Linear Algebra And Optimization For Machine Learning
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Linear Algebra And Optimization For Machine Learning
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Author : Charu C. Aggarwal
language : en
Publisher: Springer Nature
Release Date : 2025-09-23
Linear Algebra And Optimization For Machine Learning written by Charu C. Aggarwal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-09-23 with Mathematics categories.
This textbook is the second edition of the linear algebra and optimization book that was published in 2020. The exposition in this edition is greatly simplified as compared to the first edition. The second edition is enhanced with a large number of solved examples and exercises. A frequent challenge faced by beginners in machine learning is the extensive background required in linear algebra and optimization. One problem is that the existing linear algebra and optimization courses are not specific to machine learning; therefore, one would typically have to complete more course material than is necessary to pick up machine learning. Furthermore, certain types of ideas and tricks from optimization and linear algebra recur more frequently in machine learning than other application-centric settings. Therefore, there is significant value in developing a view of linear algebra and optimization that is better suited to the specific perspective of machine learning. It is common for machine learning practitioners to pick up missing bits and pieces of linear algebra and optimization via “osmosis” while studying the solutions to machine learning applications. However, this type of unsystematic approach is unsatisfying because the primary focus on machine learning gets in the way of learning linear algebra and optimization in a generalizable way across new situations and applications. Therefore, we have inverted the focus in this book, with linear algebra/optimization as the primary topics of interest, and solutions to machine learning problems as the applications of this machinery. In other words, the book goes out of its way to teach linear algebra and optimization with machine learning examples. By using this approach, the book focuses on those aspects of linear algebra and optimization that are more relevant to machine learning, and also teaches the reader how to apply them in the machine learning context. As a side benefit, the reader will pick up knowledge of several fundamental problems in machine learning. At the end of the process, the reader will become familiar with many of the basic linear-algebra- and optimization-centric algorithms in machine learning. Although the book is not intended to provide exhaustive coverage of machine learning, it serves as a “technical starter” for the key models and optimization methods in machine learning. Even for seasoned practitioners of machine learning, a systematic introduction to fundamental linear algebra and optimization methodologies can be useful in terms of providing a fresh perspective. The chapters of the book are organized as follows. 1-Linear algebra and its applications: The chapters focus on the basics of linear algebra together with their common applications to singular value decomposition, matrix factorization, similarity matrices (kernel methods), and graph analysis. Numerous machine learning applications have been used as examples, such as spectral clustering, kernel-based classification, and outlier detection. The tight integration of linear algebra methods with examples from machine learning differentiates this book from generic volumes on linear algebra. The focus is clearly on the most relevant aspects of linear algebra for machine learning and to teach readers how to apply these concepts. 2-Optimization and its applications: Much of machine learning is posed as an optimization problem in which we try to maximize the accuracy of regression and classification models. The “parent problem” of optimization-centric machine learning is least-squares regression. Interestingly, this problem arises in both linear algebra and optimization and is one of the key connecting problems of the two fields. Least-squares regression is also the starting point for support vector machines, logistic regression, and recommender systems. Furthermore, the methods for dimensionality reduction and matrix factorization also require the development of optimization methods. A general view of optimization in computational graphs is discussed together with its applications to backpropagation in neural networks. The primary audience for this textbook is graduate level students and professors. The secondary audience is industry. Advanced undergraduates might also be interested, and it is possible to use this book for the mathematics requirements of an undergraduate data science course.
Linear Algebra And Optimization With Applications To Machine Learning Volume I Linear Algebra For Computer Vision Robotics And Machine Learning
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Author : Jean H Gallier
language : en
Publisher: World Scientific
Release Date : 2020-01-22
Linear Algebra And Optimization With Applications To Machine Learning Volume I Linear Algebra For Computer Vision Robotics And Machine Learning written by Jean H Gallier and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-22 with Mathematics categories.
This book provides the mathematical fundamentals of linear algebra to practicers in computer vision, machine learning, robotics, applied mathematics, and electrical engineering. By only assuming a knowledge of calculus, the authors develop, in a rigorous yet down to earth manner, the mathematical theory behind concepts such as: vectors spaces, bases, linear maps, duality, Hermitian spaces, the spectral theorems, SVD, and the primary decomposition theorem. At all times, pertinent real-world applications are provided. This book includes the mathematical explanations for the tools used which we believe that is adequate for computer scientists, engineers and mathematicians who really want to do serious research and make significant contributions in their respective fields.
