Low Rank Approximation

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Low-Rank Approximation

Author : Ivan Markovsky
Publisher : Springer
ISBN 13 : 9783030078171
Total Pages : 0 pages
Book Rating : 4.0/5 (781 download)

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Book Synopsis Low-Rank Approximation by : Ivan Markovsky

Download or read book Low-Rank Approximation written by Ivan Markovsky and published by Springer. This book was released on 2019-01-10 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive exposition of the theory, algorithms, and applications of structured low-rank approximation. Local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. A major part of the text is devoted to application of the theory with a range of applications from systems and control theory to psychometrics being described. Special knowledge of the application fields is not required. The second edition of /Low-Rank Approximation/ is a thoroughly edited and extensively rewritten revision. It contains new chapters and sections that introduce the topics of: • variable projection for structured low-rank approximation;• missing data estimation;• data-driven filtering and control;• stochastic model representation and identification;• identification of polynomial time-invariant systems; and• blind identification with deterministic input model. The book is complemented by a software implementation of the methods presented, which makes the theory directly applicable in practice. In particular, all numerical examples in the book are included in demonstration files and can be reproduced by the reader. This gives hands-on experience with the theory and methods detailed. In addition, exercises and MATLAB^® /Octave examples will assist the reader quickly to assimilate the theory on a chapter-by-chapter basis. “Each chapter is completed with a new section of exercises to which complete solutions are provided.” Low-Rank Approximation (second edition) is a broad survey of the Low-Rank Approximation theory and applications of its field which will be of direct interest to researchers in system identification, control and systems theory, numerical linear algebra and optimization. The supplementary problems and solutions render it suitable for use in teaching graduate courses in those subjects as well.

Low Rank Approximation

Author : Ivan Markovsky
Publisher : Springer Science & Business Media
ISBN 13 : 1447122275
Total Pages : 260 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Low Rank Approximation by : Ivan Markovsky

Download or read book Low Rank Approximation written by Ivan Markovsky and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data Approximation by Low-complexity Models details the theory, algorithms, and applications of structured low-rank approximation. Efficient local optimization methods and effective suboptimal convex relaxations for Toeplitz, Hankel, and Sylvester structured problems are presented. Much of the text is devoted to describing the applications of the theory including: system and control theory; signal processing; computer algebra for approximate factorization and common divisor computation; computer vision for image deblurring and segmentation; machine learning for information retrieval and clustering; bioinformatics for microarray data analysis; chemometrics for multivariate calibration; and psychometrics for factor analysis. Software implementation of the methods is given, making the theory directly applicable in practice. All numerical examples are included in demonstration files giving hands-on experience and exercises and MATLAB® examples assist in the assimilation of the theory.

Handbook of Variational Methods for Nonlinear Geometric Data

Author : Philipp Grohs
Publisher : Springer Nature
ISBN 13 : 3030313514
Total Pages : 701 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Handbook of Variational Methods for Nonlinear Geometric Data by : Philipp Grohs

Download or read book Handbook of Variational Methods for Nonlinear Geometric Data written by Philipp Grohs and published by Springer Nature. This book was released on 2020-04-03 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

Generalized Low Rank Models

Author : Madeleine Udell
Publisher :
ISBN 13 : 9781680831405
Total Pages : 142 pages
Book Rating : 4.8/5 (314 download)

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Book Synopsis Generalized Low Rank Models by : Madeleine Udell

Download or read book Generalized Low Rank Models written by Madeleine Udell and published by . This book was released on 2016-05-03 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal, and other data types. This framework encompasses many well-known techniques in data analysis, such as nonnegative matrix factorization, matrix completion, sparse and robust PCA, k-means, k-SVD, and maximum margin matrix factorization. The method handles heterogeneous data sets, and leads to coherent schemes for compressing, denoising, and imputing missing entries across all data types simultaneously. It also admits a number of interesting interpretations of the low rank factors, which allow clustering of examples or of features. We propose several parallel algorithms for fitting generalized low rank models, and describe implementations and numerical results.

Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics

Author : Felix Fritzen
Publisher : MDPI
ISBN 13 : 3039214098
Total Pages : 254 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics by : Felix Fritzen

Download or read book Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics written by Felix Fritzen and published by MDPI. This book was released on 2019-09-18 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics.

