- Description
- 1 online resource (xi, 136 pages) : illustrations (some color).
- Additional Authors
- Sakata, Toshio,
- Notes
- 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.Includes bibliographical references at the end of each chapters.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.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.