Download or read book Computation of Minimum Volume Covering Ellipsoids written by Peng Sun and published by . This book was released on 2002 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We present a practical algorithm for computing the minimum volume n-dimensional ellipsoid that must contain m given points a_1, ..., a_m in R^n. This convex constrained problem arises in a variety of applied computational settings, particularly in data mining and robust statistics. Its structure makes it particularly amenable to solution by interior-point methods, and it has been the subject of much theoretical complexity analysis. Here we focus on computation. We present a combined interior-point and active-set method for solving this problem. Our computational results demonstrate that our method solves very large problem instances (m=30,000 and n=30) to a high degree of accuracy in under 30 seconds on a personal computer.
Download or read book Minimum Volume Ellipsoids written by Michael J. Todd and published by SIAM. This book was released on 2016-07-11 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the first on these topics, addresses the problem of finding an ellipsoid to represent a large set of points in high-dimensional space, which has applications in computational geometry, data representations, and optimal design in statistics. The book covers the formulation of this and related problems, theoretical properties of their optimal solutions, and algorithms for their solution. Due to the high dimensionality of these problems, first-order methods that require minimal computational work at each iteration are attractive. While algorithms of this kind have been discovered and rediscovered over the past fifty years, their computational complexities and convergence rates have only recently been investigated. The optimization problems in the book have the entries of a symmetric matrix as their variables, so the author's treatment also gives an introduction to recent work in matrix optimization. This book provides historical perspective on the problems studied by optimizers, statisticians, and geometric functional analysts; demonstrates the huge computational savings possible by exploiting simple updates for the determinant and the inverse after a rank-one update, and highlights the difficulties in algorithms when related problems are studied that do not allow simple updates at each iteration; and gives rigorous analyses of the proposed algorithms, MATLAB codes, and computational results.
Download or read book Combinatorial Optimization and Applications written by T-H. Hubert Chan and published by Springer. This book was released on 2016-11-30 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Conference on Combinatorial Optimization and Applications, COCOA 2016, held in Hong Kong, China, in December 2016. The 60 full papers included in the book were carefully reviewed and selected from 122 submissions. The papers are organized in topical sections such as graph theory, geometric optimization, complexity and data structure, combinatorial optimization, and miscellaneous.
Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.
Download or read book COMPSTAT written by Albert Prat and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: COMPSTAT symposia have been held regularly since 1974 when they started in Vienna. This tradition has made COMPSTAT a major forum for the interplay of statistics and computer sciences with contributions from many well known scientists all over the world. The scientific programme of COMPSTAT '96 covers all aspects of this interplay, from user-experiences and evaluation of software through the development and implementation of new statistical ideas. All papers presented belong to one of the three following categories: - Statistical methods (preferable new ones) that require a substantial use of computing; - Computer environments, tools and software useful in statistics; - Applications of computational statistics in areas of substantial interest (environment, health, industry, biometrics, etc.).
Download or read book Design of Experiments in Nonlinear Models written by Luc Pronzato and published by Springer Science & Business Media. This book was released on 2013-04-10 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Design of Experiments in Nonlinear Models: Asymptotic Normality, Optimality Criteria and Small-Sample Properties provides a comprehensive coverage of the various aspects of experimental design for nonlinear models. The book contains original contributions to the theory of optimal experiments that will interest students and researchers in the field. Practitionners motivated by applications will find valuable tools to help them designing their experiments. The first three chapters expose the connections between the asymptotic properties of estimators in parametric models and experimental design, with more emphasis than usual on some particular aspects like the estimation of a nonlinear function of the model parameters, models with heteroscedastic errors, etc. Classical optimality criteria based on those asymptotic properties are then presented thoroughly in a special chapter. Three chapters are dedicated to specific issues raised by nonlinear models. The construction of design criteria derived from non-asymptotic considerations (small-sample situation) is detailed. The connection between design and identifiability/estimability issues is investigated. Several approaches are presented to face the problem caused by the dependence of an optimal design on the value of the parameters to be estimated. A survey of algorithmic methods for the construction of optimal designs is provided.
