of this approach is multichannel nonnegative matrix factorization (MNMF) based on a full-rank spatial model and a low-rank source model. MNMF, however, is computationally expensive and often works poorly due to the difficulty of estimating the unconstrained full-rank SCMs. Instead of restricting the SCMs to rank-1 matrices with the severe loss of the spatial modeling ability as in independent low-rank matrix analysis (ILRMA), we restrict the SCMs of each frequency bin to jointly-diagonalizable but still full-rank matrices. For such a fast version of MNMF, we propose a computationally-efficient and convergence-guaranteed algorithm that is similar in form to that of ILRMA. Similarly, we propose a fast version of a state-of-the-art speech enhancement method based on a deep speech model and a low-rank noise model. Experimental results showed that the fast versions of MNMF and the deep speech enhancement method were several times faster and performed even better than the original versions of those methods, respectively.

Solving LR fuzzy linear matrix equation

Abstract: In this paper, the fuzzy matrix equation $Awidetilde{X}B=widetilde{C}$ in which $A,B$ are $n times n$crisp matrices respectively and $widetilde{C}$ is an $n times n$ arbitrary LR fuzzy numbers matrix, is investigated. A new numerical procedure for calculating the fuzzy solution is designed and a sufficient condition for the existence of strong fuzzy solution is derived. Some examples are given to illustrate the proposed method.

On Some Study of the Fine Spectra of Triangular Band Matrices

Abstract: The present article is a continuation of the work done by Birbonshi and Srivastava (Complex Anal Oper Theory 11:739–753, 2017) where the authors obtained the spectrum and fine spectrum of banded triangular matrices such that the entries of each band are constant. In this article, we consider the same problem for triangular band matrices such that each band is a convergent sequence. These kind of matrix can be expressed as a compact perturbation of banded Toeplitz matrices. In this connection, a result regarding the location of the roots of a polynomial with respect to the unit circle is obtained. Some results on the compactnees of the operator are also derived. Finally, suitable examples are given in support of our results.

Characteristic matrices of compound operations of coverings and their relationships with rough sets

Abstract: As the matrix can compactly represent numeric data, simplify problem formulation and reduce time complexity, it has many applications in most of the scientific fields. For this purpose, some types of generalized rough sets have been connected with matrices. However, covering-based rough sets which play an important role in data mining and machine learning are seldom connected with matrices. In this paper, we define three composition operations of coverings and study their characteristic matrices; Moreover, the relationships between the characteristic matrices and covering approximation operators are investigated. First, for a covering, an existing matrix representation of indiscernible neighborhoods called the type-1 characteristic matrix of the covering is recalled and a new matrix representation of neighborhoods called the type-2 characteristic matrix of the covering is proposed. Second, considering the importance of knowledge fusion and decomposition, we define three types of composition operations of coverings. Specifically, their type-1 and type-2 characteristic matrices are studied. Finally, we also explore the representable properties of covering approximation operators with respect to any covering generated by each composition operation. It is interesting to find that three types of approximation operators, which are induced by each type of composition operation of coverings, can be expressed as the Boolean product of a coefficient matrix and a characteristic vector. These interesting results suggest the potential for studying covering-based rough sets by matrix approaches.

Crosstalk analysis at near-end and far-end of the coupled transmission lines based on eigenvector decomposition

Abstract: In this paper, a new analytical method is proposed to accurately estimate the near-end and far-end crosstalk of a coupled Transmission Lines (TLs) based on eigenvector decomposition. For a non-homogenous two coupled lines, the related linear differential equations system (LDES) is derived for distributed voltage and current and then using matrix analysis, its four distinct eigenvalues and their associated eigenvectors are determined. It is shown that the two eigenvalues represent the self-propagation constant, while the other ones are linked to the mutual propagation constant of the coupled lines. In addition to, for these lines a closed form expression for near-end and far-end crosstalk is presented. In special case of homogenous coupled lines, the LDES is also determined and it is shown that they provide two couples of eigenvalues. Using the concept of generalized eigenvalues, the solution of these systems is derived and a closed form formula is derived for crosstalk. In order to verify the accuracy of the proposed method a few types of coupled lines, including homogeneous or non-homogeneous are investigated and the amount of crosstalk is estimated. The calculated crosstalk is presented and compared with those obtained by numerical investigation. It is shown that a good agreement is obtained between the calculated and measured results.

