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Inexact subspace iteration to accelerate the solution of linear systems with multiple right-hand sides

Balsa, Carlos
Fonte: University of Porto Publicador: University of Porto
Tipo: Conferência ou Objeto de Conferência
Português
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We analyze the convergence and propose some strategy to monitor an inexact subspace iteration type of algorithm called BlockCGSI. This algorithm is purely iterative and combines the block Conjugate Gradient (blockCG) algorithm with the Subspace Iteration. We proceed to an inner-outer convergence analyze and exploit the possibility of reducing the total amount of computational work by controlling the accuracy during the solution of linear systems at each inverse iteration. The proposed method can be adequate for large scale problems where we need to solve consecutively several linear systems with the same coefficient matrix (or with very close spectral properties) but with changing right-hand sides. The BlockCGSI algorithm can be used to compute some spectral information, which is then used to remove the effect of the smallest eigenvalues in two different ways: either by building a Spectral Low Rank Update (SLRU) preconditioner that basically adds the value 1 to these eigenvalues, or by performing a deflation of the initial residual in order to remove part of the solution corresponding to the smallest eigenvalues. Both techniques can reduce substantially the total number of iterations and computational work in each subsequent runs of the Conjugate Gradient algorithm.

Controle preditivo com enfoque em subespaços.; Subspace predictive control.

Fernandez, Erika Maria Francischinelli
Fonte: Biblioteca Digitais de Teses e Dissertações da USP Publicador: Biblioteca Digitais de Teses e Dissertações da USP
Tipo: Dissertação de Mestrado Formato: application/pdf
Publicado em 27/11/2009 Português
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Controle preditivo baseado em modelos (MPC) é uma técnica de controle amplamente utilizada na indústria de processos químicos. Por outro lado, o método de identificação em subespaços (SID) tem se mostrado uma alternativa eficiente para os métodos clássicos de identificação de sistemas. Pela combinação dos conceitos de MPC e SID, surgiu, no final da década de 90, uma nova técnica de controle, denominada controle preditivo com enfoque em subespaços (SPC). Essa técnica também é conhecida como controle preditivo orientado a dados. Ela substitui por um único passo as três etapas do projeto de um MPC: a identificação do modelo, o cálculo do observador de estados e a construção das matrizes de predição. Este trabalho tem como principal objetivo revisar estudos feitos na área de SPC, aplicar esse método em sistemas típicos da indústria química e propor novos algoritmos. São desenvolvidos três algoritmos de excitação interna para o método SPC, que permitem gerar dados persistentemente excitantes enquanto um controle mínimo do processo é garantido. Esses algoritmos possibilitam aplicar identificação em malha fechada, na qual o modelo do controlador SPC é reidentificado utilizando dados previamente excitados. Os controladores SPC e SPC com excitação interna são testados e comparados ao MPC por meio de simulações em dois processos distintos. O primeiro consiste em uma coluna debutanizadora de uma unidade de destilação...

On the generalization of subspace detection in unordered multidimensional data; Sobre a generalização da detecção de subespaços em dados multidimensionais não ordenados

Fernandes, Leandro Augusto Frata
Fonte: Universidade Federal do Rio Grande do Sul Publicador: Universidade Federal do Rio Grande do Sul
Tipo: Tese de Doutorado Formato: application/pdf
Português
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Este trabalho apresenta uma solução geral para a detecção de alinhamentos de dados em conjuntos multidimensionais não ordenados e ruidosos. Nesta abordagem, o tipo requerido de alinhamento de dados pode ser uma forma geométrica (e.g., linha reta, plano, círculo, esfera, seção cônica, entre outras) ou qualquer estrutura, com dimensionalidade arbitrária, que possa ser caracterizada por um subespaço linear. A detecção é realizada por meio de um procedimento composto por três etapas. Na etapa de inicialização, um espaço de parâmetros com p (n − p) dimensões é definido de modo que cada ponto neste espaço represente uma instância do alinhamento requerido, descrito por um subespaço p-dimensional em um domínio n-dimensional. Em seguida, uma grade de acumuladores é criada como sendo a representação discreta do espaço de parâmetros. Na segunda etapa do procedimento, cada elemento no conjunto de dados de entrada (também um subespaço no domínio n-dimensional) é mapeado para o espaço de parâmetros como os pontos (no espaço de parâmetros) representando os subespaços requeridos que contém ou que estão contidos no elemento de entrada. À medida que os elementos de entrada são mapeados, as células do acumulador relacionadas com o mapeamento são incrementadas pelo valor de importância do elemento mapeado. A etapa final do procedimento recupera os subespaços p-dimensionais que melhor se ajustam aos dados de entrada como sendo os máximos locais na grade de acumuladores. A parametrização proposta é independente das propriedades geométricas dos alinhamentos a serem detectados. Além disso...

