Applied matrix and tensor variate data analysis [electronic resource] / Toshio Sakata, editor.

Preface; Contents; Contributors; 1 Three-Way Principal Component Analysis with Its Applications to Psychology; 1.1 Principal Component Analysis Modified for Three-Way Data; 1.2 Hierarchy in PCA and 3WPCA; 1.3 Alternating Least Squares Algorithm; 1.3.1 Parafac Algorithm; 1.3.2 Tucker3 Algorithm; 1.3.3 Tucker2 Algorithm; 1.4 Rotation of Components; 1.4.1 Rotational Freedom; 1.4.2 Joint Orthomax Rotation; 1.4.3 Three-Way Simplimax Rotation; 1.5 Applications to Stimulus-Response Data; 1.5.1 Network Representations of Three-Way PCA; 1.5.2 Color-Adjective Data; 1.5.3 Parafac Solution

1.5.4 Tucker3 Solution1.6 Conclusions; References; 2 Non-negative Matrix Factorization and Its Variants for Audio Signal Processing; 2.1 Introduction; 2.2 What Is NMF?; 2.3 Basic Properties of NMF; 2.4 NMF Algorithms; 2.4.1 Positive Matrix Factorization and NMF; 2.4.2 Divergence Measures; 2.4.3 Auxiliary Function Approach; 2.4.4 NMF Algorithm with Euclidean Distance; 2.4.5 NMF Algorithm with I Divergence; 2.4.6 NMF Algorithm with IS Divergence; 2.4.7 NMF Algorithm with β Divergence; 2.5 Interpretation of NMF as Generative Model; 2.5.1 β Divergence Versus Tweedie Distribution

2.5.2 Bregman Divergence Versus Natural Exponential Family2.6 Relation to Probabilistic Latent Semantic Analysis (pLSA); 2.7 Applications to Audio Signal Processing Problems; 2.7.1 Audio Source Separation and Music Transcription; 2.7.2 Complex NMF; 2.7.3 Itakura-Saito NMF; 2.7.4 NMF with Time-Varying Bases; 2.7.5 Other NMF Variants; 2.7.6 Other Applications; 2.8 Bayesian Nonparametric NMF; 2.8.1 Determination of Basis Number; 2.8.2 Beta Process NMF and Gamma Process NMF; 2.9 Summary; References; 3 Generalized Tensor PCA and Its Applications to Image Analysis; 3.1 Introduction

3.2 Generalized Tensor PCA3.3 Derivation of Tensor PCA Variants; 3.3.1 Multilinear PCA (MPCA); 3.3.2 Robust MPCA (RMPCA); 3.3.3 Simultaneous Low-Rank Approximation of Tensors (SLRAT); 3.3.4 Robust SLRAT; 3.4 Applications to Image Analysis; 3.4.1 Removing Outliers; 3.4.2 Hyperspectral Image Compression; 3.4.3 Face Recognition; 3.5 Conclusion; References; 4 Matrix Factorization for Image Processing; 4.1 Introduction; 4.2 Data Representation by Matrix Factorization; 4.2.1 Principal Component Analysis; 4.2.2 Independent Component Analysis; 4.2.3 Non-negative Matrix Factorization

4.2.4 Sparse Representation4.3 Characteristics of Sparseness; 4.3.1 Robustness; 4.3.2 Shrinkage Estimation; 4.4 Algorithms for Dictionary Learning; 4.4.1 Coefficient Estimation; 4.4.2 Dictionary Optimization; 4.5 Applications to Image Processing; References; 5 Array Normal Model and Incomplete Array Variate Observations; 5.1 Introduction; 5.2 Arrays and Array Variate Random Variables; 5.3 Array Normal Random Variable; 5.4 Dealing with Incomplete Arrays; 5.5 Flip-Flop Algorithm for Incomplete Arrays; 5.6 A Semi-parametric Mixed-Effects Model; 5.6.1 Models for the Mean