Spectral Algorithms

Author : Ravindran Kannan
Publisher : Now Publishers Inc
ISBN 13 : 1601982747
Total Pages : 153 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Spectral Algorithms by : Ravindran Kannan

Download or read book Spectral Algorithms written by Ravindran Kannan and published by Now Publishers Inc. This book was released on 2009 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral methods refer to the use of eigenvalues, eigenvectors, singular values and singular vectors. They are widely used in Engineering, Applied Mathematics and Statistics. More recently, spectral methods have found numerous applications in Computer Science to "discrete" as well as "continuous" problems. Spectral Algorithms describes modern applications of spectral methods, and novel algorithms for estimating spectral parameters. The first part of the book presents applications of spectral methods to problems from a variety of topics including combinatorial optimization, learning and clustering. The second part of the book is motivated by efficiency considerations. A feature of many modern applications is the massive amount of input data. While sophisticated algorithms for matrix computations have been developed over a century, a more recent development is algorithms based on "sampling on the fly" from massive matrices. Good estimates of singular values and low rank approximations of the whole matrix can be provably derived from a sample. The main emphasis in the second part of the book is to present these sampling methods with rigorous error bounds. It also presents recent extensions of spectral methods from matrices to tensors and their applications to some combinatorial optimization problems.

Low-Rank Semidefinite Programming

Author : Alex Lemon
Publisher : Now Publishers
ISBN 13 : 9781680831368
Total Pages : 180 pages
Book Rating : 4.8/5 (313 download)

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Book Synopsis Low-Rank Semidefinite Programming by : Alex Lemon

Download or read book Low-Rank Semidefinite Programming written by Alex Lemon and published by Now Publishers. This book was released on 2016-05-04 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finding low-rank solutions of semidefinite programs is important in many applications. For example, semidefinite programs that arise as relaxations of polynomial optimization problems are exact relaxations when the semidefinite program has a rank-1 solution. Unfortunately, computing a minimum-rank solution of a semidefinite program is an NP-hard problem. This monograph reviews the theory of low-rank semidefinite programming, presenting theorems that guarantee the existence of a low-rank solution, heuristics for computing low-rank solutions, and algorithms for finding low-rank approximate solutions. It then presents applications of the theory to trust-region problems and signal processing.

Symbolic-Numeric Computation

Author : Dongming Wang
Publisher : Springer Science & Business Media
ISBN 13 : 3764379839
Total Pages : 391 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Symbolic-Numeric Computation by : Dongming Wang

Download or read book Symbolic-Numeric Computation written by Dongming Wang and published by Springer Science & Business Media. This book was released on 2007-01-22 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: The growing demand of speed, accuracy, and reliability in scientific and engineering computing has been accelerating the merging of symbolic and numeric computations. These two types of computation coexist in mathematics yet are separated in traditional research of mathematical computation. This book presents 27 research articles on the integration and interaction of symbolic and numeric computation.

Deep Learning through Sparse and Low-Rank Modeling

Author : Zhangyang Wang
Publisher : Academic Press
ISBN 13 : 0128136596
Total Pages : 296 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Deep Learning through Sparse and Low-Rank Modeling by : Zhangyang Wang

Download or read book Deep Learning through Sparse and Low-Rank Modeling written by Zhangyang Wang and published by Academic Press. This book was released on 2019-04-26 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deep Learning through Sparse Representation and Low-Rank Modeling bridges classical sparse and low rank models-those that emphasize problem-specific Interpretability-with recent deep network models that have enabled a larger learning capacity and better utilization of Big Data. It shows how the toolkit of deep learning is closely tied with the sparse/low rank methods and algorithms, providing a rich variety of theoretical and analytic tools to guide the design and interpretation of deep learning models. The development of the theory and models is supported by a wide variety of applications in computer vision, machine learning, signal processing, and data mining. This book will be highly useful for researchers, graduate students and practitioners working in the fields of computer vision, machine learning, signal processing, optimization and statistics. Combines classical sparse and low-rank models and algorithms with the latest advances in deep learning networks Shows how the structure and algorithms of sparse and low-rank methods improves the performance and interpretability of Deep Learning models Provides tactics on how to build and apply customized deep learning models for various applications

