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Preface 6 Contents 8 Acronyms 10 Notation 12 1 Multidimensional Data and the Concept of Visualization 14 2 Strategies for Multidimensional Data Visualization 18 2.1 Direct Visualization 18 2.1.1 Geometric Methods 18 2.1.2 Iconographic Displays 26 2.1.3 Hierarchical Displays 27 2.2 Dimensionality Reduction 28 2.2.1 Proximity Measures 33 2.2.2 Principal Component Analysis 34 2.2.3 Linear Discriminant Analysis 39 2.2.4 Multidimensional Scaling 40 2.2.4.1 SMACOF Algorithm 41 2.2.4.2 Relative Mapping 42 2.2.4.3 Sammon's Mapping 43 2.2.5 Manifold-Based Visualization 44 2.2.6 Isometric Feature Mapping 45 2.2.7 Locally Linear Embedding 48 2.3 Quantitative Criteria of Mapping 51 2.3.1 Spearman's Coefficient 52 2.3.2 König's Topology Preservation Measure 53 3 Optimization-Based Visualization 54 3.1 Formulation of Optimization Problems in Multidimensional Scaling 54 3.2 Differentiability Analysis of the Least Squares Stress Function 57 3.3 Optimization Algorithms for Scaling 60 3.4 Hybrid Evolutionary Algorithm for Multidimensional Scaling 64 3.5 Two-Level Optimization of Stress with City-Block Distances 67 3.5.1 Explicit Enumeration in Two-Level Optimization 74 3.5.2 Branch-and-Bound Algorit

Author

Adobe InDesign CS6 (Windows)

Language

EN