00000cmm a22000004a 4500 UP-99796217611273234 Buklod 20230504003249.0 m go j cr cn |||aaaaa 120427s2011 xx u eng d 9783642274978 (eBook) 3642274978 (eBook) (iLib)UPD-00217904413 DLC DML eng DMLUC QA 76.9 D35 W364 2011eb Wang, Jianzhong. Geometric structure of high-dimensional data and dimensionality reduction [electronic resource] by Jianzhong Wang. Berlin, Heidelberg Springer Berlin Heidelberg 2011. 1 online resource (xix, 356 p.) ill. Pt. 1. Data geometry -- pt. 2. Linear dimensionality reduction -- pt. 3. Nonlinear dimensionality reduction. Introduction -- Part I. Data geometry. Preliminary calculus on manifolds -- Geometric structure of high-dimensional data -- Data models and structures of kernels of DR -- Part II. Linear dimensionality reduction. Principal component analysis -- Classical multidimensional scaling -- Random projection -- Part III. Nonlinear dimensionality reduction. Isomaps -- Maximum variance unfolding -- Locally linear embedding -- Local tangent space alignment -- Laplacian Eigenmaps -- Hessian locally linear embedding -- Diffusion maps -- Fast algorithms for DR approximation -- Appendix A. Differential forms and operators on manifolds -- Index. IP-based subscription, access limited to within on-campus computer network. Access via Electronic Resources of the UPD University Library Website. "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. Electronic reproduction. New York SpringerLink c2011. Available via World Wide Web through SpringerLink. Data structures (Computer science) Dimension reduction (Statistics) Electronic books. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://dx.doi.org/10.1007/978-3-642-27497-8 FO Monograph UPD DMLR Electronic Resource