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Linear Algebra For Pattern Processing

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Linear Algebra For Pattern Processing

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Author : Kenichi Kanatani
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2021-04-30

Linear Algebra For Pattern Processing written by Kenichi Kanatani and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-30 with Mathematics categories.

Linear algebra is one of the most basic foundations of a wide range of scientific domains, and most textbooks of linear algebra are written by mathematicians. However, this book is specifically intended to students and researchers of pattern information processing, analyzing signals such as images and exploring computer vision and computer graphics applications. The author himself is a researcher of this domain. Such pattern information processing deals with a large amount of data, which are represented by high-dimensional vectors and matrices. There, the role of linear algebra is not merely numerical computation of large-scale vectors and matrices. In fact, data processing is usually accompanied with "geometric interpretation." For example, we can think of one data set being "orthogonal" to another and define a "distance" between them or invoke geometric relationships such as "projecting" some data onto some space. Such geometric concepts not only help us mentally visualize abstract high-dimensional spaces in intuitive terms but also lead us to find what kind of processing is appropriate for what kind of goals. First, we take up the concept of "projection" of linear spaces and describe "spectral decomposition," "singular value decomposition," and "pseudoinverse" in terms of projection. As their applications, we discuss least-squares solutions of simultaneous linear equations and covariance matrices of probability distributions of vector random variables that are not necessarily positive definite. We also discuss fitting subspaces to point data and factorizing matrices in high dimensions in relation to motion image analysis. Finally, we introduce a computer vision application of reconstructing the 3D location of a point from three camera views to illustrate the role of linear algebra in dealing with data with noise. This book is expected to help students and researchers of pattern information processing deepen the geometric understanding of linear algebra.

Linear Algebra For Pattern Processing

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Author : Kenichi Kanatani
language : en
Publisher: Springer Nature
Release Date : 2022-06-01

Linear Algebra For Pattern Processing written by Kenichi Kanatani and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Technology & Engineering categories.

Matrix Methods In Data Mining And Pattern Recognition

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Author : Lars Elden
language : en
Publisher: SIAM
Release Date : 2007-07-12

Matrix Methods In Data Mining And Pattern Recognition written by Lars Elden and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-12 with Computers categories.

Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application.Matrix Methods in Data Mining and Pattern Recognition is divided into three parts. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB®. Some mathematical proofs that emphasize the existence and properties of the matrix decompositions are included. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed by the author are: classification of handwritten digits, text mining, text summarization, pagerank computations related to the GoogleÔ search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.Audience The book is intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. Graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques will also find the book useful.Contents Preface; Part I: Linear Algebra Concepts and Matrix Decompositions. Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition; Chapter 2: Vectors and Matrices; Chapter 3: Linear Systems and Least Squares; Chapter 4: Orthogonality; Chapter 5: QR Decomposition; Chapter 6: Singular Value Decomposition; Chapter 7: Reduced-Rank Least Squares Models; Chapter 8: Tensor Decomposition; Chapter 9: Clustering and Nonnegative Matrix Factorization; Part II: Data Mining Applications. Chapter 10: Classification of Handwritten Digits; Chapter 11: Text Mining; Chapter 12: Page Ranking for a Web Search Engine; Chapter 13: Automatic Key Word and Key Sentence Extraction; Chapter 14: Face Recognition Using Tensor SVD. Part III: Computing the Matrix Decompositions. Chapter 15: Computing Eigenvalues and Singular Values; Bibliography; Index.

Linear Algebra Tools For Data Mining

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Author : Dan A. Simovici
language : en
Publisher: World Scientific
Release Date : 2012

Linear Algebra Tools For Data Mining written by Dan A. Simovici and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Computers categories.

This comprehensive volume presents the foundations of linear algebra ideas and techniques applied to data mining and related fields. Linear algebra has gained increasing importance in data mining and pattern recognition, as shown by the many current data mining publications, and has a strong impact in other disciplines like psychology, chemistry, and biology. The basic material is accompanied by more than 550 exercises and supplements, many accompanied with complete solutions and MATLAB applications. Key Features Integrates the mathematical developments to their applications in data mining without sacrificing the mathematical rigor Presented applications with full mathematical justifications and are often accompanied by MATLAB code Highlights strong links between linear algebra, topology and graph theory because these links are essentially important for applications A self-contained book that deals with mathematics that is immediately relevant for data mining Book jacket.

Introduction To Applied Linear Algebra

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Author : Stephen Boyd
language : en
Publisher: Cambridge University Press
Release Date : 2018-06-07

Introduction To Applied Linear Algebra written by Stephen Boyd 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 2018-06-07 with Business & Economics categories.

