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Dissertations / Theses on the topic 'Sparse and low-rank decomposition'

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Published: 4 June 2021

Last updated: 16 February 2022

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1

Ebadi, Salehe Erfanian. "Robust subspace estimation via low-rank and sparse decomposition and applications in computer vision." Thesis, Queen Mary, University of London, 2018. http://qmro.qmul.ac.uk/xmlui/handle/123456789/31790.

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Recent advances in robust subspace estimation have made dimensionality reduction and noise and outlier suppression an area of interest for research, along with continuous improvements in computer vision applications. Due to the nature of image and video signals that need a high dimensional representation, often storage, processing, transmission, and analysis of such signals is a difficult task. It is therefore desirable to obtain a low-dimensional representation for such signals, and at the same time correct for corruptions, errors, and outliers, so that the signals could be readily used for l

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2

Cordolino, Sobral Andrews. "Robust low-rank and sparse decomposition for moving object detection : from matrices to tensors." Thesis, La Rochelle, 2017. http://www.theses.fr/2017LAROS007/document.

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Dans ce manuscrit de thèse, nous introduisons les avancées récentes sur la décomposition en matrices (et tenseurs) de rang faible et parcimonieuse ainsi que les contributions pour faire face aux principaux problèmes dans ce domaine. Nous présentons d’abord un aperçu des méthodes matricielles et tensorielles les plus récentes ainsi que ses applications sur la modélisation d’arrière-plan et la segmentation du premier plan. Ensuite, nous abordons le problème de l’initialisation du modèle de fond comme un processus de reconstruction à partir de données manquantes ou corrompues. Une nouvelle méthod

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3

Oreifej, Omar. "Robust Subspace Estimation Using Low-Rank Optimization. Theory and Applications in Scene Reconstruction, Video Denoising, and Activity Recognition." Doctoral diss., University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5684.

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In this dissertation, we discuss the problem of robust linear subspace estimation using low-rank optimization and propose three formulations of it. We demonstrate how these formulations can be used to solve fundamental computer vision problems, and provide superior performance in terms of accuracy and running time. Consider a set of observations extracted from images (such as pixel gray values, local features, trajectories...etc). If the assumption that these observations are drawn from a liner subspace (or can be linearly approximated) is valid, then the goal is to represent each observati

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Bomma, Sushma. "Sparse and low rank approximations for action recognition." Thesis, Heriot-Watt University, 2016. http://hdl.handle.net/10399/3189.

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Action recognition is crucial area of research in computer vision with wide range of applications in surveillance, patient-monitoring systems, video indexing, Human- Computer Interaction and many more. These applications require automated action recognition. Robust classification methods are sought-after despite influential research in this field over past decade. The data resources have grown tremendously owing to the advances in the digital revolution which cannot be compared to the meagre resources in the past. The main limitation on a system when dealing with video data is the computationa

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5

Kang, Zhao. "LOW RANK AND SPARSE MODELING FOR DATA ANALYSIS." OpenSIUC, 2017. https://opensiuc.lib.siu.edu/dissertations/1366.

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Nowadays, many real-world problems must deal with collections of high-dimensional data. High dimensional data usually have intrinsic low-dimensional representations, which are suited for subsequent analysis or processing. Therefore, finding low-dimensional representations is an essential step in many machine learning and data mining tasks. Low-rank and sparse modeling are emerging mathematical tools dealing with uncertainties of real-world data. Leveraging on the underlying structure of data, low-rank and sparse modeling approaches have achieved impressive performance in many data analysis tas

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6

Sundin, Martin. "Bayesian methods for sparse and low-rank matrix problems." Doctoral thesis, KTH, Signalbehandling, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-191139.

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Many scientific and engineering problems require us to process measurements and data in order to extract information. Since we base decisions on information,it is important to design accurate and efficient processing algorithms. This is often done by modeling the signal of interest and the noise in the problem. One type ofmodeling is Compressed Sensing, where the signal has a sparse or low-rank representation. In this thesis we study different approaches to designing algorithms for sparse and low-rank problems. Greedy methods are fast methods for sparse problems which iteratively detects and e

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7

Lou, Jian. "Study on efficient sparse and low-rank optimization and its applications." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/543.

