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Table of Contents
Intro; Preface; Acknowledgements; Contents; List of Abbreviations; Abstract; 1 Motivation, Problems and Approach; 1.1 Motivation; 1.2 Visualization: From n-D Points to 2-D Points; 1.3 Visualization: From n-D Points to 2-D Structures; 1.4 Analysis of Alternatives; 1.5 Approach; References; 2 General Line Coordinates (GLC); 2.1 Reversible General Line Coordinates; 2.1.1 Generalization of Parallel and Radial Coordinates; 2.1.2 n-Gon and Circular Coordinates; 2.1.3 Types of GLC in 2-D and 3-D; 2.1.4 In-Line Coordinates; 2.1.5 Dynamic Coordinates; 2.1.6 Bush and Parallel Coordinates with Shifts.
2.2 Reversible Paired Coordinates2.2.1 Paired Orthogonal Coordinates; 2.2.2 Paired Coordinates with Non-linear Scaling; 2.2.3 Partially Collocated and Non-orthogonal Collocated Coordinates; 2.2.4 Paired Radial (Star) Coordinates; 2.2.5 Paired Elliptical Coordinates; 2.2.6 Open and Closed Paired Crown Coordinates; 2.2.7 Clutter Suppressing in Paired Coordinates; 2.3 Discussion on Reversible and Non-reversible Visualization Methods; References; 3 Theoretical and Mathematical Basis of GLC; 3.1 Graphs in General Line Coordinates; 3.2 Steps and Properties of Graph Construction Algorithms.
3.3 Fixed Single Point Approach3.3.1 Single Point Algorithm; 3.3.2 Statements Based on Single Point Algorithm; 3.3.3 Generalization of a Fixed Point to GLC; 3.4 Theoretical Limits to Preserve n-D Distances in 2-D: Johnson-Lindenstrauss Lemma; 3.5 Visual Representation of n-D Relations in GLC; 3.5.1 Hyper-cubes and Clustering in CPC; 3.5.2 Comparison of Linear Dependencies in PC, CPC and SPC; 3.5.3 Visualization of n-D Linear Functions and Operators in CPC, SPC and PC; References; 4 Adjustable GLCs for Decreasing Occlusion and Pattern Simplification.
4.1 Decreasing Occlusion by Shifting and Disconnecting Radial Coordinates4.2 Simplifying Patterns by Relocating and Scaling Parallel Coordinates; 4.2.1 Shifting and Tilting Parallel Coordinates; 4.2.2 Shifting and Reordering of Parallel Coordinates; 4.3 Simplifying Patterns and Decreasing Occlusion by Relocating, Reordering, and Negating Shifted Paired Coordinates; 4.3.1 Negating Shifted Paired Coordinates for Removing Crossings; 4.3.2 Relocating Shifted Paired Coordinates for Making the Straight Horizontal Lines; 4.3.3 Relocating Shifted Paired Coordinates for Making a Single 2-D Point.
4.4 Simplifying Patterns by Relocating and Scaling Circular and n-Gon Coordinates4.5 Decreasing Occlusion with the Expanding and Shrinking Datasets; 4.5.1 Expansion Alternatives; 4.5.2 Rules and Classification Accuracy for Vicinity in E1; 4.6 Case Studies for the Expansion E1; 4.7 Discussion; References; 5 GLC Case Studies; 5.1 Case Study 1: Glass Processing with CPC, APC and SPC; 5.2 Case Study 2: Simulated Data with PC and CPC; 5.3 Case Study 3: World Hunger Data; 5.4 Case Study 4: Challenger USA Space Shuttle Disaster with PC and CPC.
2.2 Reversible Paired Coordinates2.2.1 Paired Orthogonal Coordinates; 2.2.2 Paired Coordinates with Non-linear Scaling; 2.2.3 Partially Collocated and Non-orthogonal Collocated Coordinates; 2.2.4 Paired Radial (Star) Coordinates; 2.2.5 Paired Elliptical Coordinates; 2.2.6 Open and Closed Paired Crown Coordinates; 2.2.7 Clutter Suppressing in Paired Coordinates; 2.3 Discussion on Reversible and Non-reversible Visualization Methods; References; 3 Theoretical and Mathematical Basis of GLC; 3.1 Graphs in General Line Coordinates; 3.2 Steps and Properties of Graph Construction Algorithms.
3.3 Fixed Single Point Approach3.3.1 Single Point Algorithm; 3.3.2 Statements Based on Single Point Algorithm; 3.3.3 Generalization of a Fixed Point to GLC; 3.4 Theoretical Limits to Preserve n-D Distances in 2-D: Johnson-Lindenstrauss Lemma; 3.5 Visual Representation of n-D Relations in GLC; 3.5.1 Hyper-cubes and Clustering in CPC; 3.5.2 Comparison of Linear Dependencies in PC, CPC and SPC; 3.5.3 Visualization of n-D Linear Functions and Operators in CPC, SPC and PC; References; 4 Adjustable GLCs for Decreasing Occlusion and Pattern Simplification.
4.1 Decreasing Occlusion by Shifting and Disconnecting Radial Coordinates4.2 Simplifying Patterns by Relocating and Scaling Parallel Coordinates; 4.2.1 Shifting and Tilting Parallel Coordinates; 4.2.2 Shifting and Reordering of Parallel Coordinates; 4.3 Simplifying Patterns and Decreasing Occlusion by Relocating, Reordering, and Negating Shifted Paired Coordinates; 4.3.1 Negating Shifted Paired Coordinates for Removing Crossings; 4.3.2 Relocating Shifted Paired Coordinates for Making the Straight Horizontal Lines; 4.3.3 Relocating Shifted Paired Coordinates for Making a Single 2-D Point.
4.4 Simplifying Patterns by Relocating and Scaling Circular and n-Gon Coordinates4.5 Decreasing Occlusion with the Expanding and Shrinking Datasets; 4.5.1 Expansion Alternatives; 4.5.2 Rules and Classification Accuracy for Vicinity in E1; 4.6 Case Studies for the Expansion E1; 4.7 Discussion; References; 5 GLC Case Studies; 5.1 Case Study 1: Glass Processing with CPC, APC and SPC; 5.2 Case Study 2: Simulated Data with PC and CPC; 5.3 Case Study 3: World Hunger Data; 5.4 Case Study 4: Challenger USA Space Shuttle Disaster with PC and CPC.