Denoising using local projective subspace methods

Gruber, P.; Stadlthanner, K.; Böhm, M.; Theis, F. J.; Lang, E. W.; Tomé, A. M.; Teixeira, A. R.; Puntonet, C. G.; Gorriz Saéz, J. M.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
Português
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In this paper we present denoising algorithms for enhancing noisy signals based on Local ICA (LICA), Delayed AMUSE (dAMUSE) and Kernel PCA (KPCA). The algorithm LICA relies on applying ICA locally to clusters of signals embedded in a high-dimensional feature space of delayed coordinates. The components resembling the signals can be detected by various criteria like estimators of kurtosis or the variance of autocorrelations depending on the statistical nature of the signal. The algorithm proposed can be applied favorably to the problem of denoising multi-dimensional data. Another projective subspace denoising method using delayed coordinates has been proposed recently with the algorithm dAMUSE. It combines the solution of blind source separation problems with denoising efforts in an elegant way and proofs to be very efficient and fast. Finally, KPCA represents a non-linear projective subspace method that is well suited for denoising also. Besides illustrative applications to toy examples and images, we provide an application of all algorithms considered to the analysis of protein NMR spectra.; BMBF (project ModKog); DFG (GRK 638: Non-linearity and Non-equilibrium in Condensed Matter)

How to apply nonlinear subspace techniques to univariate biomedical time series

Teixeira, A. R.; Tomé, A. M.; Böhm, M.; Puntonet, Carlos G.; Lang, Elmar W.
Fonte: Institute of Electrical and Electronics Engineers (IEEE) Publicador: Institute of Electrical and Electronics Engineers (IEEE)
Tipo: Artigo de Revista Científica
Português
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In this paper, we propose an embedding technique for univariate single-channel biomedical signals to apply projective subspace techniques. Biomedical signals are often recorded as 1-D time series; hence, they need to be transformed to multidimensional signal vectors for subspace techniques to be applicable. The transformation can be achieved by embedding an observed signal in its delayed coordinates. We propose the application of two nonlinear subspace techniques to embedded multidimensional signals and discuss their relation. The techniques consist of modified versions of singular-spectrum analysis (SSA) and kernel principal component analysis (KPCA). For illustrative purposes, both nonlinear subspace projection techniques are applied to an electroencephalogram (EEG) signal recorded in the frontal channel to extract its dominant electrooculogram (EOG) interference. Furthermore, to evaluate the performance of the algorithms, an experimental study with artificially mixed signals is presented and discussed.; FCT - SFRH/BD/28404/2006

Subspace techniques and biomedical time series analysis

Tomé, A. M.; Teixeira, A. R.; Lang, E. W.
Fonte: Bentham Science Publishers Publicador: Bentham Science Publishers
Tipo: Parte de Livro
Português
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The application of subspace techniques to univariate (single-sensor) biomedical time series is presented. Both linear and non-linear methods are described using algebraic models, and the dot product is the most important operation concerning data manipulations. The covariance/correlationmatrices, computed in the space of time-delayed coordinates or in a feature space created by a non-linear mapping, are employed to deduce orthogonal models. Linear methods encompass singular spectrum analysis (SSA), singular value decomposition (SVD) or principal component analysis (PCA). Local SSA is a variant of SSA which can approximate non-linear trajectories of the embedded signal by introducing a clustering step. Generically non-linear methods encompass kernel principal component analysis (KPCA) and greedy KPCA. The latter is a variant where the subspace model is based on a selected subset of data only.; FCT - SFRH/BD/28404/2006

Subspace identification for industrial processes

Borjas,S.D.M.; Garcia,C.
Fonte: Sociedade Brasileira de Matemática Aplicada e Computacional Publicador: Sociedade Brasileira de Matemática Aplicada e Computacional
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/12/2011 Português
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Subspace identification has been a topic of research along the last years. Methods as MOESP and N4SID are well known and they use the LQ decomposition of certain matrices of input and output data. Based on these methods, it is introduced the MON4SID method, which uses the techniques MOESP and N4SID.

Generalized Broadband Beamforming Using a Modal Subspace Decomposition

Williams, Michael I Y; Abhayapala, Thushara D; Kennedy, Rodney A
Fonte: SpringerOpen Publicador: SpringerOpen
Tipo: Artigo de Revista Científica
Português
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We propose a new broadband beamformer design technique which produces an optimal receiver beam pattern for any set of field measurements in space and time. The modal subspace decomposition (MSD) technique is based on projecting a desired pattern into the subspace of patterns achievable by a particular set of space-time sampling positions. This projection is the optimal achievable pattern in the sense that it minimizes the mean-squared error (MSE) between the desired and actual patterns. The main advantage of the technique is versatility as it can be applied to both sparse and dense arrays, nonuniform and asynchronous time sampling, and dynamic arrays where sensors can move throughout space. It can also be applied to any beam pattern type, including frequency-invariant and spot pattern designs. A simple extension to the technique is presented for oversampled arrays, which allows high-resolution beamforming whilst carefully controlling input energy and error sensitivity.

Subspace-based face recognition: Outlier detection and a new distance criterion

Chen, P.; Suter, D.
Fonte: World Scientific Publ Co Pte Ltd Publicador: World Scientific Publ Co Pte Ltd
Tipo: Artigo de Revista Científica
Publicado em //2005 Português
Relevância na Pesquisa
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Illumination effects, including shadows and varying lighting, make the problem of face recognition challenging. Experimental and theoretical results show that the face images under different illumination conditions approximately lie in a low-dimensional subspace, hence principal component analysis (PCA) or low-dimensional subspace techniques have been used. Following this spirit, we propose new techniques for the face recognition problem, including an outlier detection strategy (mainly for those points not following the Lambertian reflectance model), and a new error criterion for the recognition algorithm. Experiments using the Yale-B face database show the effectiveness of the new strategies.; Pei Chen and David Suter

Subspace-based face recognition: outlier detection and a new distance criterion

Chen, Pei; Suter, David
Fonte: Monash University Publicador: Monash University
Tipo: Relatório
Publicado em //2003 Português
Relevância na Pesquisa
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Illumination effects, including shadows and varying lighting, makes the problem of face recognition challenging. Experimental and theoretical results show that the face images under different illumination conditions lie in a low-dimensional subspace, hence principal component analysis (PCA) or low-dimensional subspace techniques have been used. Following this spirit, we propose new techniques for the face recognition problem, including an outlier detection strategy (mainly for those points not following the Lambertian reflectance model), and a new Bayesian-based error criterion for the recognition algorithm. Experiments using the Yale-B face database show the effectiveness of the new strategies; Pei Chen and David Suter

Tracking Fading Multipath Channel Parameters, in CDMA Systems, Using a Subspace-based Method - An Implementation Perspective

Sengupta, Chaitali; Cavallaro, Joseph R.; Aazhang, Behnaam; Sengupta, Chaitali; Cavallaro, Joseph R.; Aazhang, Behnaam
Fonte: Universidade Rice Publicador: Universidade Rice
Tipo: Conference paper
Português
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Conference Paper; In this paper, we evaluate several implementation issues in the application of subspace based methods to tracking channel parameters in code division multiple access (CDMA) communication systems, in the presence of multipath fading. We focus on the behavior of singular value decomposition (SVD) based schemes while tracking the time variations in the signal subspace, due to fading. We also evaluate the application of several techniques to reduce the complexity of the computationally expensive SVD procedure, to the channel estimation problem.

