© 2016

Applied Matrix and Tensor Variate Data Analysis

  • Toshio Sakata
  • Reviews applications of matrix and tensor variate data analysis by world-leading researchers in several representative applied fields including, psychology, audio signals, image data and genetics

  • Treats the most important concepts of tensor principal component analysis in details

  • The first book-length review of multivariate statistical inference under tensor normal distributions


Part of the SpringerBriefs in Statistics book series (BRIEFSSTATIST)

Also part of the JSS Research Series in Statistics book sub series (JSSRES)

About this book


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.


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

Editors and affiliations

  • Toshio Sakata
    • 1
  1. 1.Faculty of DesignKyushu UniversityFukuokaJapan

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“In its six chapters it covers a large span of methods and problems of eigenvector analysis of matrices, and many-way arrays, also known as tensors. Seven authors contribute to describing and developing these techniques for practical applications of computational statistical analysis in various fields of high-dimensional data. … This monograph can serve to lecturers, graduate students, and researchers working with theoretical methods and numerical estimations in modern multivariate statistical analysis.” (Stan Lipovetsky, Technometrics, Vol. 58 (3), August, 2016)