SVD and Signal Processing, III

Author : M. Moonen
Publisher : Elsevier
ISBN 13 : 9780080542157
Total Pages : 485 pages
Book Rating : 4.5/5 (421 download)

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Book Synopsis SVD and Signal Processing, III by : M. Moonen

Download or read book SVD and Signal Processing, III written by M. Moonen and published by Elsevier. This book was released on 1995-03-16 with total page 485 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix Singular Value Decomposition (SVD) and its application to problems in signal processing is explored in this book. The papers discuss algorithms and implementation architectures for computing the SVD, as well as a variety of applications such as systems and signal modeling and detection. The publication presents a number of keynote papers, highlighting recent developments in the field, namely large scale SVD applications, isospectral matrix flows, Riemannian SVD and consistent signal reconstruction. It also features a translation of a historical paper by Eugenio Beltrami, containing one of the earliest published discussions of the SVD. With contributions sourced from internationally recognised scientists, the book will be of specific interest to all researchers and students involved in the SVD and signal processing field.

Artificial Intelligence Research

Author : Edgar Jembere
Publisher : Springer Nature
ISBN 13 : 3030950700
Total Pages : 345 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Artificial Intelligence Research by : Edgar Jembere

Download or read book Artificial Intelligence Research written by Edgar Jembere and published by Springer Nature. This book was released on 2022-01-29 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second Southern African Conference on Artificial Intelligence Research, SACAIR 2021, held in Durban, South Africa, in December 2021. Due to the COVID-19 pandemic the SACAIR 2021 was held online. The 22 papers presented were thoroughly reviewed and selected from the 70 submissions. They are organized on the topical sections on AI in the humanities and society, AI in and for information systems, computer vision and image processing, deep learning, knowledge representation and reasoning, machine learning, philosophy and ethics of AI.

Applied Machine Learning

Author : David Forsyth
Publisher : Springer
ISBN 13 : 3030181146
Total Pages : 496 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Applied Machine Learning by : David Forsyth

Download or read book Applied Machine Learning written by David Forsyth and published by Springer. This book was released on 2019-07-12 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine learning methods are now an important tool for scientists, researchers, engineers and students in a wide range of areas. This book is written for people who want to adopt and use the main tools of machine learning, but aren’t necessarily going to want to be machine learning researchers. Intended for students in final year undergraduate or first year graduate computer science programs in machine learning, this textbook is a machine learning toolkit. Applied Machine Learning covers many topics for people who want to use machine learning processes to get things done, with a strong emphasis on using existing tools and packages, rather than writing one’s own code. A companion to the author's Probability and Statistics for Computer Science, this book picks up where the earlier book left off (but also supplies a summary of probability that the reader can use). Emphasizing the usefulness of standard machinery from applied statistics, this textbook gives an overview of the major applied areas in learning, including coverage of:• classification using standard machinery (naive bayes; nearest neighbor; SVM)• clustering and vector quantization (largely as in PSCS)• PCA (largely as in PSCS)• variants of PCA (NIPALS; latent semantic analysis; canonical correlation analysis)• linear regression (largely as in PSCS)• generalized linear models including logistic regression• model selection with Lasso, elasticnet• robustness and m-estimators• Markov chains and HMM’s (largely as in PSCS)• EM in fairly gory detail; long experience teaching this suggests one detailed example is required, which students hate; but once they’ve been through that, the next one is easy• simple graphical models (in the variational inference section)• classification with neural networks, with a particular emphasis onimage classification• autoencoding with neural networks• structure learning

Exact and Approximate Modeling of Linear Systems

Author : Ivan Markovsky
Publisher : SIAM
ISBN 13 : 0898716039
Total Pages : 210 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Exact and Approximate Modeling of Linear Systems by : Ivan Markovsky

Download or read book Exact and Approximate Modeling of Linear Systems written by Ivan Markovsky and published by SIAM. This book was released on 2006-01-31 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact and Approximate Modeling of Linear Systems: A Behavioral Approach elegantly introduces the behavioral approach to mathematical modeling, an approach that requires models to be viewed as sets of possible outcomes rather than to be a priori bound to particular representations. The authors discuss exact and approximate fitting of data by linear, bilinear, and quadratic static models and linear dynamic models, a formulation that enables readers to select the most suitable representation for a particular purpose. This book presents exact subspace-type and approximate optimization-based identification methods, as well as representation-free problem formulations, an overview of solution approaches, and software implementation. Readers will find an exposition of a wide variety of modeling problems starting from observed data. The presented theory leads to algorithms that are implemented in C language and in MATLAB.