Linear Algebra And Optimization With Applications To Machine Learning
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Author : Jean H. Gallier
language : en
Publisher: World Scientific Publishing Company
Release Date : 2020
Linear Algebra And Optimization With Applications To Machine Learning written by Jean H. Gallier and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Computers categories.
Volume I. Linear algebra for computer vision, robotics, and machine learning.
Linear Algebra And Optimization With Applications To Machine Learning
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Author : Jean H. Gallier
language : en
Publisher: World Scientific Publishing Company
Release Date : 2020
Linear Algebra And Optimization With Applications To Machine Learning written by Jean H. Gallier and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020 with Computers categories.
Volume I. Linear algebra for computer vision, robotics, and machine learning.
Linear Algebra And Optimization With Applications To Machine Learning
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Author : Jean Gallier
language : en
Publisher: World Scientific Publishing Company
Release Date : 2020-03-06
Linear Algebra And Optimization With Applications To Machine Learning written by Jean Gallier and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-06 with Mathematics categories.
Volume 2 applies the linear algebra concepts presented in Volume 1 to optimization problems which frequently occur throughout machine learning. This book blends theory with practice by not only carefully discussing the mathematical under pinnings of each optimization technique but by applying these techniques to linear programming, support vector machines (SVM), principal component analysis (PCA), and ridge regression. Volume 2 begins by discussing preliminary concepts of optimization theory such as metric spaces, derivatives, and the Lagrange multiplier technique for finding extrema of real valued functions. The focus then shifts to the special case of optimizing a linear function over a region determined by affine constraints, namely linear programming. Highlights include careful derivations and applications of the simplex algorithm, the dual-simplex algorithm, and the primal-dual algorithm. The theoretical heart of this book is the mathematically rigorous presentation of various nonlinear optimization methods, including but not limited to gradient decent, the Karush-Kuhn-Tucker (KKT) conditions, Lagrangian duality, alternating direction method of multipliers (ADMM), and the kernel method. These methods are carefully applied to hard margin SVM, soft margin SVM, kernel PCA, ridge regression, lasso regression, and elastic-net regression. Matlab programs implementing these methods are included.
Practical Linear Algebra For Machine Learning
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Author : Amirsina Torfi
language : en
Publisher:
Release Date : 2019-12-26
Practical Linear Algebra For Machine Learning written by Amirsina Torfi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-26 with categories.
Machine Learning is everywhere these days and a lot of fellows desire to learn it and even master it! This burning desire creates a sense of impatience. We are looking for shortcuts and willing to ONLY jump to the main concept. If you do a simple search on the web, you see thousands of people asking "How can I learn Machine Learning?", "What is the fastest approach to learn Machine Learning?", and "What are the best resources to start Machine Learning?" \textit. Mastering a branch of science is NOT just a feel-good exercise. It has its own requirements.One of the most critical requirements for Machine Learning is Linear Algebra. Basically, the majority of Machine Learning is working with data and optimization. How can you want to learn those without Linear Algebra? How would you process and represent data without vectors and matrices? On the other hand, Linear Algebra is a branch of mathematics after all. A lot of people trying to avoid mathematics or have the temptation to "just learn as necessary." I agree with the second approach, though. \textit: You cannot escape Linear Algebra if you want to learn Machine Learning and Deep Learning. There is NO shortcut.The good news is there are numerous resources out there. In fact, the availability of numerous resources made me ponder whether writing this book was necessary? I have been blogging about Machine Learning for a while and after searching and searching I realized there is a deficiency of an organized book which \textbf teaches the most used Linear Algebra concepts in Machine Learning, \textbf provides practical notions using everyday used programming languages such as Python, and \textbf be concise and NOT unnecessarily lengthy.In this book, you get all of what you need to learn about Linear Algebra that you need to master Machine Learning and Deep Learning.
Multidisciplinary Research In Arts Science Commerce Volume 12
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Author : Chief Editor- Biplab Auddya, Editor- Dr. Rajendran L, Dr. Sarika Chhabria Talreja, Dr. Richi Simon , Dr. Thenmozhi P., Dr. Pragyasa Harshendu Upadhyaya, Abhendra Pratap Singh
language : en
Publisher: The Hill Publication
Release Date : 2024-11-12
Multidisciplinary Research In Arts Science Commerce Volume 12 written by Chief Editor- Biplab Auddya, Editor- Dr. Rajendran L, Dr. Sarika Chhabria Talreja, Dr. Richi Simon , Dr. Thenmozhi P., Dr. Pragyasa Harshendu Upadhyaya, Abhendra Pratap Singh and has been published by The Hill Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-12 with Antiques & Collectibles categories.