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Sparse and low-rank models have been becoming fundamental machine learning tools and have wide applications in areas including computer vision, data mining, bioinformatics and so on. It is of vital importance, yet of great difficulty, to develop efficient optimization algorithms for solving these models, especially under practical design considerations of computational, communicational and privacy restrictions for ever-growing larger scale problems. This thesis proposes a set of new algorithms to improve the efficiency of the sparse and low-rank models optimization. First, facing a large numbe

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8

Shi, Qiquan. "Low rank tensor decomposition for feature extraction and tensor recovery." HKBU Institutional Repository, 2018. https://repository.hkbu.edu.hk/etd_oa/549.

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Feature extraction and tensor recovery problems are important yet challenging, particularly for multi-dimensional data with missing values and/or noise. Low-rank tensor decomposition approaches are widely used for solving these problems. This thesis focuses on three common tensor decompositions (CP, Tucker and t-SVD) and develops a set of decomposition-based approaches. The proposed methods aim to extract low-dimensional features from complete/incomplete data and recover tensors given partial and/or grossly corrupted observations.;Based on CP decomposition, semi-orthogonal multilinear principa

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9

Primadhanty, Audi. "Low-rank regularization for high-dimensional sparse conjunctive feature spaces in information extraction." Doctoral thesis, Universitat Politècnica de Catalunya, 2017. http://hdl.handle.net/10803/461682.

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One of the challenges in Natural Language Processing (NLP) is the unstructured nature of texts, in which useful information is not easily identifiable. Information Extraction (IE) aims to alleviate it by enabling automatic extraction of structured information from such text sources. The resulting structured information will facilitate easier querying, organizing, and analyzing of data from texts. In this thesis, we are interested in two IE related tasks: (i) named entity classification and (ii) template filling. Specifically, this thesis examines the problem of learning classifiers of text sp

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10

Wang, Tianming. "Non-convex methods for spectrally sparse signal reconstruction via low-rank Hankel matrix completion." Diss., University of Iowa, 2018. https://ir.uiowa.edu/etd/6331.

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Spectrally sparse signals arise in many applications of signal processing. A spectrally sparse signal is a mixture of a few undamped or damped complex sinusoids. An important problem from practice is to reconstruct such a signal from partial time domain samples. Previous convex methods have the drawback that the computation and storage costs do not scale well with respect to the signal length. This common drawback restricts their applicabilities to large and high-dimensional signals. The reconstruction of a spectrally sparse signal from partial samples can be formulated as a low-rank Hankel ma

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11

Tremoulheac, Benjamin R. "Low-rank and sparse reconstruction in dynamic magnetic resonance imaging via proximal splitting methods." Thesis, University College London (University of London), 2015. http://discovery.ucl.ac.uk/1458052/.

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Dynamic magnetic resonance imaging (MRI) consists of collecting multiple MR images in time, resulting in a spatio-temporal signal. However, MRI intrinsically suffers from long acquisition times due to various constraints. This limits the full potential of dynamic MR imaging, such as obtaining high spatial and temporal resolutions which are crucial to observe dynamic phenomena. This dissertation addresses the problem of the reconstruction of dynamic MR images from a limited amount of samples arising from a nuclear magnetic resonance experiment. The term limited can be explained by the approach

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12

Alora, John Irvin P. "Automated synthesis of low-rank stochastic dynamical systems using the tensor-train decomposition." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/105006.

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Thesis: S.M., Massachusetts Institute of Technology, Department of Aeronautics and Astronautics, 2016.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (pages 79-83).<br>Cyber-physical systems are increasingly becoming integrated in various fields such as medicine, finance, robotics, and energy. In these systems and their applications, safety and correctness of operation is of primary concern, spar

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13

Han, Xu. "Robust low-rank tensor approximations using group sparsity." Thesis, Rennes 1, 2019. http://www.theses.fr/2019REN1S001/document.

