Linear algebra for pattern processing : projection, singular value decomposition, and pseudoinverse (Record no. 34040)

000 -LEADER
fixed length control field a
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 250610b xxu||||| |||| 00| 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9783031014161
082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 512.5
Item number KAN
100 ## - MAIN ENTRY--PERSONAL NAME
Personal name Kanatani, Kenichi
245 ## - TITLE STATEMENT
Title Linear algebra for pattern processing : projection, singular value decomposition, and pseudoinverse
260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Name of publisher, distributor, etc Springer,
Date of publication, distribution, etc 2022.
Place of publication, distribution, etc Cham :
300 ## - PHYSICAL DESCRIPTION
Extent xiv, 141 p. ;
Other physical details ill.,
Dimensions 24 cm.
365 ## - TRADE PRICE
Price amount 54.99
Price type code
Unit of pricing 100.40
490 ## - SERIES STATEMENT
Series statement Synthesis lectures on signal processing
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc Includes bibliographical references and index.
520 ## - SUMMARY, ETC.
Summary, etc 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
650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element Linear algebra
Topical term or geographic name as entry element Signals and signal processing
Topical term or geographic name as entry element Technology and engineering
942 ## - ADDED ENTRY ELEMENTS (KOHA)
Source of classification or shelving scheme
Item type Books
Holdings
Withdrawn status Lost status Source of classification or shelving scheme Damaged status Not for loan Permanent location Current location Date acquired Source of acquisition Cost, normal purchase price Full call number Barcode Date last seen Koha item type
          DAU DAU 2025-05-26 KB 5521.00 512.5 KAN 035572 2025-06-10 Books

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