Resonance states 0+ of the Boron isotope B8 from the Jost-matrix analysis of experimental data

Abstract: The available R-matrix parametrization of experimental data on the excitation functions for the elastic and inelastic p-Be7 scattering at the collision energies up to 3.4 MeV is used to generate the corresponding partial-wave cross sections in the states with J^pi=0+. Thus obtained data are considered as experimental partial cross sections and are fitted using the semi-analytic two-channel Jost matrix with proper analytic structure and some adjustable parameters. Then the spectral points are sought as zeros of the Jost matrix determinant (which correspond to the S-matrix poles) at complex energies. The correct analytic structure makes it possible to calculate the fitted Jost matrix on any sheet of the Riemann surface whose topology involves not only the square-root but also the logarithmic branching caused by the Coulomb interaction. In this way, two overlapping 0+ resonances at the excitation energies ~1.79 MeV and ~1.96 MeV have been found.

Global product structure for a space of special matrices

Abstract: The importance of the Hurwitz–Metzler matrices and the Hurwitz symmetric matrices can be appreciated in different applications: communication networks, biology and economics are some of them. In this paper, we use an approach of differential topology for studying such matrices. Our results are as follows: the space of the $$n\times n$$ Hurwitz symmetric matrices has a product manifold structure given by the space of the $$(n-1)\times (n-1)$$ Hurwitz symmetric matrices and the Euclidean space. Additionally we study the space of Hurwitz–Metzler matrices and these ideas let us do an analysis of robustness of Hurwitz–Metzler matrices. In particular, we study the insulin model as an application.

PMCMA: Pattern Mining in SAR Time Series by Change Matrix Analysis

Abstract: This paper presents a novel change detection scheme for synthetic aperture radar (SAR) time series, named Pattern Mining by Change Matrix Analysis (PMCMA). This scheme involves three steps: 1) change detection in SAR time series via the statistic of change matrix; 2) change matrix clustering by the simultaneous clustering and model selection (SCAMS) algorithm; 3) change pattern classification using the clustering results of change matrices. The procedure is executed with an automatic clustering algorithm and does not require the default number of clusters. The proposed approach is tested on two SAR time series of 12 TerraSAR-X images acquired from September, 2013 to October, 2014 over the Shanghai, China. Experimental results show the effectiveness of the proposed PMCMA scheme.

Causal Inference from Possibly Unbalanced Split-Plot Designs: A Randomization-based Perspective

Abstract: Split-plot designs find wide applicability in multifactor experiments with randomization restrictions. Practical considerations often warrant the use of unbalanced designs. This paper investigates randomization based causal inference in split-plot designs that are possibly unbalanced. Extension of ideas from the recently studied balanced case yields an expression for the sampling variance of a treatment contrast estimator as well as a conservative estimator of the sampling variance. However, the bias of this variance estimator does not vanish even when the treatment effects are strictly additive. A careful and involved matrix analysis is employed to overcome this difficulty, resulting in a new variance estimator, which becomes unbiased under milder conditions. A construction procedure that generates such an estimator with minimax bias is proposed.

Multi-dimensional data matrix analysis method and system based on database

Abstract: The invention provides a multi-dimensional data matrix analysis method and system based on a database. The method comprises the following steps: setting characteristic parameters of to-be-analyzed data; identifying the characteristic parameters, classifying the data to be analyzed according to the characteristic parameters to obtain unit object data, respectively recording the unit object data asrelation characteristics of row variables, column variables and summarized unit object data of a relation table, and recording the relation characteristics as relation characteristic variables; enabling the row variable, the column variable and the relation feature variable to draw a matrix data table, and outputting the matrix data table to a data consumption end. According to the method, different types of data of large data volume data are merged into classified data with different characteristics by using a parameter preset rule, so that different purposes are met. The number of times of communication with an external medium is reduced in the process of frequently retrieving data by using the database, the performance is improved, meanwhile, a matrix table is drawn at a time, methods such as circulation are avoided, and the analysis performance is improved.

