Non-convex Optimization for Machine Learning
Non-convex Optimization for Machine Learning

Author: Prateek Jain

Publisher: Foundations and Trends in Machine Learning

Published: 2017-12-04

Total Pages: 218

ISBN-13: 9781680833683

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Non-convex Optimization for Machine Learning takes an in-depth look at the basics of non-convex optimization with applications to machine learning. It introduces the rich literature in this area, as well as equips the reader with the tools and techniques needed to apply and analyze simple but powerful procedures for non-convex problems. Non-convex Optimization for Machine Learning is as self-contained as possible while not losing focus of the main topic of non-convex optimization techniques. The monograph initiates the discussion with entire chapters devoted to presenting a tutorial-like treatment of basic concepts in convex analysis and optimization, as well as their non-convex counterparts. The monograph concludes with a look at four interesting applications in the areas of machine learning and signal processing, and exploring how the non-convex optimization techniques introduced earlier can be used to solve these problems. The monograph also contains, for each of the topics discussed, exercises and figures designed to engage the reader, as well as extensive bibliographic notes pointing towards classical works and recent advances. Non-convex Optimization for Machine Learning can be used for a semester-length course on the basics of non-convex optimization with applications to machine learning. On the other hand, it is also possible to cherry pick individual portions, such the chapter on sparse recovery, or the EM algorithm, for inclusion in a broader course. Several courses such as those in machine learning, optimization, and signal processing may benefit from the inclusion of such topics.

Handbook of Robust Low-Rank and Sparse Matrix Decomposition
Handbook of Robust Low-Rank and Sparse Matrix Decomposition

Author: Thierry Bouwmans

Publisher: CRC Press

Published: 2016-09-20

Total Pages: 510

ISBN-13: 1315353539

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Handbook of Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing shows you how robust subspace learning and tracking by decomposition into low-rank and sparse matrices provide a suitable framework for computer vision applications. Incorporating both existing and new ideas, the book conveniently gives you one-stop access to a number of different decompositions, algorithms, implementations, and benchmarking techniques. Divided into five parts, the book begins with an overall introduction to robust principal component analysis (PCA) via decomposition into low-rank and sparse matrices. The second part addresses robust matrix factorization/completion problems while the third part focuses on robust online subspace estimation, learning, and tracking. Covering applications in image and video processing, the fourth part discusses image analysis, image denoising, motion saliency detection, video coding, key frame extraction, and hyperspectral video processing. The final part presents resources and applications in background/foreground separation for video surveillance. With contributions from leading teams around the world, this handbook provides a complete overview of the concepts, theories, algorithms, and applications related to robust low-rank and sparse matrix decompositions. It is designed for researchers, developers, and graduate students in computer vision, image and video processing, real-time architecture, machine learning, and data mining.

Handbook of Convex Optimization Methods in Imaging Science
Handbook of Convex Optimization Methods in Imaging Science

Author: Vishal Monga

Publisher: Springer

Published: 2017-10-27

Total Pages: 238

ISBN-13: 3319616099

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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.

Nonuniform Sampling
Nonuniform Sampling

Author: Farokh Marvasti

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 938

ISBN-13: 1461512298

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Our understanding of nature is often through nonuniform observations in space or time. In space, one normally observes the important features of an object, such as edges. The less important features are interpolated. History is a collection of important events that are nonuniformly spaced in time. Historians infer between events (interpolation) and politicians and stock market analysts forecast the future from past and present events (extrapolation). The 20 chapters of Nonuniform Sampling: Theory and Practice contain contributions by leading researchers in nonuniform and Shannon sampling, zero crossing, and interpolation theory. Its practical applications include NMR, seismology, speech and image coding, modulation and coding, optimal content, array processing, and digital filter design. It has a tutorial outlook for practising engineers and advanced students in science, engineering, and mathematics. It is also a useful reference for scientists and engineers working in the areas of medical imaging, geophysics, astronomy, biomedical engineering, computer graphics, digital filter design, speech and video processing, and phased array radar.

Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging
Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author: Ke Chen

Publisher: Springer Nature

Published: 2023-02-24

Total Pages: 1981

ISBN-13: 3030986616

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This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning. No other framework can provide comparable accuracy and precision to imaging and vision. Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services. This work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.

