Author : Sohail Bahmani
Publisher : Springer Science & Business Media
Page : 124 pages
File Size : 46,40 MB
Release : 2013-10-07
Category : Technology & Engineering
ISBN : 3319018817
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.
Author : Francis Bach
Publisher :
Page : 124 pages
File Size : 42,39 MB
Release : 2011-12-23
Category : Computers
ISBN : 9781601985101
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate nonsmooth norms. Optimization with Sparsity-Inducing Penalties presents optimization tools and techniques dedicated to such sparsity-inducing penalties from a general perspective. It covers proximal methods, block-coordinate descent, reweighted ?2-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provides an extensive set of experiments to compare various algorithms from a computational point of view. The presentation of Optimization with Sparsity-Inducing Penalties is essentially based on existing literature, but the process of constructing a general framework leads naturally to new results, connections and points of view. It is an ideal reference on the topic for anyone working in machine learning and related areas.
Author : Amir Beck
Publisher : SIAM
Page : 286 pages
File Size : 26,39 MB
Release : 2014-10-27
Category : Mathematics
ISBN : 1611973651
This book provides the foundations of the theory of nonlinear optimization as well as some related algorithms and presents a variety of applications from diverse areas of applied sciences. The author combines three pillars of optimization?theoretical and algorithmic foundation, familiarity with various applications, and the ability to apply the theory and algorithms on actual problems?and rigorously and gradually builds the connection between theory, algorithms, applications, and implementation. Readers will find more than 170 theoretical, algorithmic, and numerical exercises that deepen and enhance the reader's understanding of the topics. The author includes offers several subjects not typically found in optimization books?for example, optimality conditions in sparsity-constrained optimization, hidden convexity, and total least squares. The book also offers a large number of applications discussed theoretically and algorithmically, such as circle fitting, Chebyshev center, the Fermat?Weber problem, denoising, clustering, total least squares, and orthogonal regression and theoretical and algorithmic topics demonstrated by the MATLAB? toolbox CVX and a package of m-files that is posted on the book?s web site.
Author : Masaaki Nagahara
Publisher :
Page : 220 pages
File Size : 35,28 MB
Release : 2020-09-30
Category :
ISBN : 9781680837247
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.
Author : Boris S. Mordukhovich
Publisher : Springer Science & Business Media
Page : 598 pages
File Size : 21,88 MB
Release : 2006-08-08
Category : Mathematics
ISBN : 3540312471
Comprehensive and state-of-the art study of the basic concepts and principles of variational analysis and generalized differentiation in both finite-dimensional and infinite-dimensional spaces Presents numerous applications to problems in the optimization, equilibria, stability and sensitivity, control theory, economics, mechanics, etc.
Author : Guanghui Lan
Publisher : Springer Nature
Page : 591 pages
File Size : 25,84 MB
Release : 2020-05-15
Category : Mathematics
ISBN : 3030395685
This book covers not only foundational materials but also the most recent progresses made during the past few years on the area of machine learning algorithms. In spite of the intensive research and development in this area, there does not exist a systematic treatment to introduce the fundamental concepts and recent progresses on machine learning algorithms, especially on those based on stochastic optimization methods, randomized algorithms, nonconvex optimization, distributed and online learning, and projection free methods. This book will benefit the broad audience in the area of machine learning, artificial intelligence and mathematical programming community by presenting these recent developments in a tutorial style, starting from the basic building blocks to the most carefully designed and complicated algorithms for machine learning.
Author : Stephen Boyd
Publisher : Now Publishers Inc
Page : 138 pages
File Size : 37,90 MB
Release : 2011
Category : Computers
ISBN : 160198460X
Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.
