Linear Algebra For Pattern Processing

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Linear Algebra for Pattern Processing

Kenichi Kanatani
Linear Algebra for Pattern Processing Book PDF

Author : Kenichi Kanatani
Publisher : Morgan & Claypool Publishers
Page : 157 pages
File Size : 43,5 Mb
Release : 2021-04-30
Category : Mathematics
ISBN : 9781636391083

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Linear Algebra for Pattern Processing by Kenichi Kanatani Pdf

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

Kenichi Kanatani
Linear Algebra for Pattern Processing Book PDF

Author : Kenichi Kanatani
Publisher : Springer Nature
Page : 141 pages
File Size : 49,9 Mb
Release : 2022-06-01
Category : Technology & Engineering
ISBN : 9783031025440

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Linear Algebra for Pattern Processing by Kenichi Kanatani Pdf

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.

Matrix Methods in Data Mining and Pattern Recognition

Lars Elden
Matrix Methods in Data Mining and Pattern Recognition Book PDF

Author : Lars Elden
Publisher : SIAM
Page : 226 pages
File Size : 51,8 Mb
Release : 2007-07-12
Category : Computers
ISBN : 9780898716269

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Matrix Methods in Data Mining and Pattern Recognition by Lars Elden Pdf

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

Dan A. Simovici
Linear Algebra Tools for Data Mining Book PDF

Author : Dan A. Simovici
Publisher : World Scientific
Page : 878 pages
File Size : 43,6 Mb
Release : 2012
Category : Computers
ISBN : 9789814383493

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Linear Algebra Tools for Data Mining by Dan A. Simovici Pdf

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.

Advanced Linear Algebra for Engineers with MATLAB

Sohail A. Dianat,Eli Saber
Advanced Linear Algebra for Engineers with MATLAB Book PDF

Author : Sohail A. Dianat,Eli Saber
Publisher : CRC Press
Page : 346 pages
File Size : 44,8 Mb
Release : 2017-12-19
Category : Mathematics
ISBN : 9781420095241

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Advanced Linear Algebra for Engineers with MATLAB by Sohail A. Dianat,Eli Saber Pdf

Arming readers with both theoretical and practical knowledge, Advanced Linear Algebra for Engineers with MATLAB® provides real-life problems that readers can use to model and solve engineering and scientific problems in fields ranging from signal processing and communications to electromagnetics and social and health sciences. Facilitating a unique understanding of rapidly evolving linear algebra and matrix methods, this book: Outlines the basic concepts and definitions behind matrices, matrix algebra, elementary matrix operations, and matrix partitions, describing their potential use in signal and image processing applications Introduces concepts of determinants, inverses, and their use in solving linear equations that result from electrical and mechanical-type systems Presents special matrices, linear vector spaces, and fundamental principles of orthogonality, using an appropriate blend of abstract and concrete examples and then discussing associated applications to enhance readers’ visualization of presented concepts Discusses linear operators, eigenvalues, and eigenvectors, and explores their use in matrix diagonalization and singular value decomposition Extends presented concepts to define matrix polynomials and compute functions using several well-known methods, such as Sylvester’s expansion and Cayley-Hamilton Introduces state space analysis and modeling techniques for discrete and continuous linear systems, and explores applications in control and electromechanical systems, to provide a complete solution for the state space equation Shows readers how to solve engineering problems using least square, weighted least square, and total least square techniques Offers a rich selection of exercises and MATLAB® assignments that build a platform to enhance readers’ understanding of the material Striking the appropriate balance between theory and real-life applications, this book provides both advanced students and professionals in the field with a valuable reference that they will continually consult.

A Matrix Algebra Approach to Artificial Intelligence

Xian-Da Zhang
A Matrix Algebra Approach to Artificial Intelligence Book PDF

Author : Xian-Da Zhang
Publisher : Springer Nature
Page : 844 pages
File Size : 54,8 Mb
Release : 2020-05-23
Category : Computers
ISBN : 9789811527708

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A Matrix Algebra Approach to Artificial Intelligence by Xian-Da Zhang Pdf

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.

