Random Graphs for Statistical Pattern Recognition (eBook)

David J. Marchette (Autor)

eBook Download: PDF

2005 | 1. Auflage
264 Seiten
John Wiley & Sons (Verlag)
978-0-471-72208-3 (ISBN)

Infos

A timely convergence of two widely used disciplines

Random Graphs for Statistical Pattern Recognition is the first
book to address the topic of random graphs as it applies to
statistical pattern recognition. Both topics are of vital interest
to researchers in various mathematical and statistical fields and
have never before been treated together in one book. The use of
data random graphs in pattern recognition in clustering and
classification is discussed, and the applications for both
disciplines are enhanced with new tools for the statistical pattern
recognition community. New and interesting applications for random
graph users are also introduced.

This important addition to statistical literature
features:

* Information that previously has been available only through
scattered journal articles

* Practical tools and techniques for a wide range of real-world
applications

* New perspectives on the relationship between pattern
recognition and computational geometry

* Numerous experimental problems to encourage practical
applications

With its comprehensive coverage of two timely fields, enhanced
with many references and real-world examples, Random Graphs for
Statistical Pattern Recognition is a valuable resource for
industry professionals and students alike.

Autor

DAVID J. MARCHETTE, PhD, is a researcher at the Naval Surface Warfare Center in Dahlgren, Virginia, where he investigates computational statistics and pattern recognition, primarily as it applies to image processing, automatic target recognition, and computer security. He is also an adjunct professor at George Mason University and a lecturer at Johns Hopkins University.

Inhalt

Preface.

Acknowledgments.

1. Preliminaries.

1.1 Graphs and Digraphs.

1.2 Statistical Pattern Recognition.

1.3 Statistical Issues.

1.4 Applications.

1.5 Further Reading.

2. Computational Geometry.

2.1 Introduction.

2.2 Voronoi Cells and Delaunay Triangularization.

2.3 Alpha Hulls.

2.4 Minimum Spanning Trees.

2.5 Further Reading.

3. Neighborhood Graphs.

3.1 Introduction.

3.2 Nearest-Neighbor Graphs.

3.3 k-Nearest Neighbor Graphs.

3.4 Relative Neighborhood Graphs.

3.5 Gabriel Graphs.

3.6 Application: Nearest Neighbor Prototypes.

3.7 Sphere of Influence Graphs.

3.8 Other Relatives.

3.9 Asymptotics.

3.10 Further Reading.

4. Class Cover Catch Digraphs.

4.1 Catch Digraphs.

4.2 Class Covers.

4.3 Dominating Sets.

4.4 Distributional Results for Cn,m-graphs.

4.5 Characterizations.

4.6 Scale Dimension.

4.7 (alpha,beta) Graphs

4.8 CCCD Classification.

4.9 Homogeneous CCCDs.

4.10 Vector Quantization.

4.11 Random Walk Version.

4.12 Further Reading.

5. Cluster Catch Digraphs.

5.1 Basic Definitions.

5.2 Dominating Sets.

5.3 Connected Components.

5.4 Variable Metric Clustering.

6. Computational Methods.

6.1 Introduction.

6.2 Kd-Trees.

6.3 Class Cover Catch Digraphs.

6.4 Cluster Catch Digraphs.

6.5 Voroni Regions and Delaunay Triangularizations.

6.6 Further Reading.

References.

Author Index.

Subject Index.

Rezensionen

"...constructed...as a book on random graphs, this is quite
a good one." (Journal of the American Statistical
Association, September 2006)

"...I recommend this book to those who...wish to explore the
exciting place where graph theory and pattern recognition meet."
(Statistics in Medical Research, October 2005)

"This well-written book presents practical tools, and
information that was previously found scattered in various
journals." (Computing Reviews.com, March 9, 2005)

"...an excellent resource book that would be a valuable
addition..." (Technometrics, February 2005)

"...clearly and accessible written, and nicely conveys
the power, breadth and applicability of some very elegant
ideas..." (Short Book Reviews, Vol.24, No.3, December
2004)

"Buy this book if use graphs in cluster and classification
analysis." (Journal of Classification, Vol.21, No.2,
2004)

Produkt-Details

• Erscheint lt. Verlag: 11.2.2005
• Reihe/Serie: Wiley Series in Probability and Statistics
• Reihe/Serie: Wiley Series in Probability and Statistics
• Sprache: englisch
• Themenwelt: Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Graphentheorie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Computational & Graphical Statistics • Computer Science • Computer Science - General Interest • Discrete Mathematics • Diskrete Mathematik • Informatik • Mathematics • Mathematik • Populäre Themen i. d. Informatik • Populäre Themen i. d. Informatik • Rechnergestützte u. graphische Statistik • Rechnergestützte u. graphische Statistik • Statistics • Statistik
• ISBN-10: 0-471-72208-1 / 0471722081
• ISBN-13: 978-0-471-72208-3 / 9780471722083