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Le développement de méthodes de décomposition de tableaux multi-dimensionnels suscite toujours autant d'attention, notamment d'un point de vue applicatif. La plupart des algorithmes, de décompositions tensorielles, existants requièrent une estimation du rang du tenseur et sont sensibles à une surestimation de ce dernier. Toutefois, une telle estimation peut être difficile par exemple pour des rapports signal à bruit faibles. D'un autre côté, estimer simultanément le rang et les matrices de facteurs du tenseur ou du tenseur cœur n'est pas tâche facile tant les problèmes de minimisation de rang

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14

Biradar, Rakesh. "Analysis and Prediction of Community Structure Using Unsupervised Learning." Digital WPI, 2016. https://digitalcommons.wpi.edu/etd-theses/138.

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In this thesis, we perform analysis and prediction for community structures in graphs using unsupervised learning. The methods we use require the data matrices to be of low rank, and such matrices appear quite often in real world problems across a broad range of domains. Such a modelling assumption is widely considered by classical algorithms such as principal component analysis (PCA), and the same assumption is often used to achieve dimensionality reduction. Dimension reduction, which is a classic method in unsupervised learning, can be leveraged in a wide array of problems, including predict

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15

Slawski, Martin [Verfasser], and Matthias [Akademischer Betreuer] Hein. "Topics in learning sparse and low-rank models of non-negative data / Martin Slawski. Betreuer: Matthias Hein." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2015. http://d-nb.info/1072409860/34.

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16

Neumann, Patrick [Verfasser], Russell [Akademischer Betreuer] Luke, and Max [Akademischer Betreuer] Wardetzky. "Projection Methods in Sparse and Low Rank Feasibility / Patrick Neumann. Gutachter: Russell Luke ; Max Wardetzky. Betreuer: Russell Luke." Göttingen : Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2015. http://d-nb.info/1074040139/34.

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17

Benedikt, Udo. "Low-Rank Tensor Approximation in post Hartree-Fock Methods." Doctoral thesis, Universitätsbibliothek Chemnitz, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa-133194.

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In this thesis the application of novel tensor decomposition and tensor representation techniques in highly accurate post Hartree-Fock methods is evaluated. These representation techniques can help to overcome the steep scaling behaviour of high level ab-initio calculations with increasing system size and therefore break the "curse of dimensionality". After a comparison of various tensor formats the application of the "canonical polyadic" format (CP) is described in detail. There, especially the casting of a normal, index based tensor into the CP format (tensor decomposition) and a method for

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18

Penzl, T. "A cyclic low rank Smith method for large, sparse Lyapunov equations with applications in model reduction and optimal control." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199801035.

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We present a new method for the computation of low rank approximations to the solution of large, sparse, stable Lyapunov equations. It is based on a generalization of the classical Smith method and profits by the usual low rank property of the right hand side matrix. The requirements of the method are moderate with respect to both computational cost and memory. Hence, it provides a possibility to tackle large scale control problems. Besides the efficient solution of the matrix equation itself, a thorough integration of the method into several control algorithms can improve their performance to

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19

Pichon, Grégoire. "On the use of low-rank arithmetic to reduce the complexity of parallel sparse linear solvers based on direct factorization techniques." Thesis, Bordeaux, 2018. http://www.theses.fr/2018BORD0249/document.

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La résolution de systèmes linéaires creux est un problème qui apparaît dans de nombreuses applications scientifiques, et les solveurs creux sont une étape coûteuse pour ces applications ainsi que pour des solveurs plus avancés comme les solveurs hybrides direct-itératif. Pour ces raisons, optimiser la performance de ces solveurs pour les architectures modernes est un problème critique. Cependant, les contraintes mémoire et le temps de résolution limitent l’utilisation de ce type de solveur pour des problèmes de très grande taille. Pour les approches concurrentes, par exemple les méthodes itéra

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20

Weisbecker, Clément. "Improving multifrontal solvers by means of algebraic Block Low-Rank representations." Phd thesis, Toulouse, INPT, 2013. http://oatao.univ-toulouse.fr/10506/1/weisbecker.pdf.

