Algorithms For Sparsity Constrained Optimization

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.

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.

A popular way to assess the “effort” needed to solve a problem is to count how many evaluations of the problem functions (and their derivatives) are required. In many cases, this is often the dominating computational cost. Given an optimization problem satisfying reasonable assumptions—and given access to problem-function values and derivatives of various degrees—how many evaluations might be required to approximately solve the problem? Evaluation Complexity of Algorithms for Nonconvex Optimization: Theory, Computation, and Perspectives addresses this question for nonconvex optimization problems, those that may have local minimizers and appear most often in practice. This is the first book on complexity to cover topics such as composite and constrained optimization, derivative-free optimization, subproblem solution, and optimal (lower and sharpness) bounds for nonconvex problems. It is also the first to address the disadvantages of traditional optimality measures and propose useful surrogates leading to algorithms that compute approximate high-order critical points, and to compare traditional and new methods, highlighting the advantages of the latter from a complexity point of view. This is the go-to book for those interested in solving nonconvex optimization problems. It is suitable for advanced undergraduate and graduate students in courses on advanced numerical analysis, data science, numerical optimization, and approximation theory.

This Special Issue with 35 published articles shows the significance of the topic “Signal Processing and Analysis of Electrical Circuit”. This topic has been gaining increasing attention in recent times. The presented articles can be categorized into four different areas: signal processing and analysis methods of electrical circuits; electrical measurement technology; applications of signal processing of electrical equipment; fault diagnosis of electrical circuits. It is a fact that the development of electrical systems, signal processing methods, and circuits has been accelerating. Electronics applications related to electrical circuits and signal processing methods have gained noticeable attention in recent times. The methods of signal processing and electrical circuits are widely used by engineers and scientists all over the world. The constituent papers represent a significant contribution to electronics and present applications that can be used in industry. Further improvements to the presented approaches are required for realizing their full potential.

Continuing in the footsteps of the pioneering first edition, Signal and Image Processing for Remote Sensing, Second Edition explores the most up-to-date signal and image processing methods for dealing with remote sensing problems. Although most data from satellites are in image form, signal processing can contribute significantly in extracting information from remotely sensed waveforms or time series data. This book combines both, providing a unique balance between the role of signal processing and image processing. Featuring contributions from worldwide experts, this book continues to emphasize mathematical approaches. Not limited to satellite data, it also considers signals and images from hydroacoustic, seismic, microwave, and other sensors. Chapters cover important topics in signal and image processing and discuss techniques for dealing with remote sensing problems. Each chapter offers an introduction to the topic before delving into research results, making the book accessible to a broad audience. This second edition reflects the considerable advances that have occurred in the field, with 23 of 27 chapters being new or entirely rewritten. Coverage includes new mathematical developments such as compressive sensing, empirical mode decomposition, and sparse representation, as well as new component analysis methods such as non-negative matrix and tensor factorization. The book also presents new experimental results on SAR and hyperspectral image processing. The emphasis is on mathematical techniques that will far outlast the rapidly changing sensor, software, and hardware technologies. Written for industrial and academic researchers and graduate students alike, this book helps readers connect the "dots" in image and signal processing. New in This Edition The second edition includes four chapters from the first edition, plus 23 new or entirely rewritten chapters, and 190 new figures. New topics covered include: Compressive sensing The mixed pixel problem with hyperspectral images Hyperspectral image (HSI) target detection and classification based on sparse representation An ISAR technique for refocusing moving targets in SAR images Empirical mode decomposition for signal processing Feature extraction for classification of remote sensing signals and images Active learning methods in classification of remote sensing images Signal subspace identification of hyperspectral data Wavelet-based multi/hyperspectral image restoration and fusion The second edition is not intended to replace the first edition entirely and readers are encouraged to read both editions of the book for a more complete picture of signal and image processing in remote sensing. See Signal and Image Processing for Remote Sensing (CRC Press 2006).

The three-volume set LNCS 11857, 11858, and 11859 constitutes the refereed proceedings of the Second Chinese Conference on Pattern Recognition and Computer Vision, PRCV 2019, held in Xi’an, China, in November 2019. The 165 revised full papers presented were carefully reviewed and selected from 412 submissions. The papers have been organized in the following topical sections: Part I: Object Detection, Tracking and Recognition, Part II: Image/Video Processing and Analysis, Part III: Data Analysis and Optimization.

This book constitutes the refereed proceedings of the 5th International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2005, held in St. Augustine, FL, USA in November 2005. The 24 revised full papers and 18 poster papers presented were carefully reviewed and selected from 120 submissions. The papers are organized in topical sections on probabilistic and informational approaches, combinatorial approaches, variational approaches, and other approaches and applications.

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.