Sparsity

Sparsity

Author: Jaroslav Nešetřil

Publisher: Springer Science & Business Media

Published: 2012-04-24

Total Pages: 472

ISBN-13: 3642278752

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This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010.


Book Synopsis Sparsity by : Jaroslav Nešetřil

Download or read book Sparsity written by Jaroslav Nešetřil and published by Springer Science & Business Media. This book was released on 2012-04-24 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book devoted to the systematic study of sparse graphs and sparse finite structures. Although the notion of sparsity appears in various contexts and is a typical example of a hard to define notion, the authors devised an unifying classification of general classes of structures. This approach is very robust and it has many remarkable properties. For example the classification is expressible in many different ways involving most extremal combinatorial invariants. This study of sparse structures found applications in such diverse areas as algorithmic graph theory, complexity of algorithms, property testing, descriptive complexity and mathematical logic (homomorphism preservation,fixed parameter tractability and constraint satisfaction problems). It should be stressed that despite of its generality this approach leads to linear (and nearly linear) algorithms. Jaroslav Nešetřil is a professor at Charles University, Prague; Patrice Ossona de Mendez is a CNRS researcher et EHESS, Paris. This book is related to the material presented by the first author at ICM 2010.

Statistical Learning with Sparsity

Statistical Learning with Sparsity

Author: Trevor Hastie

Publisher: CRC Press

Published: 2015-05-07

Total Pages: 354

ISBN-13: 1498712177

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Discover New Methods for Dealing with High-Dimensional DataA sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underl


Book Synopsis Statistical Learning with Sparsity by : Trevor Hastie

Download or read book Statistical Learning with Sparsity written by Trevor Hastie and published by CRC Press. This book was released on 2015-05-07 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover New Methods for Dealing with High-Dimensional DataA sparse statistical model has only a small number of nonzero parameters or weights; therefore, it is much easier to estimate and interpret than a dense model. Statistical Learning with Sparsity: The Lasso and Generalizations presents methods that exploit sparsity to help recover the underl

Sparsity Methods for Systems and Control

Sparsity Methods for Systems and Control

Author: Masaaki Nagahara

Publisher:

Published: 2020-09-30

Total Pages: 220

ISBN-13: 9781680837247

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The method of sparsity has been attracting a lot of attention in the fields related not only to signal processing, machine learning, and statistics, but also systems and control. The method is known as compressed sensing, compressive sampling, sparse representation, or sparse modeling. More recently, the sparsity method has been applied to systems and control to design resource-aware control systems. This book gives a comprehensive guide to sparsity methods for systems and control, from standard sparsity methods in finite-dimensional vector spaces (Part I) to optimal control methods in infinite-dimensional function spaces (Part II). The primary objective of this book is to show how to use sparsity methods for several engineering problems. For this, the author provides MATLAB programs by which the reader can try sparsity methods for themselves. Readers will obtain a deep understanding of sparsity methods by running these MATLAB programs. Sparsity Methods for Systems and Control is suitable for graduate level university courses, though it should also be comprehendible to undergraduate students who have a basic knowledge of linear algebra and elementary calculus. Also, especially part II of the book should appeal to professional researchers and engineers who are interested in applying sparsity methods to systems and control.


Book Synopsis Sparsity Methods for Systems and Control by : Masaaki Nagahara

Download or read book Sparsity Methods for Systems and Control written by Masaaki Nagahara and published by . This book was released on 2020-09-30 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The method of sparsity has been attracting a lot of attention in the fields related not only to signal processing, machine learning, and statistics, but also systems and control. The method is known as compressed sensing, compressive sampling, sparse representation, or sparse modeling. More recently, the sparsity method has been applied to systems and control to design resource-aware control systems. This book gives a comprehensive guide to sparsity methods for systems and control, from standard sparsity methods in finite-dimensional vector spaces (Part I) to optimal control methods in infinite-dimensional function spaces (Part II). The primary objective of this book is to show how to use sparsity methods for several engineering problems. For this, the author provides MATLAB programs by which the reader can try sparsity methods for themselves. Readers will obtain a deep understanding of sparsity methods by running these MATLAB programs. Sparsity Methods for Systems and Control is suitable for graduate level university courses, though it should also be comprehendible to undergraduate students who have a basic knowledge of linear algebra and elementary calculus. Also, especially part II of the book should appeal to professional researchers and engineers who are interested in applying sparsity methods to systems and control.

Sparsity and Its Applications

Sparsity and Its Applications

Author: David J. Evans

Publisher: CUP Archive

Published: 1985-01-10

Total Pages: 364

ISBN-13: 9780521262729

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Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.


Book Synopsis Sparsity and Its Applications by : David J. Evans

Download or read book Sparsity and Its Applications written by David J. Evans and published by CUP Archive. This book was released on 1985-01-10 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Good,No Highlights,No Markup,all pages are intact, Slight Shelfwear,may have the corners slightly dented, may have slight color changes/slightly damaged spine.

Estimation and Testing Under Sparsity

Estimation and Testing Under Sparsity

Author: Sara van de Geer

Publisher: Springer

Published: 2016-06-28

Total Pages: 274

ISBN-13: 3319327747

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Taking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. It also provides a semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing methods have proven to be very useful in the analysis of high-dimensional data. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm. The illustrations provided include generalized linear models, density estimation, matrix completion and sparse principal components. Each chapter ends with a problem section. The book can be used as a textbook for a graduate or PhD course.


Book Synopsis Estimation and Testing Under Sparsity by : Sara van de Geer

Download or read book Estimation and Testing Under Sparsity written by Sara van de Geer and published by Springer. This book was released on 2016-06-28 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Taking the Lasso method as its starting point, this book describes the main ingredients needed to study general loss functions and sparsity-inducing regularizers. It also provides a semi-parametric approach to establishing confidence intervals and tests. Sparsity-inducing methods have proven to be very useful in the analysis of high-dimensional data. Examples include the Lasso and group Lasso methods, and the least squares method with other norm-penalties, such as the nuclear norm. The illustrations provided include generalized linear models, density estimation, matrix completion and sparse principal components. Each chapter ends with a problem section. The book can be used as a textbook for a graduate or PhD course.

Algorithms for Sparsity-Constrained Optimization

Algorithms for Sparsity-Constrained Optimization

Author: Sohail Bahmani

Publisher: Springer Science & Business Media

Published: 2013-10-07

Total Pages: 124

ISBN-13: 3319018817

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This thesis demonstrates techniques that provide faster and more accurate solutions to a variety of problems in machine learning and signal processing. The author proposes a "greedy" algorithm, deriving sparse solutions with guarantees of optimality. The use of this algorithm removes many of the inaccuracies that occurred with the use of previous models.


Book Synopsis Algorithms for Sparsity-Constrained Optimization by : Sohail Bahmani

Download or read book Algorithms for Sparsity-Constrained Optimization written by Sohail Bahmani and published by Springer Science & Business Media. This book was released on 2013-10-07 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis demonstrates techniques that provide faster and more accurate solutions to a variety of problems in machine learning and signal processing. The author proposes a "greedy" algorithm, deriving sparse solutions with guarantees of optimality. The use of this algorithm removes many of the inaccuracies that occurred with the use of previous models.

Study on Signal Detection and Recovery Methods with Joint Sparsity

Study on Signal Detection and Recovery Methods with Joint Sparsity

Author: Xueqian Wang

Publisher: Springer Nature

Published: 2023-09-30

Total Pages: 135

ISBN-13: 9819941172

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The task of signal detection is deciding whether signals of interest exist by using their observed data. Furthermore, signals are reconstructed or their key parameters are estimated from the observations in the task of signal recovery. Sparsity is a natural characteristic of most of signals in practice. The fact that multiple sparse signals share the common locations of dominant coefficients is called by joint sparsity. In the context of signal processing, joint sparsity model results in higher performance of signal detection and recovery. This book focuses on the task of detecting and reconstructing signals with joint sparsity. The main contents include key methods for detection of joint sparse signals and their corresponding theoretical performance analysis, and methods for joint sparse signal recovery and their application in the context of radar imaging.


Book Synopsis Study on Signal Detection and Recovery Methods with Joint Sparsity by : Xueqian Wang

Download or read book Study on Signal Detection and Recovery Methods with Joint Sparsity written by Xueqian Wang and published by Springer Nature. This book was released on 2023-09-30 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The task of signal detection is deciding whether signals of interest exist by using their observed data. Furthermore, signals are reconstructed or their key parameters are estimated from the observations in the task of signal recovery. Sparsity is a natural characteristic of most of signals in practice. The fact that multiple sparse signals share the common locations of dominant coefficients is called by joint sparsity. In the context of signal processing, joint sparsity model results in higher performance of signal detection and recovery. This book focuses on the task of detecting and reconstructing signals with joint sparsity. The main contents include key methods for detection of joint sparse signals and their corresponding theoretical performance analysis, and methods for joint sparse signal recovery and their application in the context of radar imaging.