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We consider the solution of large sparse linear systems by means of direct factorization based on a multifrontal approach. Although numerically robust and easy to use (it only needs algebraic information: the input matrix A and a right-hand side b, even if it can also digest preprocessing strategies based on geometric information), direct factorization methods are computationally intensive both in terms of memory and operations, which limits their scope on very large problems (matrices with up to few hundred millions of equations). This work focuses on exploiting low-rank approximations on mul

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21

Benner, Peter, and Heike Faßbender. "On the numerical solution of large-scale sparse discrete-time Riccati equations." Universitätsbibliothek Chemnitz, 2010. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-201000182.

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The numerical solution of Stein (aka discrete Lyapunov) equations is the primary step in Newton's method for the solution of discrete-time algebraic Riccati equations (DARE). Here we present a low-rank Smith method as well as a low-rank alternating-direction-implicit-iteration to compute low-rank approximations to solutions of Stein equations arising in this context. Numerical results are given to verify the efficiency and accuracy of the proposed algorithms.

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22

Nussbaum, Frank [Verfasser], Joachim [Gutachter] Giesen, Kristian [Gutachter] Kersting, and Christopher [Gutachter] Schneider. "Models with low-rank and group-sparse components and their recovery via convex optimization / Frank Nussbaum ; Gutachter: Joachim Giesen, Kristian Kersting, Christopher Schneider." Jena : Friedrich-Schiller-Universität Jena, 2021. http://nbn-resolving.de/urn:nbn:de:gbv:27-dbt-20210917-083904-007.

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23

Guerrero, Flores Danny Joel. "On Updating Preconditioners for the Iterative Solution of Linear Systems." Doctoral thesis, Universitat Politècnica de València, 2018. http://hdl.handle.net/10251/104923.

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El tema principal de esta tesis es el desarrollo de técnicas de actualización de precondicionadores para resolver sistemas lineales de gran tamaño y dispersos Ax=b mediante el uso de métodos iterativos de Krylov. Se consideran dos tipos interesantes de problemas. En el primero se estudia la solución iterativa de sistemas lineales no singulares y antisimétricos, donde la matriz de coeficientes A tiene parte antisimétrica de rango bajo o puede aproximarse bien con una matriz antisimétrica de rango bajo. Sistemas como este surgen de la discretización de PDEs con ciertas condiciones de frontera de

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Xiong, Liang. "On Learning from Collective Data." Research Showcase @ CMU, 2013. http://repository.cmu.edu/dissertations/560.

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In many machine learning problems and application domains, the data are naturally organized by groups. For example, a video sequence is a group of images, an image is a group of patches, a document is a group of paragraphs/words, and a community is a group of people. We call them the collective data. In this thesis, we study how and what we can learn from collective data. Usually, machine learning focuses on individual objects, each of which is described by a feature vector and studied as a point in some metric space. When approaching collective data, researchers often reduce the groups into v

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Kümmerle, Christian [Verfasser], Felix [Akademischer Betreuer] Krahmer, Rayan [Gutachter] Saab, Felix [Gutachter] Krahmer, and Daniel [Gutachter] Potts. "Understanding and Enhancing Data Recovery Algorithms : From Noise-Blind Sparse Recovery to Reweighted Methods for Low-Rank Matrix Optimization / Christian Kümmerle ; Gutachter: Rayan Saab, Felix Krahmer, Daniel Potts ; Betreuer: Felix Krahmer." München : Universitätsbibliothek der TU München, 2019. http://d-nb.info/1202922694/34.

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Kang, Kingston. "ESTIMATING THE RESPIRATORY LUNG MOTION MODEL USING TENSOR DECOMPOSITION ON DISPLACEMENT VECTOR FIELD." VCU Scholars Compass, 2018. https://scholarscompass.vcu.edu/etd/5254.