Subspace-based Tracking of Multipath Channel Parameters for CDMA Systems

Sengupta, Chaitali; Cavallaro, Joseph R.; Aazhang, Behnaam; Sengupta, Chaitali; Cavallaro, Joseph R.; Aazhang, Behnaam
Fonte: Universidade Rice Publicador: Universidade Rice
Tipo: Artigo de Revista Científica
Português
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Journal Paper; In this paper, we evaluate several issues in the application of subspace based methods to tracking channel parameters in Code Division Multiple Access (CDMA) communication systems, in the presence of multipath fading. We focus on two aspects of the problem - the performance of Singular Value Decomposition (SVD) based schemes while tracking the time variations in the signal subspace, due to fading, and, the performance trades involved in using several complexity reducing approximate schemes. The performance benefits to be obtained from application of subspace based methods to channel estimation has been well studied. The aim of this work is to lay the groundwork for real time implementation of this computationally complex problem.

Subspace-based channel estimation for code division multiple access communication systems

Bensley, Stephen E; Aazhang, Behnaam; Bensley, Stephen E; Aazhang, Behnaam
Fonte: Universidade Rice Publicador: Universidade Rice
Tipo: Journal article; Text; Text
Português
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Journal Paper; We consider the estimation of channel parameters for code-division multiple access (CDMA) communication systems operating over channels with either single or multiple propagation paths. The multiuser channel estimation problem is decomposed into a series of single user problems through a subspace-based approach. By exploiting the eigenstructure of the received signal's sample correlation matrix, the observation space can be partitioned into a signal subspace and a noise subspace without prior knowledge of the unknown parameters. The channel estimate is formed by projecting a given user's spreading waveform into the estimated noise subspace and then either minimizing the likelihood or minimizing the Euclidean norm of this projection. Both of these approaches yield algorithms which are near-far resistant and do not require a preamble.; Texas Advanced Technology Program; National Aeronautics and Space Administration

Generalised FastICA for Independent Subspace Analysis

Shen, Hao; Hueper, Knut
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Conference paper
Português
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Independent Subspace Analysis (ISA) was developed as an extension of Independent Component Analysis (ICA) when statistical independences are assumed to exist between groups of components rather than between individual components. Due to the superiority of

Generalized Broadband Beamforming Using a Modal Subspace Decomposition

Williams, Mick; Abhayapala, Thushara; Kennedy, Rodney
Fonte: Hindawi Publishing Corporation Publicador: Hindawi Publishing Corporation
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
36.6324%
We propose a new broadband beamformer design technique which produces an optimal receiver beam pattern for any set of field measurements in space and time. The modal subspace decomposition(MSD) technique is based on projecting a desired pattern into the s

Higgledy-piggledy subspaces and uniform subspace designs

Fancsali, Szabolcs L.; Sziklai, Péter
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Publicado em 22/09/2014 Português
Relevância na Pesquisa
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In this article, we investigate collections of `well-spread-out' projective (and linear) subspaces. Projective $k$-subspaces in $\mathsf{PG}(d,\mathbb{F})$ are in `higgledy-piggledy arrangement' if they meet each projective subspace of co-dimension $k$ in a generator set of points. We prove that the set $\mathcal{H}$ of higgledy-piggledy $k$-subspaces has to contain more than $\min{|\mathbb{F}|,\sum_{i=0}^k\lfloor\frac{d-k+i}{i+1}\rfloor}$ elements. We also prove that $\mathcal{H}$ has to contain more than $(k+1)\cdot(d-k)$ elements if the field $\mathbb{F}$ is algebraically closed. An $r$-uniform weak $(s,A)$ subspace design is a set of linear subspaces $H_1,..,H_N\le\mathbb{F}^m$ each of rank $r$ such that each linear subspace $W\le\mathbb{F}^m$ of rank $s$ meets at most $A$ among them. This subspace design is an $r$-uniform strong $(s,A)$ subspace design if $\sum_{i=1}^N\mathrm{rank}(H_i\cap W)\le A$ for $\forall W\le\mathbb{F}^m$ of rank $s$. We prove that if $m=r+s$ then the dual ($\{H_1^\bot,...,H_N^\bot\}$) of an $r$-uniform weak (strong) subspace design of parameter $(s,A)$ is an $s$-uniform weak (strong) subspace design of parameter $(r,A)$. We show the connection between uniform weak subspace designs and higgledy-piggledy subspaces proving that $A\ge\min{|\mathbb{F}|...