Linear Algebra for Data Science, Machine Learning, and Signal Processing

Jeffrey A. Fessler,Raj Rao Nadakuditi
Linear Algebra for Data Science Machine Learning and Signal Processing Book PDF

Author : Jeffrey A. Fessler,Raj Rao Nadakuditi
Publisher : Cambridge University Press
Page : 453 pages
File Size : 49,7 Mb
Release : 2024-04-30
Category : Computers
ISBN : 9781009418140

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Linear Algebra for Data Science, Machine Learning, and Signal Processing by Jeffrey A. Fessler,Raj Rao Nadakuditi Pdf

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

Introduction to Lattice Algebra

Gerhard X. Ritter,Gonzalo Urcid
Introduction to Lattice Algebra Book PDF

Author : Gerhard X. Ritter,Gonzalo Urcid
Publisher : CRC Press
Page : 432 pages
File Size : 44,7 Mb
Release : 2021-08-23
Category : Mathematics
ISBN : 9781000412567

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Introduction to Lattice Algebra by Gerhard X. Ritter,Gonzalo Urcid Pdf

Lattice theory extends into virtually every branch of mathematics, ranging from measure theory and convex geometry to probability theory and topology. A more recent development has been the rapid escalation of employing lattice theory for various applications outside the domain of pure mathematics. These applications range from electronic communication theory and gate array devices that implement Boolean logic to artificial intelligence and computer science in general. Introduction to Lattice Algebra: With Applications in AI, Pattern Recognition, Image Analysis, and Biomimetic Neural Networks lays emphasis on two subjects, the first being lattice algebra and the second the practical applications of that algebra. This textbook is intended to be used for a special topics course in artificial intelligence with a focus on pattern recognition, multispectral image analysis, and biomimetic artificial neural networks. The book is self-contained and – depending on the student’s major – can be used for a senior undergraduate level or first-year graduate level course. The book is also an ideal self-study guide for researchers and professionals in the above-mentioned disciplines. Features Filled with instructive examples and exercises to help build understanding Suitable for researchers, professionals and students, both in mathematics and computer science Contains numerous exercises.

Introduction to Pattern Recognition

Menahem Friedman,Abraham Kandel
Introduction to Pattern Recognition Book PDF

Author : Menahem Friedman,Abraham Kandel
Publisher : World Scientific Publishing Company
Page : 344 pages
File Size : 41,6 Mb
Release : 1999-03-01
Category : Computers
ISBN : 9789813105188

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Introduction to Pattern Recognition by Menahem Friedman,Abraham Kandel Pdf

This book is an introduction to pattern recognition, meant for undergraduate and graduate students in computer science and related fields in science and technology. Most of the topics are accompanied by detailed algorithms and real world applications. In addition to statistical and structural approaches, novel topics such as fuzzy pattern recognition and pattern recognition via neural networks are also reviewed. Each topic is followed by several examples solved in detail. The only prerequisites for using this book are a one-semester course in discrete mathematics and a knowledge of the basic preliminaries of calculus, linear algebra and probability theory.

Statistical Pattern Recognition

Andrew R. Webb
Statistical Pattern Recognition Book PDF

Author : Andrew R. Webb
Publisher : John Wiley & Sons
Page : 516 pages
File Size : 44,6 Mb
Release : 2003-07-25
Category : Mathematics
ISBN : 9780470854785

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Statistical Pattern Recognition by Andrew R. Webb Pdf

Statistical pattern recognition is a very active area of study andresearch, which has seen many advances in recent years. New andemerging applications - such as data mining, web searching,multimedia data retrieval, face recognition, and cursivehandwriting recognition - require robust and efficient patternrecognition techniques. Statistical decision making and estimationare regarded as fundamental to the study of pattern recognition. Statistical Pattern Recognition, Second Edition has been fullyupdated with new methods, applications and references. It providesa comprehensive introduction to this vibrant area - with materialdrawn from engineering, statistics, computer science and the socialsciences - and covers many application areas, such as databasedesign, artificial neural networks, and decision supportsystems. * Provides a self-contained introduction to statistical patternrecognition. * Each technique described is illustrated by real examples. * Covers Bayesian methods, neural networks, support vectormachines, and unsupervised classification. * Each section concludes with a description of the applicationsthat have been addressed and with further developments of thetheory. * Includes background material on dissimilarity, parameterestimation, data, linear algebra and probability. * Features a variety of exercises, from 'open-book' questions tomore lengthy projects. The book is aimed primarily at senior undergraduate and graduatestudents studying statistical pattern recognition, patternprocessing, neural networks, and data mining, in both statisticsand engineering departments. It is also an excellent source ofreference for technical professionals working in advancedinformation development environments. For further information on the techniques and applicationsdiscussed in this book please visit ahref="http://www.statistical-pattern-recognition.net/"www.statistical-pattern-recognition.net/a

Photonic Signal Processing, Second Edition

Le Nguyen Binh
Photonic Signal Processing Second Edition Book PDF

Author : Le Nguyen Binh
Publisher : CRC Press
Page : 506 pages
File Size : 55,7 Mb
Release : 2019-01-15
Category : Technology & Engineering
ISBN : 9780429792632

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Photonic Signal Processing, Second Edition by Le Nguyen Binh Pdf

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.