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Modern big data often emerge as tensors. Standard statistical methods are inadequate to deal with datasets of large volume, high dimensionality, and complex structure. Therefore, it is important to develop algorithms such as low-rank tensor decomposition for data compression, dimensionality reduction, and approximation. With the advancement in technology, high-dimensional images are becoming ubiquitous in the medical field. In lung radiation therapy, the respiratory motion of the lung introduces variabilities during treatment as the tumor inside the lung is moving, which brings challenges to t

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Falco, Aurélien. "Bridging the Gap Between H-Matrices and Sparse Direct Methods for the Solution of Large Linear Systems." Thesis, Bordeaux, 2019. http://www.theses.fr/2019BORD0090/document.

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De nombreux phénomènes physiques peuvent être étudiés au moyen de modélisations et de simulations numériques, courantes dans les applications scientifiques. Pour être calculable sur un ordinateur, des techniques de discrétisation appropriées doivent être considérées, conduisant souvent à un ensemble d’équations linéaires dont les caractéristiques dépendent des techniques de discrétisation. D’un côté, la méthode des éléments finis conduit généralement à des systèmes linéaires creux, tandis que les méthodes des éléments finis de frontière conduisent à des systèmes linéaires denses. La taille des

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Zhang, Yu. "Investigating Key Techniques to Leverage the Functionality of Ground/Wall Penetrating Radar." ScholarWorks @ UVM, 2017. http://scholarworks.uvm.edu/graddis/799.

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Ground penetrating radar (GPR) has been extensively utilized as a highly efficient and non-destructive testing method for infrastructure evaluation, such as highway rebar detection, bridge decks inspection, asphalt pavement monitoring, underground pipe leakage detection, railroad ballast assessment, etc. The focus of this dissertation is to investigate the key techniques to tackle with GPR signal processing from three perspectives: (1) Removing or suppressing the radar clutter signal; (2) Detecting the underground target or the region of interest (RoI) in the GPR image; (3) Imaging the undergr

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Kim, Jingu. "Nonnegative matrix and tensor factorizations, least squares problems, and applications." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42909.

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Nonnegative matrix factorization (NMF) is a useful dimension reduction method that has been investigated and applied in various areas. NMF is considered for high-dimensional data in which each element has a nonnegative value, and it provides a low-rank approximation formed by factors whose elements are also nonnegative. The nonnegativity constraints imposed on the low-rank factors not only enable natural interpretation but also reveal the hidden structure of data. Extending the benefits of NMF to multidimensional arrays, nonnegative tensor factorization (NTF) has been shown to be successful in

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30

Fanelli, Francesco. "Mathematical analysis of models of non-homogeneous fluids and of hyperbolic equations with low regularity coefficients." Phd thesis, Université Paris-Est, 2012. http://tel.archives-ouvertes.fr/tel-00794508.

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The present thesis is devoted both to the study of strictly hyperbolic operators with low regularity coefficients and of the density-dependent incompressible Euler system. On the one hand, we show a priori estimates for a second order strictly hyperbolic operator whose highest order coefficients satisfy a log-Zygmund continuity condition in time and a log-Lipschitz continuity condition with respect to space. Such an estimate involves a time increasing loss of derivatives. Nevertheless, this is enough to recover well-posedness for the associated Cauchy problem in the space $H^infty$ (for suitab

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Hrbáček, Radek. "Využití řídké reprezentace signálu při snímání a rekonstrukci v nukleární magnetické rezonanci." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2013. http://www.nusl.cz/ntk/nusl-220303.

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This thesis deals with the nuclear magnetic resonance field, especially spectroscopy and spectroscopy imaging, sparse signal representation and low-rank approximation approaches. Spectroscopy imaging methods are becoming very popular in clinical praxis, however, long measurement times and low resolution prevent them from their spreading. The goal of this thesis is to improve state of the art methods by using sparse signal representation and low-rank approximation approaches. The compressed sensing technique is demonstrated on the examples of magnetic resonance imaging speedup and hyperspectral

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Harmouch, Jouhayna. "Décomposition de petit rang, problèmes de complétion et applications : décomposition de matrices de Hankel et des tenseurs de rang faible." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4236/document.