Geometric Numerical Integration

Author : Ernst Hairer
Publisher : Springer Science & Business Media
ISBN 13 : 3662050188
Total Pages : 526 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Geometric Numerical Integration by : Ernst Hairer

Download or read book Geometric Numerical Integration written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book is illustrated by numerous figures, treats applications from physics and astronomy, and contains many numerical experiments and comparisons of different approaches.

Sketching as a Tool for Numerical Linear Algebra

Author : David P. Woodruff
Publisher : Now Publishers
ISBN 13 : 9781680830040
Total Pages : 168 pages
Book Rating : 4.8/5 (3 download)

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Book Synopsis Sketching as a Tool for Numerical Linear Algebra by : David P. Woodruff

Download or read book Sketching as a Tool for Numerical Linear Algebra written by David P. Woodruff and published by Now Publishers. This book was released on 2014-11-14 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sketching as a Tool for Numerical Linear Algebra highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compressed it to a much smaller matrix by multiplying it by a (usually) random matrix with certain properties. Much of the expensive computation can then be performed on the smaller matrix, thereby accelerating the solution for the original problem. It is an ideal primer for researchers and students of theoretical computer science interested in how sketching techniques can be used to speed up numerical linear algebra applications.

Data-Driven Science and Engineering

Author : Steven L. Brunton
Publisher : Cambridge University Press
ISBN 13 : 1009098489
Total Pages : 615 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Data-Driven Science and Engineering by : Steven L. Brunton

Download or read book Data-Driven Science and Engineering written by Steven L. Brunton and published by Cambridge University Press. This book was released on 2022-05-05 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.

Through-the-Wall Radar Imaging

Author : Moeness G. Amin
Publisher : CRC Press
ISBN 13 : 1439814775
Total Pages : 604 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Through-the-Wall Radar Imaging by : Moeness G. Amin

Download or read book Through-the-Wall Radar Imaging written by Moeness G. Amin and published by CRC Press. This book was released on 2017-12-19 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through-the-wall radar imaging (TWRI) allows police, fire and rescue personnel, first responders, and defense forces to detect, identify, classify, and track the whereabouts of humans and moving objects. Electromagnetic waves are considered the most effective at achieving this objective, yet advances in this multi-faceted and multi-disciplinary technology require taking phenomenological issues into consideration and must be based on a solid understanding of the intricacies of EM wave interactions with interior and exterior objects and structures. Providing a broad overview of the myriad factors involved, namely size, weight, mobility, acquisition time, aperture distribution, power, bandwidth, standoff distance, and, most importantly, reliable performance and delivery of accurate information, Through-the-Wall Radar Imaging examines this technology from the algorithmic, modeling, experimentation, and system design perspectives. It begins with coverage of the electromagnetic properties of walls and building materials, and discusses techniques in the design of antenna elements and array configurations, beamforming concepts and issues, and the use of antenna array with collocated and distributed apertures. Detailed chapters discuss several suitable waveforms inverse scattering approaches and revolve around the relevance of physical-based model approaches in TWRI along with theoretical and experimental research in 3D building tomography using microwave remote sensing, high-frequency asymptotic modeling methods, synthetic aperture radar (SAR) techniques, impulse radars, airborne radar imaging of multi-floor buildings strategies for target detection, and detection of concealed targets. The book concludes with a discussion of how the Doppler principle can be used to measure motion at a very fine level of detail. The book provides a deep understanding of the challenges of TWRI, stressing its multidisciplinary and phenomenological nature. The breadth and depth of topics covered presents a highly detailed treatment of this potentially life-saving technology.