Download or read book Data Mining and Mathematical Programming written by Panos M. Pardalos and published by American Mathematical Soc.. This book was released on 2008-04-09 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data mining aims at finding interesting, useful or profitable information in very large databases. The enormous increase in the size of available scientific and commercial databases (data avalanche) as well as the continuing and exponential growth in performance of present day computers make data mining a very active field. In many cases, the burgeoning volume of data sets has grown so large that it threatens to overwhelm rather than enlighten scientists. Therefore, traditional methods are revised and streamlined, complemented by many new methods to address challenging new problems. Mathematical Programming plays a key role in this endeavor. It helps us to formulate precise objectives (e.g., a clustering criterion or a measure of discrimination) as well as the constraints imposed on the solution (e.g., find a partition, a covering or a hierarchy in clustering). It also provides powerful mathematical tools to build highly performing exact or approximate algorithms. This book is based on lectures presented at the workshop on "Data Mining and Mathematical Programming" (October 10-13, 2006, Montreal) and will be a valuable scientific source of information to faculty, students, and researchers in optimization, data analysis and data mining, as well as people working in computer science, engineering and applied mathematics.
Download or read book Proceedings in Computational Statistics written by Albert Prat and published by . This book was released on 1996 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: COMPSTAT symposia have been held regularly since 1974 when they started in Vienna. This tradition has made COMPSTAT a major forum for the interplay of statistics and computer sciences with contributions from many well known scientists all over the world. The scientific programme of COMPSTAT '96 covers all aspects of this interplay, from user-experiences and evaluation of software through the development and implementation of new statistical ideas. All papers presented belong to one of the three following categories: - Statistical methods (preferable new ones) that require a substantial use of computing; - Computer environments, tools and software useful in statistics; - Applications of computational statistics in areas of substantial interest (environment, health, industry, biometrics, etc.).
Download or read book Computation Aware Algorithmic Design for Cyber Physical Systems written by Maria Prandini and published by Springer Nature. This book was released on 2023-12-16 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume aims to build the foundation of a framework for computationally aware algorithmic design for cyber-physical systems (CPSs), focusing on approaches that take computation into account at the design stage to address their impact on performance and safety. It demonstrates how novel techniques may emerge from the combination of formal methods, model predictive control, distributed optimization, data-driven methods, reconfigurable/adaptive methods, and information-theoretic techniques. Chapters are written by both researchers and practitioners and cover such topics as analysis and design of uncertain CPSs, cooperative and non-cooperative paradigms for handling complexity in large scale CPSs, task-relevant environment abstractions for autonomous systems based on information theory, information flow in event-based stabilization of CPSs, set-valued model predictive control, and automated synthesis of certifiable controllers for CPSs. State-of-the-art applications and case studies are provided throughout with a special focus on intelligent transportation systems and autonomous vehicles. Graduate students and researchers with an interest in CPS verification and control will find this volume to be a valuable resource in their work. It will also appeal to researchers from disciplines other than control, such as computer science, operations research, applied mathematics, and robotics.
Download or read book Combinatorial and Algorithmic Mathematics written by Baha Alzalg and published by John Wiley & Sons. This book was released on 2024-10-21 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed review of optimization from first principles, supported by rigorous math and computer science explanations and various learning aids Supported by rigorous math and computer science foundations, Combinatorial and Algorithmic Mathematics: From Foundation to Optimization provides a from-scratch understanding to the field of optimization, discussing 70 algorithms with roughly 220 illustrative examples, 160 nontrivial end-of-chapter exercises with complete solutions to ensure readers can apply appropriate theories, principles, and concepts when required, and Matlab codes that solve some specific problems. This book helps readers to develop mathematical maturity, including skills such as handling increasingly abstract ideas, recognizing mathematical patterns, and generalizing from specific examples to broad concepts. Starting from first principles of mathematical logic, set-theoretic structures, and analytic and algebraic structures, this book covers both combinatorics and algorithms in separate sections, then brings the material together in a final section on optimization. This book focuses on topics essential for anyone wanting to develop and apply their understanding of optimization to areas such as data structures, algorithms, artificial intelligence, machine learning, data science, computer systems, networks, and computer security. Combinatorial and Algorithmic Mathematics includes discussion on: Propositional logic and predicate logic, set-theoretic structures such as sets, relations, and functions, and basic analytic and algebraic structures such as sequences, series, subspaces, convex structures, and polyhedra Recurrence-solving techniques, counting methods, permutations, combinations, arrangements of objects and sets, and graph basics and properties Asymptotic notations, techniques for analyzing algorithms, and computational complexity of various algorithms Linear optimization and its geometry and duality, simplex and non-simplex algorithms for linear optimization, second-order cone programming, and semidefinite programming Combinatorial and Algorithmic Mathematics is an ideal textbook resource on the subject for students studying discrete structures, combinatorics, algorithms, and optimization. It also caters to scientists across diverse disciplines that incorporate algorithms and academics and researchers who wish to better understand some modern optimization methodologies.
