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Covariances in computer vision and machine learning / (Record no. 562298)

000 -LEADER
fixed length control field 08225nam a2200745 i 4500
001 - CONTROL NUMBER
control field 8106904
003 - CONTROL NUMBER IDENTIFIER
control field IEEE
005 - DATE AND TIME OF LATEST TRANSACTION
control field 20200413152926.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS
fixed length control field m eo d
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field cr cn |||m|||a
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field 171122s2018 caua foab 000 0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number 9781681730141
Qualifying information ebook
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Canceled/invalid ISBN 9781681730134
Qualifying information print
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code 10.2200/S00801ED1V01Y201709COV011
Source of number or code doi
035 ## - SYSTEM CONTROL NUMBER
System control number (CaBNVSL)swl00407992
035 ## - SYSTEM CONTROL NUMBER
System control number (OCoLC)1012748003
040 ## - CATALOGING SOURCE
Original cataloging agency CaBNVSL
Language of cataloging eng
Description conventions rda
Transcribing agency CaBNVSL
Modifying agency CaBNVSL
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number TA1634
Item number .H23 2018
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number 006.37
Edition number 23
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Hà, Quang Minh,
Dates associated with a name 1977-,
Relator term author.
245 10 - TITLE STATEMENT
Title Covariances in computer vision and machine learning /
Statement of responsibility, etc. Hà Quang Minh, Vittorio Murino.
264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE
Place of production, publication, distribution, manufacture [San Rafael, California] :
Name of producer, publisher, distributor, manufacturer Morgan & Claypool,
Date of production, publication, distribution, manufacture, or copyright notice 2018.
300 ## - PHYSICAL DESCRIPTION
Extent 1 PDF (xiii, 156 pages) :
Other physical details illustrations.
336 ## - CONTENT TYPE
Content type term text
Source rdacontent
337 ## - MEDIA TYPE
Media type term electronic
Source isbdmedia
338 ## - CARRIER TYPE
Carrier type term online resource
Source rdacarrier
490 1# - SERIES STATEMENT
Series statement Synthesis lectures on computer vision,
International Standard Serial Number 2153-1064 ;
Volume/sequential designation # 13
538 ## - SYSTEM DETAILS NOTE
System details note Mode of access: World Wide Web.
538 ## - SYSTEM DETAILS NOTE
System details note System requirements: Adobe Acrobat Reader.
500 ## - GENERAL NOTE
General note Part of: Synthesis digital library of engineering and computer science.
504 ## - BIBLIOGRAPHY, ETC. NOTE
Bibliography, etc. note Includes bibliographical references (pages 143-154).
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note Part I. Covariance matrices and applications -- 1. Data representation by covariance matrices -- 1.1 Covariance matrices for data representation -- 1.2 Statistical interpretation -- 2. Geometry of SPD matrices -- 2.1 Euclidean distance -- 2.2 Interpretations and motivations for the different invariances -- 2.3 Basic Riemannian geometry -- 2.4 Affine-invariant Riemannian metric on SPD matrices -- 2.4.1 Connection with the Fisher-Rao metric -- 2.5 Log-Euclidean metric -- 2.5.1 Log-Euclidean distance as an approximation of the affine-invariant Riemannian distance -- 2.5.2 Log-Euclidean distance as a Riemannian distance -- 2.5.3 Log-Euclidean vs. Euclidean -- 2.6 Bregman divergences -- 2.6.1 Log-determinant divergences -- 2.6.2 Connection with the Rényi and Kullback-Leibler divergences -- 2.7 Alpha-Beta Log-Det divergences -- 2.8 Power Euclidean metrics -- 2.9 Distances and divergences between empirical covariance matrices -- 2.10 Running time comparison -- 2.11 Summary -- 3. Kernel methods on covariance matrices -- 3.1 Positive definite kernels and reproducing kernel Hilbert spaces -- 3.2 Positive definite kernels on SPD matrices -- 3.2.1 Positive definite kernels with the Euclidean metric -- 3.2.2 Positive definite kernels with the log-Euclidean metric -- 3.2.3 Positive definite kernels with the symmetric Stein divergence -- 3.2.4 Positive definite kernels with the affine-invariant Riemannian metric -- 3.3 Kernel methods on covariance matrices -- 3.4 Experiments on image classification -- 3.4.1 Datasets -- 3.4.2 Results -- 3.5 Related approaches --
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note Part II. Covariance operators and applications -- 4. Data representation by covariance operators -- 4.1 Positive definite kernels and feature maps -- 4.2 Covariance operators in RKHS -- 4.3 Data representation by RKHS covariance operators -- 5. Geometry of covariance operators -- 5.1 Hilbert-Schmidt distance -- 5.2 Riemannian distances between covariance operators -- 5.2.1 The affine-invariant Riemannian metric -- 5.2.2 Log-Hilbert-Schmidt metric -- 5.3 Infinite-dimensional alpha log-determinant divergences -- 5.4 Summary -- 6. Kernel methods on covariance operators -- 6.1 Positive definite kernels on covariance operators -- 6.1.1 Kernels defined using the Hilbert-Schmidt metric -- 6.1.2 Kernels defined using the log-Hilbert-Schmidt metric -- 6.2 Two-layer kernel machines -- 6.3 Approximate methods -- 6.3.1 Approximate log-Hilbert-Schmidt distance and approximate affine-invariant Riemannian distance -- 6.3.2 Computational complexity -- 6.3.3 Approximate log-Hilbert-Schmidt inner product -- 6.3.4 Two-layer kernel machine with the approximate log-Hilbert-Schmidt distance -- 6.3.5 Case study: approximation by Fourier feature maps -- 6.4 Experiments in image classification -- 6.5 Summary -- 7. Conclusion and future outlook --
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note A. Supplementary technical information -- Mean squared errors for empirical covariance matrices -- Matrix exponential and principal logarithm Fréchet derivative -- The quasi-random Fourier features -- Low-discrepancy sequences -- The Gaussian case -- Proofs of several mathematical results -- Bibliography -- Authors' biographies.