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On étudie la décomposition de matrice de Hankel comme une somme des matrices de Hankel de rang faible en corrélation avec la décomposition de son symbole σ comme une somme des séries exponentielles polynomiales. On présente un nouvel algorithme qui calcule la décomposition d’un opérateur de Hankel de petit rang et sa décomposition de son symbole en exploitant les propriétés de l’algèbre quotient de Gorenstein . La base de est calculée à partir la décomposition en valeurs singuliers d’une sous-matrice de matrice de Hankel . Les fréquences et les poids se déduisent des vecteurs propres généralis

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Kolbábková, Anežka. "Algoritmy doplňování chybějících dat v audiosignálech." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2014. http://www.nusl.cz/ntk/nusl-231131.

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Tato práce se zabývá doplňováním chybějících dat do audio signálů a algoritmy řešícími problém založenými na řídké reprezentaci audio signálu. Práce se zaměřuje na některé algoritmy, které řeší doplňování chybějících dat do audio signálů pomocí řídké reprezentace signálů. Součástí práce je také návrh algoritmu, který používá řídkou reprezentaci signálu a také nízkou hodnost signálu ve spektrogramu audio signálu. Dále práce uvádí implementaci tohoto algoritmu v programu Matlab a jeho vyhodnocení.

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Mangová, Marie. "Komprimované snímání v perfuzním zobrazování pomocí magnetické rezonance." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2014. http://www.nusl.cz/ntk/nusl-231150.

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Magnetic resonance perfusion imaging is a today's very promising method for medicine diagnosis. This thesis deals with a sparse representation of signals, low-rank matrix recovery and compressed sensing, which allows overcoming present physical limitations of magnetic resonance perfusion imaging. Several models for reconstruction of measured perfusion data is introduced and numerical methods for their software implementation, which is an important part of the thesis, is mentioned. Proposed models are verified on simulated and real perfusion data from magnetic resonance.

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Boizard, Maxime. "Développement et études de performances de nouveaux détecteurs/filtres rang faible dans des configurations RADAR multidimensionnelles." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00996967.

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Dans le cadre du traitement statistique du signal, la plupart des algorithmes couramment utilisés reposent sur l'utilisation de la matrice de covariance des signaux étudiés. En pratique, ce sont les versions adaptatives de ces traitements, obtenues en estimant la matrice de covariance à l'aide d'échantillons du signal, qui sont utilisés. Ces algorithmes présentent un inconvénient : ils peuvent nécessiter un nombre d'échantillons important pour obtenir de bons résultats. Lorsque la matrice de covariance possède une structure rang faible, le signal peut alors être décomposé en deux sous-espaces

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Mary, Théo. "Solveurs multifrontaux exploitant des blocs de rang faible : complexité, performance et parallélisme." Thesis, Toulouse 3, 2017. http://www.theses.fr/2017TOU30305/document.

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Nous nous intéressons à l'utilisation d'approximations de rang faible pour réduire le coût des solveurs creux directs multifrontaux. Parmi les différents formats matriciels qui ont été proposés pour exploiter la propriété de rang faible dans les solveurs multifrontaux, nous nous concentrons sur le format Block Low-Rank (BLR) dont la simplicité et la flexibilité permettent de l'utiliser facilement dans un solveur multifrontal algébrique et généraliste. Nous présentons différentes variantes de la factorisation BLR, selon comment les mises à jour de rang faible sont effectuées, et comment le pivo

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Goulart, José Henrique De Morais. "Estimation de modèles tensoriels structurés et récupération de tenseurs de rang faible." Thesis, Université Côte d'Azur (ComUE), 2016. http://www.theses.fr/2016AZUR4147/document.

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Dans la première partie de cette thèse, on formule deux méthodes pour le calcul d'une décomposition polyadique canonique avec facteurs matriciels linéairement structurés (tels que des facteurs de Toeplitz ou en bande): un algorithme de moindres carrés alternés contraint (CALS) et une solution algébrique dans le cas où tous les facteurs sont circulants. Des versions exacte et approchée de la première méthode sont étudiées. La deuxième méthode fait appel à la transformée de Fourier multidimensionnelle du tenseur considéré, ce qui conduit à la résolution d'un système d'équations monomiales homogè

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Jalali, Ali 1982. "Dirty statistical models." Thesis, 2012. http://hdl.handle.net/2152/ETD-UT-2012-05-5088.

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In fields across science and engineering, we are increasingly faced with problems where the number of variables or features we need to estimate is much larger than the number of observations. Under such high-dimensional scaling, for any hope of statistically consistent estimation, it becomes vital to leverage any potential structure in the problem such as sparsity, low-rank structure or block sparsity. However, data may deviate significantly from any one such statistical model. The motivation of this thesis is: can we simultaneously leverage more than one such statistical structural model, to

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Neumann, Patrick. "Projection Methods in Sparse and Low Rank Feasibility." Doctoral thesis, 2015. http://hdl.handle.net/11858/00-1735-0000-0022-604A-E.

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Plan, Yaniv. "Compressed Sensing, Sparse Approximation, and Low-Rank Matrix Estimation." Thesis, 2011. https://thesis.library.caltech.edu/6259/1/thesis.pdf.

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<p>The importance of sparse signal structures has been recognized in a plethora of applications ranging from medical imaging to group disease testing to radar technology. It has been shown in practice that various signals of interest may be (approximately) sparsely modeled, and that sparse modeling is often beneficial, or even indispensable to signal recovery. Alongside an increase in applications, a rich theory of sparse and compressible signal recovery has recently been developed under the names compressed sensing (CS) and sparse approximation (SA). This revolutionary research has demonst

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Wang, Yu-Sheng, and 王裕盛. "Moving Object Detection via Sparse and Low-Rank Tensor Modeling." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/14647869094424654385.

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碩士<br>國立清華大學<br>資訊工程學系<br>101<br>Background subtraction is a common method utilized to detect moving objects. The main idea is estimate the background model according to the non-occluded background. However, when the foreground is comparatively large or the moving displacement of foreground is negligible, the estimated result will be inaccurate because the background is occluded by foreground most of the time. In order to overcome the occluded background problem, we consider the spatial low-rank property of background, and propose to combine the spatial low-rank property and the temporal low-r

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Lin, Yu-Tin, and 林昱廷. "Detection of Gene×Gene Interactions by Multistage Sparse Low-Rank Regression." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/78417364698364747889.

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碩士<br>國立臺灣大學<br>數學研究所<br>100<br>Researchers in biological sciences nowadays often encounter the curse of high-dimensionality. A serious consequence is that many traditional statistical methods fail to fit for high-dimensional models. The problem becomes even more severe when the interest is in interactions between variables, as there will be p(p−1)/2 interaction terms with p variables. To improve the performance, in this thesis we model the interaction effects utilizing its matrix form with a low-rank structure. A low-rank model for symmetric matrix then greatly reduces the number of parameter

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"Video-based face alignment using efficient sparse and low-rank approach." 2011. http://library.cuhk.edu.hk/record=b5894817.

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Wu, King Keung.<br>"August 2011."<br>Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.<br>Includes bibliographical references (p. 119-126).<br>Abstracts in English and Chinese.<br>Abstract --- p.i<br>Acknowledgement --- p.v<br>Chapter 1 --- Introduction --- p.1<br>Chapter 1.1 --- Overview of Face Alignment Algorithms --- p.1<br>Chapter 1.1.1 --- Objectives --- p.1<br>Chapter 1.1.2 --- Motivation: Photo-realistic Talking Head --- p.2<br>Chapter 1.1.3 --- Existing methods --- p.5<br>Chapter 1.2 --- Contributions --- p.8<br>Chapter 1.3 --- Outline of the Thesis --- p.11<br>Chapter

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Ma, Shiqian. "Algorithms for Sparse and Low-Rank Optimization: Convergence, Complexity and Applications." Thesis, 2011. https://doi.org/10.7916/D8PC38BZ.