Robust Subspace Estimation Using Low-Rank Optimization
Robust Subspace Estimation Using Low-Rank Optimization

Author: Omar Oreifej

Publisher: Springer Science & Business Media

Published: 2014-03-24

Total Pages: 116

ISBN-13: 3319041843

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Various fundamental applications in computer vision and machine learning require finding the basis of a certain subspace. Examples of such applications include face detection, motion estimation, and activity recognition. An increasing interest has been recently placed on this area as a result of significant advances in the mathematics of matrix rank optimization. Interestingly, robust subspace estimation can be posed as a low-rank optimization problem, which can be solved efficiently using techniques such as the method of Augmented Lagrange Multiplier. In this book, the authors discuss fundamental formulations and extensions for low-rank optimization-based subspace estimation and representation. By minimizing the rank of the matrix containing observations drawn from images, the authors demonstrate how to solve four fundamental computer vision problems, including video denosing, background subtraction, motion estimation, and activity recognition.

Large-Scale Convex Optimization
Large-Scale Convex Optimization

Author: Ernest K. Ryu

Publisher: Cambridge University Press

Published: 2022-12-01

Total Pages: 320

ISBN-13: 1009191063

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Starting from where a first course in convex optimization leaves off, this text presents a unified analysis of first-order optimization methods – including parallel-distributed algorithms – through the abstraction of monotone operators. With the increased computational power and availability of big data over the past decade, applied disciplines have demanded that larger and larger optimization problems be solved. This text covers the first-order convex optimization methods that are uniquely effective at solving these large-scale optimization problems. Readers will have the opportunity to construct and analyze many well-known classical and modern algorithms using monotone operators, and walk away with a solid understanding of the diverse optimization algorithms. Graduate students and researchers in mathematical optimization, operations research, electrical engineering, statistics, and computer science will appreciate this concise introduction to the theory of convex optimization algorithms.

Deep Learning through Sparse and Low-Rank Modeling
Deep Learning through Sparse and Low-Rank Modeling

Author: Zhangyang Wang

Publisher: Academic Press

Published: 2019-04-11

Total Pages: 298

ISBN-13: 012813660X

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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

MultiMedia Modeling
MultiMedia Modeling

Author: Cathal Gurrin

Publisher: Springer

Published: 2014-01-02

Total Pages: 631

ISBN-13: 3319041142

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The two-volume set LNCS 8325 and 8326 constitutes the thoroughly refereed proceedings of the 20th Anniversary International Conference on Multimedia Modeling, MMM 2014, held in Dublin, Ireland, in January 2014. The 46 revised regular papers, 11 short papers and 9 demonstration papers were carefully reviewed and selected from 176 submissions. 28 special session papers and 6 papers from Video Browser Showdown workshop are also included in the proceedings. The papers included in these two volumes cover a diverse range of topics including: applications of multimedia modelling, interactive retrieval, image and video collections, 3D and augmented reality, temporal analysis of multimedia content, compression and streaming. Special session papers cover the following topics: Mediadrom: artful post-TV scenarios, MM analysis for surveillance video and security applications, 3D multimedia computing and modeling, social geo-media analytics and retrieval, multimedia hyperlinking and retrieval.

Pattern Recognition and Computer Vision
Pattern Recognition and Computer Vision

Author: Shiqi Yu

Publisher: Springer Nature

Published: 2022-10-27

Total Pages: 752

ISBN-13: 3031189167

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The 4-volume set LNCS 13534, 13535, 13536 and 13537 constitutes the refereed proceedings of the 5th Chinese Conference on Pattern Recognition and Computer Vision, PRCV 2022, held in Shenzhen, China, in November 2022. The 233 full papers presented were carefully reviewed and selected from 564 submissions. The papers have been organized in the following topical sections: Theories and Feature Extraction; Machine learning, Multimedia and Multimodal; Optimization and Neural Network and Deep Learning; Biomedical Image Processing and Analysis; Pattern Classification and Clustering; 3D Computer Vision and Reconstruction, Robots and Autonomous Driving; Recognition, Remote Sensing; Vision Analysis and Understanding; Image Processing and Low-level Vision; Object Detection, Segmentation and Tracking.