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Matrix Factorization (matrix + factorization)
Selected AbstractsPCA- and PMF-based methodology for air pollution sources identification and apportionmentENVIRONMETRICS, Issue 8 2009Marie Chavent Abstract Air pollution is a wide concern for human health and requires the development of air quality control strategies. In order to achieve this goal pollution sources have to be accurately identified and quantified. The case study presented in this paper is part of a scientific project initiated by the French Ministry of Ecology and Sustainable Development. For the following study measurements of chemical composition data for particles have been conducted on a French urban site. The first step of the study consists in the identification of the sources profiles which is achieved through principal component analysis (PCA) completed by a rotation technique. Then the apportionment of the sources is evaluated with a receptor modeling using positive matrix factorization (PMF) as estimation method. Finally the joint use of these two statistical methods enables to characterize and apportion five different sources of fine particulate emission. Copyright © 2008 John Wiley & Sons, Ltd. [source] On singularities in the solution of three-dimensional Stokes flow and incompressible elasticity problems with cornersINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004A. Dimitrov Abstract In this paper, a numerical procedure is presented for the computation of corner singularities in the solution of three-dimensional Stokes flow and incompressible elasticity problems near corners of various shape. For obtaining the order and mode of singularity, a neighbourhood of the singular point is considered with only local boundary conditions. The weak formulation of this problem is approximated using a mixed u, p Galerkin,Petrov finite element method. Additionally, a separation of variables is used to reduce the dimension of the original problem. As a result, the quadratic eigenvalue problem (P+,Q+,2R)d=0 is obtained, where the saddle-point-type matrices P, Q, R are defined explicitly. For a numerical solution of the algebraic eigenvalue problem an iterative technique based on the Arnoldi method in combination with an Uzawa-like scheme is used. This technique needs only one direct matrix factorization as well as few matrix,vector products for finding all eigenvalues in the interval ,,(,) , (,0.5, 1.0), as well as the corresponding eigenvectors. Some benchmark tests show that this technique is robust and very accurate. Problems from practical importance are also analysed, for instance the surface-breaking crack in an incompressible elastic material and the three-dimensional viscous flow of a Newtonian fluid past a trihedral corner. Copyright © 2004 John Wiley & Sons, Ltd. [source] Multi-component analysis: blind extraction of pure components mass spectra using sparse component analysisJOURNAL OF MASS SPECTROMETRY (INCORP BIOLOGICAL MASS SPECTROMETRY), Issue 9 2009Ivica Kopriva Abstract The paper presents sparse component analysis (SCA)-based blind decomposition of the mixtures of mass spectra into pure components, wherein the number of mixtures is less than number of pure components. Standard solutions of the related blind source separation (BSS) problem that are published in the open literature require the number of mixtures to be greater than or equal to the unknown number of pure components. Specifically, we have demonstrated experimentally the capability of the SCA to blindly extract five pure components mass spectra from two mixtures only. Two approaches to SCA are tested: the first one based on ,1 norm minimization implemented through linear programming and the second one implemented through multilayer hierarchical alternating least square nonnegative matrix factorization with sparseness constraints imposed on pure components spectra. In contrast to many existing blind decomposition methods no a priori information about the number of pure components is required. It is estimated from the mixtures using robust data clustering algorithm together with pure components concentration matrix. Proposed methodology can be implemented as a part of software packages used for the analysis of mass spectra and identification of chemical compounds. Copyright © 2009 John Wiley & Sons, Ltd. [source] Tree-based characterization of low index circuit configurations without passivity restrictionsINTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 2 2008Alfonso J. Encinas Abstract The present paper addresses index characterizations in differential-algebraic models of electrical circuits without the need for passivity assumptions. Positive definiteness conditions on the conductance, capacitance and inductance matrices are replaced by certain algebraic assumptions on the so-called proper trees for augmented node analysis and normal trees for modified node analysis. The current discussion is restricted to index-0 and index-1 systems; for the latter, the analysis is based upon certain matrix factorizations which split the topological information from the electrical features of the devices. Several examples illustrate the scope of our framework. Copyright © 2007 John Wiley & Sons, Ltd. [source] On growth factors of the modified Gram,Schmidt algorithmNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 7 2008Musheng Wei Abstract Growth factors play a central role in studying the stability properties and roundoff estimates of matrix factorizations; therefore, they have attracted many numerical analysts to study upper bounds of these growth factors. In this article, we derive several upper bounds of row-wise growth factors of the modified Gram,Schmidt (MGS) algorithm to solve the least squares (LS) problem and the weighted LS problem. We also extend the analysis to the MGS-like algorithm to solve the constrained LS problem. Copyright © 2008 John Wiley & Sons, Ltd. [source] | |||||||||||||