Geometric Structure of High-Dimensional Data and Dimensionality Reduction

"Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of dimensionality reduction. In addition to the introduction to well-known linear methods, the book moreover stresses the recently developed nonlinear methods and introduces the applications of dimensionality reduction in many areas, such as face recognition, image segmentation, data classification, data visualization, and hyperspectral imagery data analysis. Numerous tables and graphs are included to illustrate the ideas, effects, and shortcomings of the methods. MATLAB code of all dimensionality reduction algorithms is provided to aid the readers with the implementations on computers. 

The book will be useful for mathematicians, statisticians, computer scientists, and data analysts. It is also a valuable handbook for other practitioners who have a basic background in mathematics, statistics and/or computer algorithms, like internet search engine designers, physicists, geologists, electronic engineers, and economists.

Jianzhong Wang is a Professor of Mathematics at Sam Houston State University, U.S.A.

Comprehensively introducing all of popular linear and nonlinear dimensionality reduction methods

Full description of mathematical and statistical foundations of the introduced dimensionality reduction

Including most recently developed methods

Including all of feasible and effective algorithms and Matlab code for introduces methods

Including many examples and demo graphs for various application areas