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Applied Matrix and Tensor Variate Data Analysis (eBook)

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2016 | 1st ed. 2016
XI, 136 Seiten
Springer Japan (Verlag)
978-4-431-55387-8 (ISBN)

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This book provides comprehensive reviews of recent progress in matrix variate and tensor variate data analysis from applied points of view. Matrix and tensor approaches for data analysis are known to be extremely useful for recently emerging complex and high-dimensional data in various applied fields. The reviews contained herein cover recent applications of these methods in psychology (Chap. 1), audio signals (Chap. 2) , image analysis from tensor principal component analysis (Chap. 3), and image analysis from decomposition (Chap. 4), and genetic data (Chap. 5) . Readers will be able to understand the present status of these techniques as applicable to their own fields. In Chapter 5 especially, a theory of tensor normal distributions, which is a basic in statistical inference, is developed, and multi-way regression, classification, clustering, and principal component analysis are exemplified under tensor normal distributions. Chapter 6 treats one-sided tests under matrix variate and tensor variate normal distributions, whose theory under multivariate normal distributions has been a popular topic in statistics since the books of Barlow et al. (1972) and Robertson et al. (1988). Chapters 1, 5, and 6 distinguish this book from ordinary engineering books on these topics.

This book provides comprehensive reviews of recent progress in matrix variate and tensor variate data analysis from applied points of view. Matrix and tensor approaches for data analysis are known to be extremely useful for recently emerging complex and high-dimensional data in various applied fields. The reviews contained herein cover recent applications of these methods in psychology (Chap. 1), audio signals (Chap. 2) , image analysis from tensor principal component analysis (Chap. 3), and image analysis from decomposition (Chap. 4), and genetic data (Chap. 5) . Readers will be able to understand the present status of these techniques as applicable to their own fields. In Chapter 5 especially, a theory of tensor normal distributions, which is a basic in statistical inference, is developed, and multi-way regression, classification, clustering, and principal component analysis are exemplified under tensor normal distributions. Chapter 6 treats one-sided tests under matrix variate andtensor variate normal distributions, whose theory under multivariate normal distributions has been a popular topic in statistics since the books of Barlow et al. (1972) and Robertson et al. (1988). Chapters 1, 5, and 6 distinguish this book from ordinary engineering books on these topics.

1 Three-Way Principal Component Analysis with its Applications to Psychology (Kohei Adachi).- 2 Non-negative matrix factorization and its variants for audio signal processing (Hirokazu Kameoka).- 3 Generalized Tensor PCA and its Applications to Image Analysis (Kohei Inoue).- 4 Matrix Factorization for Image Processing (Noboru Murata).- 5 Arrays Normal Model and Incomplete Array Variate Observations (Deniz Akdemir).- 6 One-sided Tests for Matrix Variate Normal Distribution (Manabu Iwasa and Toshio Sakata).

Erscheint lt. Verlag	2.2.2016
Reihe/Serie	JSS Research Series in Statistics
	JSS Research Series in Statistics
	JSS Research Series in Statistics
	SpringerBriefs in Statistics
	SpringerBriefs in Statistics
Zusatzinfo	XI, 136 p. 36 illus., 23 illus. in color.
Verlagsort	Tokyo
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Informatik ► Datenbanken
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra
	Mathematik / Informatik ► Mathematik ► Statistik
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
	Sozialwissenschaften ► Soziologie ► Empirische Sozialforschung
	Technik
Schlagworte	Dictionary Learning • generalized simultaneous low rank approximation • inference under array normal distributions • Non-Negative Matrix Factorization • one-sided inference under array normal distributions • tensor PCA
ISBN-10	4-431-55387-8 / 4431553878
ISBN-13	978-4-431-55387-8 / 9784431553878

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