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

When I took Dr. Kirby's course "Pattern Analysis for Mathematical Scientists" in 1994, we were using an early version of the notes upon which this book is based, and the subsequent continuous refinement (he teaches this course every year) has produced a text that is concise, yet thorough and very readable.

This book offers a good blend of the rigorous presentation of the underlying mathematical concepts and the straightforward development of the data analysis/reduction methods. A key feature is the application of the methods to interesting "real world" problems, complimented nicely by pertinent and stimulating problem sets and computational projects.

I can without hesitation recommend this book to anyone teaching a course on the mathematical analysis of large data sets, as well as for self-study. This is applied mathematics at its finest!

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.