Download or read book Selected Applications of Convex Optimization written by Li Li and published by Springer. This book was released on 2015-03-26 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the applications of convex optimization and highlights several topics, including support vector machines, parameter estimation, norm approximation and regularization, semi-definite programming problems, convex relaxation, and geometric problems. All derivation processes are presented in detail to aid in comprehension. The book offers concrete guidance, helping readers recognize and formulate convex optimization problems they might encounter in practice.
Download or read book Pattern Recognition written by Fred A. Hamprecht and published by Springer. This book was released on 2007-09-22 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 29th Symposium of the German Association for Pattern Recognition, DAGM 2007. It covers image filtering, restoration and segmentation, shape analysis and representation, categorization and detection, computer vision and image retrieval, machine learning and statistical data analysis, biomedical data analysis, motion analysis and tracking, stereo and structure from motion, as well as 3D view registration and surface modeling.
Download or read book Nonnegative Matrix Factorization written by Nicolas Gillis and published by SIAM. This book was released on 2020-12-18 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully. Nonnegative Matrix Factorization is accessible to a wide audience and is ideal for anyone interested in the workings of NMF. It discusses some new results on the nonnegative rank and the identifiability of NMF and makes available MATLAB codes for readers to run the numerical examples presented in the book. Graduate students starting to work on NMF and researchers interested in better understanding the NMF problem and how they can use it will find this book useful. It can be used in advanced undergraduate and graduate-level courses on numerical linear algebra and on advanced topics in numerical linear algebra and requires only a basic knowledge of linear algebra and optimization.
Download or read book Pattern Recognition and Machine Intelligence written by Pradipta Maji and published by Springer Nature. This book was released on 2023-12-16 with total page 892 pages. Available in PDF, EPUB and Kindle. Book excerpt: The LNCS volume constitutes the refereed proceedings of 10th International Conference, PReMI 2023, in Kolkata, India, in December 2023. The 91 full papers, presented together with abstracts of 6 keynote and invited talks, were carefully reviewed and selected from more than 300 submissions. The conference presents topics covering different aspects of pattern recognition and machine intelligence with real life state-of-the-art applications.
Download or read book Machine Learning ECML 2006 written by Johannes Fürnkranz and published by Springer Science & Business Media. This book was released on 2006-09-19 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 17th European Conference on Machine Learning, ECML 2006, held, jointly with PKDD 2006. The book presents 46 revised full papers and 36 revised short papers together with abstracts of 5 invited talks, carefully reviewed and selected from 564 papers submitted. The papers present a wealth of new results in the area and address all current issues in machine learning.
Download or read book Modern Algorithms of Cluster Analysis written by Slawomir Wierzchoń and published by Springer. This book was released on 2017-12-29 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with a basic understanding of the formal concepts of the cluster, clustering, partition, cluster analysis etc. The book explains feature-based, graph-based and spectral clustering methods and discusses their formal similarities and differences. Understanding the related formal concepts is particularly vital in the epoch of Big Data; due to the volume and characteristics of the data, it is no longer feasible to predominantly rely on merely viewing the data when facing a clustering problem. Usually clustering involves choosing similar objects and grouping them together. To facilitate the choice of similarity measures for complex and big data, various measures of object similarity, based on quantitative (like numerical measurement results) and qualitative features (like text), as well as combinations of the two, are described, as well as graph-based similarity measures for (hyper) linked objects and measures for multilayered graphs. Numerous variants demonstrating how such similarity measures can be exploited when defining clustering cost functions are also presented. In addition, the book provides an overview of approaches to handling large collections of objects in a reasonable time. In particular, it addresses grid-based methods, sampling methods, parallelization via Map-Reduce, usage of tree-structures, random projections and various heuristic approaches, especially those used for community detection.
Download or read book Advances in Neural Networks ISNN 2007 written by Derong Liu and published by Springer. This book was released on 2007-07-14 with total page 1390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of a three volume set that constitutes the refereed proceedings of the 4th International Symposium on Neural Networks, ISNN 2007, held in Nanjing, China in June 2007. Coverage includes neural networks for control applications, robotics, data mining and feature extraction, chaos and synchronization, support vector machines, fault diagnosis/detection, image/video processing, and applications of neural networks.