Massively Parallel, Optical, and Neural Computing in the United States

Gilbert Kalb,Robert Moxley
Massively Parallel Optical and Neural Computing in the United States Book PDF

Author : Gilbert Kalb,Robert Moxley
Publisher : IOS Press
Page : 220 pages
File Size : 54,8 Mb
Release : 1992
Category : Computers
ISBN : 9051990979

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Massively Parallel, Optical, and Neural Computing in the United States by Gilbert Kalb,Robert Moxley Pdf

A survey of products and research projects in the field of highly parallel, optical and neural computers in the USA. It covers operating systems, language projects and market analysis, as well as optical computing devices and optical connections of electronic parts.

Photonic Signal Processing

Le Nguyen Binh
Photonic Signal Processing Book PDF

Author : Le Nguyen Binh
Publisher : CRC Press
Page : 382 pages
File Size : 49,6 Mb
Release : 2018-10-03
Category : Science
ISBN : 9781420019520

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Photonic Signal Processing by Le Nguyen Binh Pdf

The potential of photonic signal processing (PSP) to overcome electronic limits for processing ultra-wideband signals, provide signal conditioning that can be integrated in line with fiber optic systems, and improve signal quality makes this technology extremely attractive for improvement in receiver sensitivity performance. Spanning the current transitional period, Photonic Signal Processing: Techniques and Applications addresses the merging techniques of processing and manipulating signals propagating in the optical domain. The book begins with a historical perspective of PSP and introduces photonic components essential for photonic processing systems, such as optical amplification devices, optical fibers, and optical modulators. The author demonstrates the representation of photonic circuits via a signal flow graph technique adapted for photonic domain. He describes photonic signal processors, such as differentiators and integrators, and their applications for the generation of solitons, and then covers the application of these solitons in optically amplified fiber transmission systems. The book illustrates the compensation dispersion using a photonic processor, the design of optical filters using photonic processor techniques, and the filtering of microwave signals in the optical domain. Exploring methods for the processing of signals in the optical domain, the book includes solutions to photonic circuits that use signal flow techniques and significant applications in short pulse generation, the filtering of signals, differentiation, and the integration of signals. It delineates fundamental techniques on the processing of signals in the optical domain as well as their applications that lead to advanced aspects of performing generation of short pulses, integration, differentiation, and filtering for optical communications systems and networks and processing of ultra-high speed signals.

Recent Trends in Image Processing and Pattern Recognition

K. C. Santosh,Bharti Gawali
Recent Trends in Image Processing and Pattern Recognition Book PDF

Author : K. C. Santosh,Bharti Gawali
Publisher : Springer Nature
Page : 375 pages
File Size : 46,9 Mb
Release : 2021-03-22
Category : Computers
ISBN : 9789811604935

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Recent Trends in Image Processing and Pattern Recognition by K. C. Santosh,Bharti Gawali Pdf

This two-volume set constitutes the refereed proceedings of the Third International Conference on Recent Trends in Image Processing and Pattern Recognition (RTIP2R) 2020, held in Aurangabad, India, in January 2020. The 78 revised full papers presented were carefully reviewed and selected from 329 submissions. The papers are organized in topical sections in the two volumes. Part I: Computer vision and applications; Data science and machine learning; Document understanding and Recognition. Part II: Healthcare informatics and medical imaging; Image analysis and recognition; Signal processing and pattern recognition; Image and signal processing in Agriculture.

Matrix Methods in Data Mining and Pattern Recognition, Second Edition

Lars Elden
Matrix Methods in Data Mining and Pattern Recognition Second Edition Book PDF

Author : Lars Elden
Publisher : SIAM
Page : 229 pages
File Size : 54,5 Mb
Release : 2019-08-30
Category : Mathematics
ISBN : 9781611975864

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Matrix Methods in Data Mining and Pattern Recognition, Second Edition by Lars Elden Pdf

This thoroughly revised second edition provides an updated treatment of numerical linear algebra techniques for solving problems in data mining and pattern recognition. Adopting an application-oriented approach, the author introduces matrix theory and decompositions, describes how modern matrix methods can be applied in real life scenarios, and provides a set of tools that students can modify for a particular application. Building on material from the first edition, the author discusses basic graph concepts and their matrix counterparts. He introduces the graph Laplacian and properties of its eigenvectors needed in spectral partitioning and describes spectral graph partitioning applied to social networks and text classification. Examples are included to help readers visualize the results. This new edition also presents matrix-based methods that underlie many of the algorithms used for big data. The book provides a solid foundation to further explore related topics and presents applications such as classification of handwritten digits, text mining, text summarization, PageRank computations related to the Google search engine, and facial recognition. Exercises and computer assignments are available on a Web page that supplements the book. This book is primarily for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course and graduate students in data mining and pattern recognition areas who need an introduction to linear algebra techniques.