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Solving optimization problems with sparse or low-rank optimal solutions has been an important topic since the recent emergence of compressed sensing and its matrix extensions such as the matrix rank minimization and robust principal component analysis problems. Compressed sensing enables one to recover a signal or image with fewer observations than the "length" of the signal or image, and thus provides potential breakthroughs in applications where data acquisition is costly. However, the potential impact of compressed sensing cannot be realized without efficient optimization algorithms that ca

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Wu, Cho-Ying, and 吳卓穎. "Sparse and Low-Rank Model for Occluded Face Recognition and Nonconvex Numerical Optimization." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/pnk6uv.

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碩士<br>國立臺灣大學<br>電信工程學研究所<br>105<br>Face recognition is a very popular research topic for computer vision. However, in the real-world scenario, occlusion is a frequently occurring obstacle for recognition. With the occlusion, the information for the face of an individual is diminished. Recently, sparse representation based classification has been proposed on robust the face recognition problem. They have extraordinary performance on randomly corrupted face images. However, for real-world occlusion, this method lacks efficiency and effectiveness. Inspired by the techniques related to compressive

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Pototskaia, Vlada. "Application of AAK theory for sparse approximation." Doctoral thesis, 2017. http://hdl.handle.net/11858/00-1735-0000-0023-3F4B-1.

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Benedikt, Udo. "Low-Rank Tensor Approximation in post Hartree-Fock Methods." Doctoral thesis, 2013. https://monarch.qucosa.de/id/qucosa%3A19999.

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In this thesis the application of novel tensor decomposition and tensor representation techniques in highly accurate post Hartree-Fock methods is evaluated. These representation techniques can help to overcome the steep scaling behaviour of high level ab-initio calculations with increasing system size and therefore break the "curse of dimensionality". After a comparison of various tensor formats the application of the "canonical polyadic" format (CP) is described in detail. There, especially the casting of a normal, index based tensor into the CP format (tensor decomposition) and a method for

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Wikén, Victor. "An Investigation of Low-Rank Decomposition for Increasing Inference Speed in Deep Neural Networks With Limited Training Data." Thesis, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-235370.

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In this study, to increase inference speed of convolutional neural networks, the optimization technique low-rank tensor decomposition has been implemented and applied to AlexNet which had been trained to classify dog breeds. Due to a small training set, transfer learning was used in order to be able to classify dog breeds. The purpose of the study is to investigate how effective low-rank tensor decomposition is when the training set is limited. The results obtained from this study, compared to a previous study, indicate that there is a strong relationship between the effects of the tensor deco

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Charara, Ali. "Exploiting Data Sparsity In Covariance Matrix Computations on Heterogeneous Systems." Diss., 2018. http://hdl.handle.net/10754/627948.

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Covariance matrices are ubiquitous in computational sciences, typically describing the correlation of elements of large multivariate spatial data sets. For example, covari- ance matrices are employed in climate/weather modeling for the maximum likelihood estimation to improve prediction, as well as in computational ground-based astronomy to enhance the observed image quality by filtering out noise produced by the adap- tive optics instruments and atmospheric turbulence. The structure of these covariance matrices is dense, symmetric, positive-definite, and often data-sparse, therefore, hier- ar

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Outrata, Michal. "Aproximace maticemi malé hodnosti a jejich aplikace." Master's thesis, 2018. http://www.nusl.cz/ntk/nusl-386966.

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Consider the problem of solving a large system of linear algebraic equations, using the Krylov subspace methods. In order to find the solution efficiently, the system often needs to be preconditioned, i.e., transformed prior to the iterative scheme. A feature of the system that often enables fast solution with efficient preconditioners is the structural sparsity of the corresponding matrix. A recent development brought another and a slightly different phe- nomenon called the data sparsity. In contrast to the classical (structural) sparsity, the data sparsity refers to an uneven distribution of

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