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1 Data science context |
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1.1 Data in a metric space |
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1.1.1 Measuring dissimilarities and similarities |
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1.1.2 Neighbourhood ranks |
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1.1.3 Embedding space notations |
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1.1.4 Multidimensional data |
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1.1.5 Sequence data |
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1.1.6 Network data |
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1.1.7 A few multidimensional datasets |
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1.2 Automated tasks |
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1.2.1 Underlying distribution |
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1.2.2 Category identification |
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1.2.3 Data manifold analysis |
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1.2.4 Model learning |
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1.2.5 Regression |
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1.3 Visual exploration |
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1.3.1 Human in the loop using graphic variables |
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1.3.2 Spatialization and Gestalt principles |
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1.3.3 Scatter plots |
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1.3.4 Parallel coordinates |
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1.3.5 Colour coding |
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1.3.6 Multiple coordinated views and visual interaction |
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1.3.7 Graph drawing |
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2 Intrinsic dimensionality |
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2.1 Curse of dimensionality |
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2.1.1 Data sparsity |
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2.1.2 Norm concentration |
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2.2 ID estimation |
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2.2.1 Covariance-based approaches |
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2.2.2 Fractal approaches |
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2.2.3 Towards local estimation |
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2.3 TIDLE |
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2.3.1 Gaussian mixture modelling |
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2.3.2 Test of TIDLE on a two clusters case |
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3 Map evaluation |
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3.1 Objective and practical indicators |
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3.1.1 Subjectivity of indicators |
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3.1.2 User studies on specific tasks |
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3.2 Unsupervised global evaluation |
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3.2.1 Types of distortions |
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3.2.2 Link between distortions and mapping continuity |
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3.2.3 Reasons of distortions ubiquity |
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3.2.4 Scalar indicators |
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3.2.5 Aggregation |
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3.2.6 Diagrams |
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3.3 Class-aware indicators |
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3.3.1 Class separation and aggregation |
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3.3.2 Comparing scores between the two spaces |
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3.3.3 Class cohesion and distinction |
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3.3.4 The case of one cluster per class |
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4 Map interpretation |
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4.1 Axes recovery |
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4.1.1 Linear case: biplots |
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4.1.2 Non-linear case |
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4.2 Local evaluation |
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4.2.1 Point-wise aggregation |
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4.2.2 One to many relations with focus point |
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4.2.3 Many to many relations |
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4.3 MING |
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4.3.1 Uniform formulation of rank-based indicator |
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4.3.2 MING graphs |
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4.3.3 MING analysis for a toy dataset |
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4.3.4 Impact of MING parameters |
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4.3.5 Visual clutter |
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4.3.6 Oil flow |
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4.3.7 COIL-20 dataset |
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4.3.8 MING perspectives |
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5 Unsupervised DR |
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5.1 Spectral projections |
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5.1.1 Principal Component Analysis |
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5.1.2 Classical MultiDimensional Scaling |
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5.1.3 Kernel methods: Isompap, KPCA, LE |
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5.2 Non-linear MDS |
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5.2.1 Metric MultiDimensional Scaling |
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5.2.2 Non-metric MultiDimensional Scaling |
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5.3 Neighbourhood Embedding |
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5.3.1 General principle: SNE |
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5.3.2 Scale setting |
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5.3.3 Divergence choice: NeRV and JSE |
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5.3.4 Symmetrization |
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5.3.5 Solving the crowding problem: tSNE |
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5.3.6 Kernel choice |
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5.3.7 Adaptive Student Kernel Imbedding |
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5.4 Graph layout |
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5.4.1 Force directed graph layout: Elastic Embedding |
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5.4.2 Probabilistic graph layout: LargeVis |
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5.4.3 Topological method UMAP |
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5.5 Artificial neural networks |
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5.5.1 Auto-encoders |
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5.5.2 IVIS |
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6 Supervised DR |
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6.1 Types of supervision |
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6.1.1 Full supervision |
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6.1.2 Weak supervision |
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6.1.3 Semi-supervision |
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6.2 Parametric with class purity |
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6.2.1 Linear Discriminant Analysis |
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6.2.2 Neighbourhood Component Analysis |
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6.3 Metric learning |
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6.3.1 Mahalanobis distances |
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6.3.2 Riemannian metric |
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6.3.3 Direct distances transformation |
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6.3.4 Similarities learning |
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6.3.5 Metric learning limitations |
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6.4 Class adaptive scale |
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6.5 Classimap |
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6.6 CGNE |
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6.6.1 ClassNeRV stress |
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6.6.2 Flexibility of the supervision |
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6.6.3 Ablation study |
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6.6.4 Isolet 5 case study |
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6.6.5 Robustness to class misinformation |
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6.6.6 Extension to the type 2 mixture: ClassJSE |
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6.6.7 Extension to semi-supervision and weak-supervision |
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6.6.8 Extension to soft labels |
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7 Mapping construction |
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7.1 Optimization |
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7.1.1 Global and local optima |
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7.1.2 Descent algorithms |
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7.1.3 Initialization |
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7.1.4 Multi-scale optimization |
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7.1.5 Force-directed placement interpretation |
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7.2 Acceleration strategies |
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7.2.1 Attractive forces approximation |
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7.2.2 Binary search trees |
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7.2.3 Repulsive forces |
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7.2.4 Landmarks approximation |
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7.3 Out of sample extension |
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1 Data science context |
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1.1 Data in a metric space |
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1.1.1 Measuring dissimilarities and similarities |
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ＥＢ
