04763nam 22006494a 450 991083059010332120230617031345.01-280-27535-997866102753590-470-34946-80-471-72208-10-471-72209-X(CKB)1000000000018950(EBL)225801(OCoLC)475932211(SSID)ssj0000232529(PQKBManifestationID)11220035(PQKBTitleCode)TC0000232529(PQKBWorkID)10210490(PQKB)11319215(MiAaPQ)EBC225801(EXLCZ)99100000000001895020031107d2004 uy 0engur|n|---|||||txtccrRandom graphs for statistical pattern recognition[electronic resource] /David J. MarchetteHoboken, N.J. Wiley-Intersciencec20041 online resource (261 p.)Wiley series in probability and statisticsDescription based upon print version of record.0-471-22176-7 Includes bibliographical references (p. 213-227) and indexes.Random Graphs for Statistical Pattern Recognition; Contents; Preface; Acknowledgments; 1 Preliminaries; 1.1 Graphs and Digraphs; 1.1.1 Graphs; 1.1.2 Digraphs; 1.1.3 Random Graphs; 1.2 Statistical Pattern Recognition; 1.2.1 Classification; 1.2.2 Curse of Dimensionality; 1.2.3 Clustering; 1.3 Statistical Issues; 1.4 Applications; 1.4.1 Artificial Nose; 1.4.2 Hyperspectral Image; 1.4.3 Gene Expression; 1.5 Further Reading; 2 Computational Geometry; 2.1 Introduction; 2.2 Voronoi Cells and Delaunay Triangularization; 2.2.1 Poisson Voronoi Cells; 2.3 Alpha Hulls; 2.4 Minimum Spanning Trees2.4.1 Alpha Hulls and the MST2.4.2 Clustering; 2.4.3 Classification Complexity; 2.4.4 Application: Renyi Divergence; 2.4.5 Application: Image Segmentation; 2.5 Further Reading; 3 Neighborhood Graphs; 3.1 Introduction; 3.1.1 Application: Image Processing; 3.2 Nearest-Neighbor Graphs; 3.3 k-Nearest-Neighbor Graphs; 3.3.1 Application: Measures of Association; 3.3.2 Application: Artificial Nose; 3.3.3 Application: Outlier Detection; 3.3.4 Application: Dimensionality Reduction; 3.4 Relative Neighborhood Graphs; 3.5 Gabriel Graphs; 3.5.1 Gabriel Graphs and Alpha Hulls3.5.2 Application: Nearest-Neighbor Prototypes3.6 Sphere-of-Influence Graphs; 3.7 Sphere-of-Attraction Graphs; 3.8 Other Relatives; 3.9 Asymptotics; 3.10 Further Reading; 4 Class Cover Catch Digraphs; 4.1 Catch Digraphs; 4.1.1 Sphere Digraphs; 4.2 Class Covers; 4.2.1 Basic Definitions; 4.3 Dominating sets; 4.4 Distributional Results for Cn,m-graphs; 4.4.1 Univariate Case; 4.4.2 Multivariate CCCDs; 4.5 Characterizations; 4.6 Scale Dimension; 4.6.1 Application: Latent Class Discovery; 4.7 (a,b) Graphs; 4.8 CCCD Classification; 4.9 Homogeneous CCCDs; 4.10 Vector Quantization4.11 Random Walk Version4.11.1 Application: Face Detection; 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; 6.2.1 Data Structure; 6.2.2 Building the Tree; 6.2.3 Searching the Tree; 6.3 Class Cover Catch Digraphs; 6.4 Cluster Catch Digraphs; 6.5 Voronoi Regions and Delaunay Triangularizations; 6.6 Further Reading; References; Author Index; Subject IndexA 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 iWiley series in probability and statistics.Random graphsPattern perceptionStatistical methodsPattern recognition systemsRandom graphs.Pattern perceptionStatistical methods.Pattern recognition systems.511.5511/.5Marchette David J66281MiAaPQMiAaPQMiAaPQBOOK9910830590103321Random graphs for statistical pattern recognition4028148UNINA