Geometric Data Analysis
An Empirical Approach to Dimensionality Reduction and the Study of Patterns
1. Auflage Januar 2001
XX, 364 Seiten, Hardcover
Handbuch/Nachschlagewerk
ISBN:
978-0-471-23929-1
John Wiley & Sons
Kurzbeschreibung
Unentbehrlich für die Praxis ist dieses Handbuch der Datenanalyse, das besonders auf die Unterschiede zwischen eng verwandten Patterns und auf deren zweckdienliche Kategorisierung eingeht. Zahlreiche Übungsaufgaben helfen beim Vertiefen der erarbeiteten theoretischen Konzepte.
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.
Preface.
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.
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.
"...provides a valuable summary of data reduction." (Technometrics, May 2002)
"...effectively describes and summarizes an emerging new field, namely, scientific data modeling and analysis." (Mathematical Reviews, 2003h)
"...effectively describes and summarizes an emerging new field, namely, scientific data modeling and analysis." (Mathematical Reviews, 2003h)
MICHAEL KIRBY is a professor in the Department of Mathematics at Colorado State University in Fort Collins, Colorado. He has worked in the field of data reduction for well over a decade.
