LEADER 04797nam 22006614a 450 001 9910146082903321 005 20170815120740.0 010 $a1-280-27535-9 010 $a9786610275359 010 $a0-470-34946-8 010 $a0-471-72208-1 010 $a0-471-72209-X 035 $a(CKB)1000000000018950 035 $a(EBL)225801 035 $a(OCoLC)475932211 035 $a(SSID)ssj0000232529 035 $a(PQKBManifestationID)11220035 035 $a(PQKBTitleCode)TC0000232529 035 $a(PQKBWorkID)10210490 035 $a(PQKB)11319215 035 $a(MiAaPQ)EBC225801 035 $a(EXLCZ)991000000000018950 100 $a20031107d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aRandom graphs for statistical pattern recognition$b[electronic resource] /$fDavid J. Marchette 210 $aHoboken, N.J. $cWiley-Interscience$dc2004 215 $a1 online resource (261 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 $a0-471-22176-7 320 $aIncludes bibliographical references (p. 213-227) and indexes. 327 $aRandom 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 Trees 327 $a2.4.1 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 Hulls 327 $a3.5.2 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 Quantization 327 $a4.11 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 Index 330 $aA 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. 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