Author : Irina Rish
Publisher : CRC Press
Page : 255 pages
File Size : 13,59 MB
Release : 2014-12-01
Category : Business & Economics
ISBN : 1439828695
Sparse models are particularly useful in scientific applications, such as biomarker discovery in genetic or neuroimaging data, where the interpretability of a predictive model is essential. Sparsity can also dramatically improve the cost efficiency of signal processing. Sparse Modeling: Theory, Algorithms, and Applications provides an introduction to the growing field of sparse modeling, including application examples, problem formulations that yield sparse solutions, algorithms for finding such solutions, and recent theoretical results on sparse recovery. The book gets you up to speed on the latest sparsity-related developments and will motivate you to continue learning about the field. The authors first present motivating examples and a high-level survey of key recent developments in sparse modeling. The book then describes optimization problems involving commonly used sparsity-enforcing tools, presents essential theoretical results, and discusses several state-of-the-art algorithms for finding sparse solutions. The authors go on to address a variety of sparse recovery problems that extend the basic formulation to more sophisticated forms of structured sparsity and to different loss functions. They also examine a particular class of sparse graphical models and cover dictionary learning and sparse matrix factorizations.
Author : Vishal Monga
Publisher : Springer
Page : 238 pages
File Size : 44,45 MB
Release : 2017-10-27
Category : Computers
ISBN : 3319616099
This book covers recent advances in image processing and imaging sciences from an optimization viewpoint, especially convex optimization with the goal of designing tractable algorithms. Throughout the handbook, the authors introduce topics on the most key aspects of image acquisition and processing that are based on the formulation and solution of novel optimization problems. The first part includes a review of the mathematical methods and foundations required, and covers topics in image quality optimization and assessment. The second part of the book discusses concepts in image formation and capture from color imaging to radar and multispectral imaging. The third part focuses on sparsity constrained optimization in image processing and vision and includes inverse problems such as image restoration and de-noising, image classification and recognition and learning-based problems pertinent to image understanding. Throughout, convex optimization techniques are shown to be a critically important mathematical tool for imaging science problems and applied extensively. Convex Optimization Methods in Imaging Science is the first book of its kind and will appeal to undergraduate and graduate students, industrial researchers and engineers and those generally interested in computational aspects of modern, real-world imaging and image processing problems.
Author : Chein-I Chang
Publisher : John Wiley & Sons
Page : 612 pages
File Size : 22,36 MB
Release : 2022-12-08
Category : Technology & Engineering
ISBN : 1119687764
Advances in Hyperspectral Image Processing Techniques Authoritative and comprehensive resource covering recent hyperspectral imaging techniques from theory to applications Advances in Hyperspectral Image Processing Techniques is derived from recent developments of hyperspectral imaging (HSI) techniques along with new applications in the field, covering many new ideas that have been explored and have led to various new directions in the past few years. The work gathers an array of disparate research into one resource and explores its numerous applications across a wide variety of disciplinary areas. In particular, it includes an introductory chapter on fundamentals of HSI and a chapter on extensive use of HSI techniques in satellite on-orbit and on-board processing to aid readers involved in these specific fields. The book’s content is based on the expertise of invited scholars and is categorized into six parts. Part I provides general theory. Part II presents various Band Selection techniques for Hyperspectral Images. Part III reviews recent developments on Compressive Sensing for Hyperspectral Imaging. Part IV includes Fusion of Hyperspectral Images. Part V covers Hyperspectral Data Unmixing. Part VI offers different views on Hyperspectral Image Classification. Specific sample topics covered in Advances in Hyperspectral Image Processing Techniques include: Two fundamental principles of hyperspectral imaging Constrained band selection for hyperspectral imaging and class information-based band selection for hyperspectral image classification Restricted entropy and spectrum properties for hyperspectral imaging and endmember finding in compressively sensed band domain Hyperspectral and LIDAR data fusion, fusion of band selection methods for hyperspectral imaging, and fusion using multi-dimensional information Advances in spectral unmixing of hyperspectral data and fully constrained least squares linear spectral mixture analysis Sparse representation-based hyperspectral image classification; collaborative hyperspectral image classification; class-feature weighted hyperspectral image classification; target detection approach to hyperspectral image classification With many applications beyond traditional remote sensing, ranging from defense and intelligence, to agriculture, to forestry, to environmental monitoring, to food safety and inspection, to medical imaging, Advances in Hyperspectral Image Processing Techniques is an essential resource on the topic for industry professionals, researchers, academics, and graduate students working in the field.