Constructing the L2-Graph for Robust Subspace Learning and Subspace Clustering

Peng, Xi; Yu, Zhiding; Tang, Huajin; Yi, Zhang
Fonte: Universidade Cornell Publicador: Universidade Cornell
Tipo: Artigo de Revista Científica
Português
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27.060571%
Under the framework of graph-based learning, the key to robust subspace clustering and subspace learning is to obtain a good similarity graph that eliminates the effects of errors and retains only connections between the data points from the same subspace (i.e., intra-subspace data points). Recent works achieve good performance by modeling errors into their objective functions to remove the errors from the inputs. However, these approaches face the limitations that the structure of errors should be known prior and a complex convex problem must be solved. In this paper, we present a novel method to eliminate the effects of the errors from the projection space (representation) rather than from the input space. We first prove that $\ell_1$-, $\ell_2$-, $\ell_{\infty}$-, and nuclear-norm based linear projection spaces share the property of Intra-subspace Projection Dominance (IPD), i.e., the coefficients over intra-subspace data points are larger than those over inter-subspace data points. Based on this property, we introduce a method to construct a sparse similarity graph, called L2-Graph. The subspace clustering and subspace learning algorithms are developed upon L2-Graph. Experiments show that L2-Graph algorithms outperform the state-of-the-art methods for feature extraction...

A Newton algorithm for invariant subspace computation with large basins of attraction

Absil, P-A; Sepulchre, R; Van Dooren, P; Mahony, Robert
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Conference paper
Português
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We study the global behaviour of a Newton algorithm on the Grassmann manifold for invariant subspace computation. It is shown that the basins of attraction of the invariant subspaces may collapse in case of small eigenvalue gaps. A Levenberg-Marquardt-like modification of the algorithm with low numerical cost is proposed. A simple strategy for choosing the parameter is shown to dramatically enlarge the basins of attraction of the invariant subspaces while preserving the fast local convergence.

A Sequential Subspace Method for Blind Identification of General FIR MIMO Channels

An, Senjian; Manton, Jonathan; Hua, Yingbo
Fonte: Institute of Electrical and Electronics Engineers (IEEE Inc) Publicador: Institute of Electrical and Electronics Engineers (IEEE Inc)
Tipo: Artigo de Revista Científica
Português
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36.757969%
This correspondence addresses the problem of blindly identifying multiple input multiple output (MIMO) finite impulse response (FIR) channels without the conventional assumption of identical column degrees. A subspace-based algorithm is developed that identifies the channel's columns sequentially from the lowest degree columns to the highest degree ones. Compared with the previous generalized subspace method by Gorokhov and Loubaton, the new method is simpler and more accurate.

Model reduction and identification of wastewatertreatment plants - A subspace approach

Sotomayor,O. A. Z.; Park,S. W.; García,C.
Fonte: Latin American applied research Publicador: Latin American applied research
Tipo: Artigo de Revista Científica Formato: text/html
Publicado em 01/04/2003 Português
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In this paper, a low-order linear time-invariant (LTI) state-space model that describes the nitrate concentrations in both anoxic and aerobic zones of an activated sludge wastewater treatment plant (WWTP), for biological treatment of municipal sewage, is identified around a given operating point (a model with lumped parameters). Several subspace identification methods, such as CCA, N4SID, MOESP and DSR are applied and their performance are compared, based on performance quality criteria, in order to select the best-reduced model. The selected model is validated with a data set not used in the identification procedure and it describes well the complex dynamics of the process. This model is asymptotically stable and it can be used for control, optimization, prediction and monitoring purposes. In this work the ASWWTP-USP benchmark is used as a data generator. This benchmark simulates the biological, chemical and physical interactions that occur in a complex activated sludge plant.