## Applied Matrix and Tensor Variate Data AnalysisThis 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. |

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### Contents

1 | |

2 Nonnegative Matrix Factorization and Its Variants for Audio Signal Processing | 22 |

3 Generalized Tensor PCA and Its Applications to Image Analysis | 51 |

4 Matrix Factorization for Image Processing | 73 |

5 Array Normal Model and Incomplete Array Variate Observations | 93 |

6 OneSided Tests for Matrix Variate Normal Distribution | 123 |

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3WPCA Adachi algorithm Applications array variate assumed atoms audio signal auxiliary function Bayesian C(VIT coefficients complex spectrogram convex convex function corresponding covariance matrix data analysis data matrix decomposition defined denotes density dictionary dimensional eigenvalues elements estimation example face images face recognition follows formulated given GTPCA hk,m IEEE Transactions Independent Component Analysis intra-sample outliers iterative Journal Kameoka kernel Kiers Kronecker delta Kroonenberg kth dimension Lemma linear matrix and tensor method minimizing MPCA multivariate normal distribution multiway NMF algorithm non-negative matrix factorization non-negativity constraint nonsingular objective function observed obtained one-sided tests optimization problem orthogonal Parafac Principal component analysis procedure proposed random variables rewritten RMPCA RMSE robust SLRAT Rºº rotation sample outliers Sasabuchi Sect shown in Fig sparse coding sparse representation spectrogram subspaces super-resolution tensor PCA test statistic Theorem three-way um,n update values vectors xijk xk,n zero