This updated book proposes applications of tensor decomposition to unsupervised feature extraction and feature selection. The author posits that although supervised methods including deep learning have become popular, unsupervised methods have their own advantages. He argues that this is the case because unsupervised methods are easy to learn since tensor decomposition is a conventional linear methodology. This book starts from very basic linear algebra and reaches the cutting edge methodologies applied to difficult situations when there are many features (variables) while only small number of samples are available. The author includes advanced descriptions about tensor decomposition including Tucker decomposition using high order singular value decomposition as well as higher order orthogonal iteration, and train tensor decomposition. The author concludes by showing unsupervised methods and their application to a wide range of topics.

Allows readers to analyze data sets with small samples and many features Provides a fast algorithm, based upon linear algebra, to analyze big data Includes several applications to multi-view data analyses, with a focus on bioinformatics

Autorentext

Prof. Taguchi is currently a Professor at Department of Physics, Chuo University. Prof. Taguchi received a master degree in Statistical Physics from Tokyo Institute of Technology, Japan in 1986, and PhD degree in Non-linear Physics from Tokyo Institute of Technology, Tokyo, Japan in 1988. He worked at Tokyo Institute of Technology and Chuo University. He is with Chuo University (Tokyo, Japan) since 1997. He currently holds the Professor position at this university. His main research interests are in the area of Bioinformatics, especially, multi-omics data analysis using linear algebra. Dr. Taguchi has published a book on bioinformatics, more than 150 journal papers, book chapters and papers in conference proceedings and was recognized as top 2% scientist of the world in 3rd consecutive years (2021, 2022, 2023) according to analysis of Stanford University, USA and report of Elsevier in bioinformatics.

Inhalt

Introduction to linear algebra.- Matrix factorization.- Tensor decompositions.- PCA based unsupervised FE.- TD based unsupervised FE.- Application of PCA based unsupervised FE to bioinformatics.- Application of TD based unsupervised FE to bioinformatics.- Theoretical investigation of TD and PCA based unsupervised FE.