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Applied Matrix and Tensor Variate Data Analysis

Part of the SpringerBriefs in Statistics Book Series

Editors: Sakata, Toshio

DOI: 10.1007/978-4-431-55387-8

ISBN: 978-4-431-55386-1

Publisher: Springer Japan - Springer Journals

Feb 3, 2016

Available

Three-Way Principal Component Analysis with Its Applications to Psychology

Adachi, Kohei

Pages: 1 –21

[The principal component analysis (PCA) procedures modified for analyzing three-way data are generally called three-way PCA (3WPCA). Popular 3WPCA procedures are known as the names, Tucker2, Tucker3, and Parafac. We describe their models and algorithms with an emphasis on a hierarchical...
Available

Non-negative Matrix Factorization and Its Variants for Audio Signal Processing

Kameoka, Hirokazu

Pages: 23 –50

[In this chapter, I briefly introduce a multivariate analysis technique called non-negative matrix factorization (NMF), which has attracted a lot of attention in the field of audio signal processing in recent years. I will mention some basic properties of NMF, effects induced by the non-negative...
Available

Generalized Tensor PCA and Its Applications to Image Analysis

Inoue, Kohei

Pages: 51 –71

[Recently, principal component analysis (PCA) has made remarkable progress in some research areas including computer vision and pattern recognition. The objects handled by PCA have been extended from vectors to higher-order tensors, also known as multidimensional or N-way arrays including vectors...
Available

Matrix Factorization for Image Processing

Murata, Noboru

Pages: 73 –92

[Some of important methods for signal processing, such as principal component analysis (PCA), independent component analysis (ICA), non-negative matrix factorization (NMF), and sparse representation (SR), can be discussed in a unified framework where a data matrix is decomposed into a product of...
Available

Array Normal Model and Incomplete Array Variate Observations

Akdemir, Deniz

Pages: 93 –122

[Missing data present an important challenge when dealing with high-dimensional data arranged in the form of an array. The main purpose of this article is to introduce methods for estimation of the parameters of array variate normal probability model from partially observed multiway data. The...
Available

One-Sided Tests for Matrix Variate Normal Distribution

Iwasa, Manabu; Sakata, Toshio

Pages: 123 –136

[In this chapter, we consider one-sided tests of the mean matrix M for a matrix variate normal distribution Np,q(M,Σ,Ψ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...

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