新一代信息科学与技术丛书 高维数据几何结构及降维 英文版
作者：王建忠 编著
出版时间：2012年版
内容简介
《高维数据几何结构及降维(英文版)》以数据的几何结构为框架，介绍了不同的数据降维方法以及它们的数学原理和计算程序。除了经典的线性降维方法，《高维数据几何结构及降维(英文版)》更着重于非线性方法的探讨，针对近期发展起来的新的非线性方法，对其主要思想、数学依据、算法和程序都进行了详细描述；此外还介绍了降维方法在字母识别、人脸检测、图像分割、数据可视化、超光谱图像数据分析等领域的应用。《高维数据几何结构及降维(英文版)》提供了所有程序的MATLAB代码，以方便读者计算机实现。
目录
Chapter1Introduction
1.10verviewofDimensionalityR,eduction
1.2HighDimensionDataAcquisition
1.2.1CollectionofImagesinFaceRecognition
1.2.2HandwritingLettersandDigits
1.2.3TextDocuments
1.2.4HyperspectralImages
1.3CurseoftheDimensionality
1.3.1VolumeofCubesandSpheres
1.3.2VolumeofaThinSphericalShell
1.3.3TailProbabilityoftheMultivariateGaussianDistributions
1.3.4DiagonalsofCube
1.3.5ConcentrationofNormsandDistances
1.4IntrinsicandExtrinsicDimensions
1.4.1IntrinsicDimensionEstimation
1.4.2CorrelationDimension
1.4.3CapacityDimension
1.4.4MultiscaleEstimation
1.50utlineoftheBook
1.5.1CategoriesofDRProblems
1.5.2ScopeofThisBook
1.5.30therTopicsRelatedtoThisBook
1.5.4ArtificialSurfacesforTestingDRAlgorithms
PartIDataGeometry
Chapter2PreliminaryCalculusonManifolds
2.1LinearManifold
2.1.1SubspaceandProjection
2.1.2FunctionsonEuclideanSpaces
2.1.3LaplaceOperatorandHeatDiffusionKernel
2.2DifferentiableManifolds
2.2.1CoordinateSystemsandParameterization
2.2.2TangentSpacesandTangentVectors
2.2.3RiemannianMetrics
2.2.4GeodesicDistance
2.3FunctionsandOperatorsonManifolds
2.3.1FunctionsonManifolds
2.3.20peratorsonManifolds
Chapter3GeometricStructureofHigh-Dirnensional
3.1SimilarityandDissimilarityofData
3.1.1NeighborhoodDefinition
3.1.2AlgorithmsforConstructionofNeighborhood
3.2GraphsonDataSets
3.2.1UndirectedGraphs
3.2.2DirectedGraphs
3.2.3NeighborhoodandDataGraphs
3.3SpectralAnalysisofGraphs
3.3.1LaplacianofGraphs
3.3.2LaplacianonWeightedGraphs
3.3.3ContractingOperatoronWeightedGraph
Chapter4DataModelsandStructuresofKernelsofDR
4.1DataModelsinDimensionalityReduction
4.1.1InputDataofFirstType
4.1.2InputDataofSecondType
4.1.3ConstraintsonOutputData
4.1.4ConsistenceofDataGraph
4.1.5RobustGraphConnectionAlgorithm
4.2ConstructionsofDRKernels
4.2.1DRKernelsofLinearMethods
……
PartⅡLinearDimensionalityreduction
PartⅢNonlinearDimensionalityReduction
