Geometric data analysis. An empirical approach to dimensionality reduction and the study of patterns (Q2781440)

This textbook deals with the dimensionality reduction of large data sets with special emphasis on the geometric perspective. It is written for students and researchers with diverse mathematical backgrounds, e.g., for students of Computer Science, Physics, Engineering and Mathematics, whose work involves analyzing patterns in large, high dimensional data sets.NEWLINENEWLINENEWLINEThe book consists of four parts and an appendix which contains the mathematical preliminaries. The first part (Chapters: 1. Pattern Analysis as Data Reduction, 2. Vector Spaces and Linear Transforms) introduces the underlying concepts of dimensionality reduction and reviews the basic mathematics.NEWLINENEWLINENEWLINEThe second part (Chapters: 3. The Karhunen-Loève Expansion, 4. Additional Theory, Algorithms, Applications) develops the idea of optimal dimensionality-reducing mappings in a linear setting. The important Karhunen-Loéve transform is discussed.NEWLINENEWLINENEWLINEThe third part (Chapters: 5. Fourier Analysis, 6. Wavelet Expansions) concerns the time, frequency and scale analysis.NEWLINENEWLINENEWLINEFinally, the fourth part deals with adaptive nonlinear mappings and their application to the construction of empirical dimensionality-reducing transformations.