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Random Graphs for Statistical Pattern Recognition

Random Graphs for Statistical Pattern Recognition

David J. Marchette

ISBN: 978-0-471-22176-0

Mar 2004

237 pages

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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.

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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 (α,β) 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.


Author Index.

Subject Index.

"…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, 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)