Sparse Sensing and Sparsity Sensed in Multi-sensor Array Applications

Sparse Sensing and Sparsity Sensed in Multi-sensor Array Applications

Author: Xiangrong Wang

Publisher: Springer Nature

Published:

Total Pages: 387

ISBN-13: 9819995582

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Book Synopsis Sparse Sensing and Sparsity Sensed in Multi-sensor Array Applications by : Xiangrong Wang

Download or read book Sparse Sensing and Sparsity Sensed in Multi-sensor Array Applications written by Xiangrong Wang and published by Springer Nature. This book was released on with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs

Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs

Author: Dinh Dũng

Publisher: Springer Nature

Published: 2023-11-16

Total Pages: 216

ISBN-13: 3031383842

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The present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains. Both, forward and Bayesian inverse PDE problems subject to GRF priors are considered. Adopting a pathwise, affine-parametric representation of the GRFs, turns the random PDEs into equivalent, countably-parametric, deterministic PDEs, with nonuniform ellipticity constants. A detailed sparsity analysis of Wiener-Hermite polynomial chaos expansions of the corresponding parametric PDE solution families by analytic continuation into the complex domain is developed, in corner- and edge-weighted function spaces on the physical domain. The presented Algorithms and results are relevant for the mathematical analysis of many approximation methods for PDEs with GRF inputs, such as model order reduction, neural network and tensor-formatted surrogates of parametric solution families. They are expected to impact computational uncertainty quantification subject to GRF models of uncertainty in PDEs, and are of interest for researchers and graduate students in both, applied and computational mathematics, as well as in computational science and engineering.


Book Synopsis Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs by : Dinh Dũng

Download or read book Analyticity and Sparsity in Uncertainty Quantification for PDEs with Gaussian Random Field Inputs written by Dinh Dũng and published by Springer Nature. This book was released on 2023-11-16 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book develops the mathematical and numerical analysis of linear, elliptic and parabolic partial differential equations (PDEs) with coefficients whose logarithms are modelled as Gaussian random fields (GRFs), in polygonal and polyhedral physical domains. Both, forward and Bayesian inverse PDE problems subject to GRF priors are considered. Adopting a pathwise, affine-parametric representation of the GRFs, turns the random PDEs into equivalent, countably-parametric, deterministic PDEs, with nonuniform ellipticity constants. A detailed sparsity analysis of Wiener-Hermite polynomial chaos expansions of the corresponding parametric PDE solution families by analytic continuation into the complex domain is developed, in corner- and edge-weighted function spaces on the physical domain. The presented Algorithms and results are relevant for the mathematical analysis of many approximation methods for PDEs with GRF inputs, such as model order reduction, neural network and tensor-formatted surrogates of parametric solution families. They are expected to impact computational uncertainty quantification subject to GRF models of uncertainty in PDEs, and are of interest for researchers and graduate students in both, applied and computational mathematics, as well as in computational science and engineering.

Inverse Problems with Sparsity Constraints

Inverse Problems with Sparsity Constraints

Author: Dennis Trede

Publisher: Logos Verlag Berlin GmbH

Published: 2010

Total Pages: 137

ISBN-13: 3832524665

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This thesis contributes to the field of inverse problems with sparsity constraints. Since the pioneering work by Daubechies, Defries and De Mol in 2004, methods for solving operator equations with sparsity constraints play a central role in the field of inverse problems. This can be explained by the fact that the solutions of many inverse problems have a sparse structure, in other words, they can be represented using only finitely many elements of a suitable basis or dictionary. Generally, to stably solve an ill-posed inverse problem one needs additional assumptions on the unknown solution--the so-called source condition. In this thesis, the sparseness stands for the source condition, and with that in mind, stability results for two different approximation methods are deduced, namely, results for the Tikhonov regularization with a sparsity-enforcing penalty and for the orthogonal matching pursuit. The practical relevance of the theoretical results is shown with two examples of convolution type, namely, an example from mass spectrometry and an example from digital holography of particles.


Book Synopsis Inverse Problems with Sparsity Constraints by : Dennis Trede

Download or read book Inverse Problems with Sparsity Constraints written by Dennis Trede and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis contributes to the field of inverse problems with sparsity constraints. Since the pioneering work by Daubechies, Defries and De Mol in 2004, methods for solving operator equations with sparsity constraints play a central role in the field of inverse problems. This can be explained by the fact that the solutions of many inverse problems have a sparse structure, in other words, they can be represented using only finitely many elements of a suitable basis or dictionary. Generally, to stably solve an ill-posed inverse problem one needs additional assumptions on the unknown solution--the so-called source condition. In this thesis, the sparseness stands for the source condition, and with that in mind, stability results for two different approximation methods are deduced, namely, results for the Tikhonov regularization with a sparsity-enforcing penalty and for the orthogonal matching pursuit. The practical relevance of the theoretical results is shown with two examples of convolution type, namely, an example from mass spectrometry and an example from digital holography of particles.