Linear Algebra Data Science And Machine Learning
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Author : Jeff Calder
language : en
Publisher:
Release Date : 2025
Linear Algebra Data Science And Machine Learning written by Jeff Calder and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with categories.
This text provides a mathematically rigorous introduction to modern methods of machine learning and data analysis at the advanced undergraduate/beginning graduate level. The book is self-contained and requires minimal mathematical prerequisites. There is a strong focus on learning how and why algorithms work, as well as developing facility with their practical applications. Apart from basic calculus, the underlying mathematics linear algebra, optimization, elementary probability, graph theory, and statistics is developed from scratch in a form best suited to the overall goals. In particular, the wide-ranging linear algebra components are unique in their ordering and choice of topics, emphasizing those parts of the theory and techniques that are used in contemporary machine learning and data analysis. The book will provide a firm foundation to the reader whose goal is to work on applications of machine learning and/or research into the further development of this highly active field of contemporary applied mathematics. To introduce the reader to a broad range of machine learning algorithms and how they are used in real world applications, the programming language Python is employed and offers a platform for many of the computational exercises. Python notebooks complementing various topics in the book are available on a companion GitHub site specified in the Preface, and can be easily accessed by scanning the QR codes or clicking on the links provided within the text. Exercises appear at the end of each section, including basic ones designed to test comprehension and computational skills, while others range over proofs not supplied in the text, practical computations, additional theoretical results, and further developments in the subject. The Students Solutions Manual may be accessed from GitHub. Instructors may apply for access to the Instructors Solutions Manual from the link supplied on the text s Springer website. The book can be used in a junior or senior level course for students majoring in mathematics with a focus on applications as well as students from other disciplines who desire to learn the tools of modern applied linear algebra and optimization. It may also be used as an introduction to fundamental techniques in data science and machine learning for advanced undergraduate and graduate students or researchers from other areas, including statistics, computer science, engineering, biology, economics and finance, and so on
An Introduction To Optimization
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Author : Edwin K. P. Chong
language : en
Publisher: John Wiley & Sons
Release Date : 2023-10-10
An Introduction To Optimization written by Edwin K. P. Chong and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-10 with Business & Economics categories.
An Introduction to Optimization Accessible introductory textbook on optimization theory and methods, with an emphasis on engineering design, featuring MATLAB® exercises and worked examples Fully updated to reflect modern developments in the field, the Fifth Edition of An Introduction to Optimization fills the need for an accessible, yet rigorous, introduction to optimization theory and methods, featuring innovative coverage and a straightforward approach. The book begins with a review of basic definitions and notations while also providing the related fundamental background of linear algebra, geometry, and calculus. With this foundation, the authors explore the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. In addition, the book includes an introduction to artificial neural networks, convex optimization, multi-objective optimization, and applications of optimization in machine learning. Numerous diagrams and figures found throughout the book complement the written presentation of key concepts, and each chapter is followed by MATLAB® exercises and practice problems that reinforce the discussed theory and algorithms. The Fifth Edition features a new chapter on Lagrangian (nonlinear) duality, expanded coverage on matrix games, projected gradient algorithms, machine learning, and numerous new exercises at the end of each chapter. An Introduction to Optimization includes information on: The mathematical definitions, notations, and relations from linear algebra, geometry, and calculus used in optimization Optimization algorithms, covering one-dimensional search, randomized search, and gradient, Newton, conjugate direction, and quasi-Newton methods Linear programming methods, covering the simplex algorithm, interior point methods, and duality Nonlinear constrained optimization, covering theory and algorithms, convex optimization, and Lagrangian duality Applications of optimization in machine learning, including neural network training, classification, stochastic gradient descent, linear regression, logistic regression, support vector machines, and clustering. An Introduction to Optimization is an ideal textbook for a one- or two-semester senior undergraduate or beginning graduate course in optimization theory and methods. The text is also of value for researchers and professionals in mathematics, operations research, electrical engineering, economics, statistics, and business.
Mathematics For Machine Learning
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Author : Marc Peter Deisenroth
language : en
Publisher: Cambridge University Press
Release Date : 2020-04-23
Mathematics For Machine Learning written by Marc Peter Deisenroth and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-23 with Computers categories.
Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning.