Geometric Data Analysis
An Empirical Approach to Dimensionality Reduction and the Study of Patterns
1. Edition January 2001
XX, 364 Pages, Hardcover
Handbook/Reference Book
Short Description
Pattern analysis consists essentially of data reduction methods applied to extremely large data sets, a field which has seen rapid advances recently due to the convergence of several trends. One factor is the recent availability of large amounts of computational power at modest prices, which has spread the use of sophisticated data analysis to the desktop. The development of chaos and complexity theory has likewise increased the sophistication of algorithms for finding partial order in noisy and incomplete data sets.
This book addresses the most efficient methods of pattern analysis using wavelet decomposition. Readers will learn to analyze data in order to emphasize the differences between closely related patterns and then categorize them in a way that is useful to system users.
Acknowledgments.
INTRODUCTION.
Pattern Analysis as Data Reduction.
Vector Spaces and Linear Transformations.
OPTIMAL ORTHOGONAL PATTERN REPRESENTATIONS.
The Karhunen-Loève Expansion.
Additional Theory, Algorithms and Applications.
TIME, FREQUENCY AND SCALE ANALYSIS.
Fourier Analysis.
Wavelet Expansions.
ADAPTIVE NONLINEAR MAPPINGS.
Radial Basis Functions.
Neural Networks.
Nonlinear Reduction Architectures.
Appendix A Mathemetical Preliminaries.
References.
Index.
"...effectively describes and summarizes an emerging new field, namely, scientific data modeling and analysis." (Mathematical Reviews, 2003h)