506 ## - RESTRICTIONS ON ACCESS NOTE
Terms governing access Abstract freely available; full-text restricted to subscribers or individual document purchasers.
510 0# - CITATION/REFERENCES NOTE
Name of source Compendex
510 0# - CITATION/REFERENCES NOTE
Name of source INSPEC
510 0# - CITATION/REFERENCES NOTE
Name of source Google scholar
510 0# - CITATION/REFERENCES NOTE
Name of source Google book search
520 3# - SUMMARY, ETC.
Summary, etc. Covariance matrices play important roles in many areas of mathematics, statistics, and machine learning, as well as their applications. In computer vision and image processing, they give rise to a powerful data representation, namely the covariance descriptor, with numerous practical applications. In this book, we begin by presenting an overview of the finite-dimensional covariance matrix representation approach of images, along with its statistical interpretation. In particular, we discuss the various distances and divergences that arise from the intrinsic geometrical structures of the set of Symmetric Positive Definite (SPD) matrices, namely Riemannian manifold and convex cone structures. Computationally, we focus on kernel methods on covariance matrices, especially using the Log-Euclidean distance. We then show some of the latest developments in the generalization of the finite-dimensional covariance matrix representation to the infinite-dimensional covariance operator representation via positive definite kernels. We present the generalization of the affine-invariant Riemannian metric and the Log-Hilbert-Schmidt metric, which generalizes the Log-Euclidean distance. Computationally, we focus on kernel methods on covariance operators, especially using the Log-Hilbert-Schmidt distance. Specifically, we present a two-layer kernel machine, using the Log-Hilbert-Schmidt distance and its finite-dimensional approximation, which reduces the computational complexity of the exact formulation while largely preserving its capability. Theoretical analysis shows that, mathematically, the approximate Log-Hilbert-Schmidt distance should be preferred over the approximate Log-Hilbert-Schmidt inner product and, computationally, it should be preferred over the approximate affine-invariant Riemannian distance. Numerical experiments on image classification demonstrate significant improvements of the infinite-dimensional formulation over the finite-dimensional counterpart. Given the numerous applications of covariance matrices in many areas of mathematics, statistics, and machine learning, just to name a few, we expect that the infinite-dimensional covariance operator formulation presented here will have many more applications beyond those in computer vision.
530 ## - ADDITIONAL PHYSICAL FORM AVAILABLE NOTE
Additional physical form available note Also available in print.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note Title from PDF title page (viewed on November 22, 2017).
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Computer vision
General subdivision Mathematical models.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name entry element Machine learning
General subdivision Mathematical models.
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term covariance descriptors in computer vision
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term positive definite matrices
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term infinite-dimensional covariance operators
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term positive definite operators
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term Hilbert-Schmidt operators
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term Riemannian manifolds
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term affine-invariant Riemannian distance
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term LogEuclidean distance
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term Log-Hilbert-Schmidt distance
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term convex cone
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term Bregman divergences
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term kernel methods on Riemannian manifolds
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term visual object recognition
653 ## - INDEX TERM--UNCONTROLLED
Uncontrolled term image classification
655 #0 - INDEX TERM--GENRE/FORM
Genre/form data or focus term Electronic books.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name Murino, Vittorio,
Relator term author.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Relationship information Print version:
International Standard Book Number 9781681730134
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Synthesis digital library of engineering and computer science.
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title Synthesis lectures on computer vision ;
Volume/sequential designation # 13.
International Standard Serial Number 2153-1064
856 42 - ELECTRONIC LOCATION AND ACCESS
Materials specified Abstract with links to resource
Uniform Resource Identifier http://ieeexplore.ieee.org/servlet/opac?bknumber=8106904
Holdings
Withdrawn status Lost status Damaged status Not for loan Permanent Location Current Location Date acquired Barcode Date last seen Price effective from Koha item type
        PK Kelkar Library, IIT Kanpur PK Kelkar Library, IIT Kanpur 2020-04-13 EBKE798 2020-04-13 2020-04-13 E books

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