An inverse diffusion-wave problem defined in heterogeneous medium with additional boundary measurement

Abstract: This paper deals with an inverse problem to determine a space-dependent coefficient in a one-dimensional time fractional diffusion-wave equation defined in heterogeneous medium with additional boundary measurement. Then, we construct the explicit finite difference scheme for the direct problem based on the equivalent partial integro-differential equation and Simpson's rule. Using the matrix analysis and mathematical induction, we prove that our scheme is stable and convergent . The least squares method with homotopy regularization is introduced to determine the space-dependent coefficient, and an inversion algorithm is performed by one numerical example. This inversion algorithm is effective at least for this inverse problem.

Study of Fluid Flow Using Matrix Analysis

Abstract: Fluids are either gases or liquids. Mathematical methods in Chemistry are one of the core subjects in applied mathematics. Fluid dynamics is one of important branch of Mathematical Chemistry deals with study of motion of fluids i.e. liquid, gases and vapors. Fluid flows as a continuum. It is considered as a single entity whiles it in motion. Electricity, heat transfer, light prorogate are various forms of energy are some of the important examples of fluid flow. The all equations of motions of fluid are very important to study and it is important to note that all these equations are expressed in mathematical tools such as differential equations, nonlinear equations partial differential equations. In present paper, we are converting the Nevier-Stokes equations into matrix form. The motion of fluid is studied using properties of matrix such as determinant, rank, eigen value properties are used to study path of the motion of fluid.

Mutual Information on Tensors for Measuring the Nonlinear Correlations in Network Security

Abstract: Correlation analysis has been proposed to measure the relationship among different variables, with application in multi-view dimension reduction. However, the existing methods usually are used by covariance in a linear way rather than the nonlinear effects being considered among multiple variables and only few works on nonlinear interaction of two variables have been considered. In this paper we propose a nonlinear analysis of multiple (more than two) variables based on mutual information for tensors analysis (MITA) firstly. In addition, we extend the mutual information matrix analysis directly to mutual information tensor analysis and show the mutual information formula for multiple variables theoretically. Experiment on multi-view dimension reduction, including attacking internet traffic detection, has been done to illustrate the effectiveness of the proposed method, especially in the case of low dimensional subspace.

Solution of the Linearly Structured Partial Polynomial Inverse Eigenvalue Problem

Abstract: In this paper, linearly structured partial polynomial inverse eigenvalue problem is considered for the $n\times n$ matrix polynomial of arbitrary degree $k$. Given a set of $m$ eigenpairs ($1 \leqslant m \leqslant kn$), this problem concerns with computing the matrices $A_i\in{\mathbb{R}^{n\times n}}$ for $i=0,1,2, \ldots ,(k-1)$ of specified linear structure such that the matrix polynomial $P(\lambda)=\lambda^k I_n +\sum_{i=0}^{k-1} \lambda^{i} A_{i}$ has the given eigenpairs as its eigenvalues and eigenvectors. Many practical applications give rise to the linearly structured structured matrix polynomial. Therefore, construction of the linearly structured matrix polynomial is the most important aspect of the polynomial inverse eigenvalue problem(PIEP). In this paper, a necessary and sufficient condition for the existence of the solution of this problem is derived. Additionally, we characterize the class of all solutions to this problem by giving the explicit expressions of solutions. The results presented in this paper address some important open problems in the area of PIEP raised in De Teran, Dopico and Van Dooren [SIAM Journal on Matrix Analysis and Applications, $36(1)$ ($2015$), pp $302-328$]. An attractive feature of our solution approach is that it does not impose any restriction on the number of eigendata for computing the solution of PIEP. The proposed method is validated with various numerical examples on a spring mass problem.

Полная 16-параметрическая модель процессов калибровки и непосредственного измерения параметров четырехполюсников

Abstract: A complete mathematical model for measuring the parameters of the scattering matrix for a measurement object [Sx] in the form of a four-port network is developed, in which the mathematical model of the eight-port error is described by 16 parameters of the scattering matrix [E]. In addition, in comparison with the 12-parameter model of the eight-port error network, four parameters are included, which allow taking into account leaks, parasitic transmissions of microwave modules under study (microwave microassemblies). Due to the use of matrix analysis methods, the equations in matrix form are obtained that connect the matrices of the measurement object [Sи] and the actual values of the matrix parameters [Sx], with the aim of enabling the solution of these equations instead of the scattering matrix [E] to use a transmition matrix [T] in the form of cellular matrices [Taa], [Tab], [Tba], [Tbb].