Geometric Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns / Edition 1

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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.

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Editorial Reviews

From the Publisher
"...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)

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Product Details

  • ISBN-13: 9780471239291
  • Publisher: Wiley
  • Publication date: 1/12/2001
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 384
  • Sales rank: 536,536
  • Product dimensions: 6.46 (w) x 9.65 (h) x 0.91 (d)

Meet the Author

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.

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Table of Contents




Pattern Analysis as Data Reduction.

Vector Spaces and Linear Transformations.


The Karhunen-Loève Expansion.

Additional Theory, Algorithms and Applications.


Fourier Analysis.

Wavelet Expansions.


Radial Basis Functions.

Neural Networks.

Nonlinear Reduction Architectures.

Appendix A Mathemetical Preliminaries.



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  • Anonymous

    Posted March 3, 2001

    Is there data analysis beyond statistics?

    Yes! This book explains the cutting edge techniques. I took this course (it is a graduate level book) at Colorado State from the author, and I think that this book is unique is many aspects. It organizes a very broad array of topics under the unifying theme of 'dimensionality reduction', or the finding of patterns in data. This is why the book is unique- there are many books out there on linear algebra, many books on neural networks, wavelets, Fourier analysis, computational geometry (Kohonen's Map, LBG clustering, etc.). What is NOT out there is a book that that shows the interconnections between all of these topics. This book does that. Look over the table of contents and you'll see what I mean. Furthermore, the book is unique in its perspective- explaining the topics by the mathematical underpinnings- not from a statistical perspective (like Chris Bishop's neural nets book), or from a signals processing point of view (like Simon Haykin's filtering book). Finally, the projects and problems that are discussed are really nice- For example, 'The Rogues Gallery' is a face recognition problem (aka 'Eigenfaces'); the techniques described are the ones in actual practice. And can a computer read lips? That's described here as well. Can you obtain equations of motion from data? Described here, too. The book is not only theoretical, there are many, many algorithms listed that are explained clearly and are ready-for-implementation. If you are a mathematician, engineer, computer scientist, statistician, or just interested in pattern detection, this book is a must-have.

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