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Linear Algebra For Data Science Machine Learning And Signal Processing

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Author : Jeffrey A. Fessler
language : en
Publisher: Cambridge University Press
Release Date : 2024-04-30

Linear Algebra For Data Science Machine Learning And Signal Processing written by Jeffrey A. Fessler 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 2024-04-30 with Computers categories.

Master matrix methods via engaging data-driven applications, aided by classroom-tested quizzes, homework exercises and online Julia demos.

A Matrix Algebra Approach To Artificial Intelligence

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Author : Xian-Da Zhang
language : en
Publisher: Springer Nature
Release Date : 2020-05-23

A Matrix Algebra Approach To Artificial Intelligence written by Xian-Da Zhang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-23 with Computers categories.

Matrix algebra plays an important role in many core artificial intelligence (AI) areas, including machine learning, neural networks, support vector machines (SVMs) and evolutionary computation. This book offers a comprehensive and in-depth discussion of matrix algebra theory and methods for these four core areas of AI, while also approaching AI from a theoretical matrix algebra perspective. The book consists of two parts: the first discusses the fundamentals of matrix algebra in detail, while the second focuses on the applications of matrix algebra approaches in AI. Highlighting matrix algebra in graph-based learning and embedding, network embedding, convolutional neural networks and Pareto optimization theory, and discussing recent topics and advances, the book offers a valuable resource for scientists, engineers, and graduate students in various disciplines, including, but not limited to, computer science, mathematics and engineering.

Computer Algorithms For Solving Linear Algebraic Equations

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Author : Emilio Spedicato
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Computer Algorithms For Solving Linear Algebraic Equations written by Emilio Spedicato and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.

The NATO Advanced Study Institute on "Computer algorithms for solving linear algebraic equations: the state of the art" was held September 9-21, 1990, at II Ciocco, Barga, Italy. It was attended by 68 students (among them many well known specialists in related fields!) from the following countries: Belgium, Brazil, Canada, Czechoslovakia, Denmark, France, Germany, Greece, Holland, Hungary, Italy, Portugal, Spain, Turkey, UK, USA, USSR, Yugoslavia. Solving linear equations is a fundamental task in most of computational mathematics. Linear systems which are now encountered in practice may be of very large dimension and their solution can still be a challenge in terms of the requirements of accuracy or reasonable computational time. With the advent of supercomputers with vector and parallel features, algorithms which were previously formulated in a framework of sequential operations often need a completely new formulation, and algorithms that were not recommended in a sequential framework may become the best choice. The aim of the ASI was to present the state of the art in this field. While not all important aspects could be covered (for instance there is no presentation of methods using interval arithmetic or symbolic computation), we believe that most important topics were considered, many of them by leading specialists who have contributed substantially to the developments in these fields.

Linear Algebra And Learning From Data

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Author : Gilbert Strang
language : en
Publisher: Wellesley-Cambridge Press
Release Date : 2019-01-31

Linear Algebra And Learning From Data written by Gilbert Strang and has been published by Wellesley-Cambridge Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-31 with Computers categories.

Linear algebra and the foundations of deep learning, together at last! From Professor Gilbert Strang, acclaimed author of Introduction to Linear Algebra, comes Linear Algebra and Learning from Data, the first textbook that teaches linear algebra together with deep learning and neural nets. This readable yet rigorous textbook contains a complete course in the linear algebra and related mathematics that students need to know to get to grips with learning from data. Included are: the four fundamental subspaces, singular value decompositions, special matrices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation.

Photonic Signal Processing Second Edition

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Author : Le Nguyen Binh
language : en
Publisher: CRC Press
Release Date : 2019-01-15

Photonic Signal Processing Second Edition written by Le Nguyen Binh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-15 with Technology & Engineering categories.

This Second Edition of "Photonic Signal Processing" updates most recent R&D on processing techniques of signals in photonic domain from the fundamentals given in its first edition. Several modern techniques in Photonic Signal Processing (PSP) are described: Graphical signal flow technique to simplify the analysis of the photonic transfer functions, plus its insights into the physical phenomena of such processors. The resonance and interference of optical fields are presented by the poles and zeros of the optical circuits, respectively. Detailed design procedures for fixed and tunable optical filters. These filters, "brick-wall-like", now play a highly important role in ultra-broadband (100GBaud) to spectral shaping of sinc temporal response so as to generate truly Nyquist sampler of the received eye diagrams 3-D PSP allows multi-dimensional processing for highly complex optical signals Photonic differentiators and integrators for dark soliton generations. Optical dispersion compensating processors for ultra-long haul optical transmission systems. Some optical devices essentials for PSP. Many detailed PSP techniques are given in the chapters of this Second Edition.

Linear Algebra For Pattern Processing

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