图书简介
This book proposes tools for analysis of multidimensional and metric data, by establishing a state-of-the-art of the existing solutions and developing new ones. It mainly focuses on visual exploration of these data by a human analyst, relying on a 2D or 3D scatter plot display obtained through Dimensionality Reduction (DR). Performing diagnosis of an energy system requires identifying relations between observed monitoring variables and the associated internal state of the system. Dimensionality reduction, which allows to represent visually a multidimensional dataset, constitutes a promising tool to help domain experts to analyse these relations. This book reviews existing techniques for visual data exploration and dimensionality reduction, and proposes new solutions to challenges in that field. In order to perform diagnosis of energy systems, domain experts need to establish relations between the possible states of a given system and the measurement of a set of monitoring variables.Classical dimensionality reduction techniques such as tSNE and Isomap are presented, as well as the new unsupervised technique ASKI and the supervised methods ClassNeRV and ClassJSE. A new approach, MING for local map quality evaluation, is also introduced. These methods are then applied to the representation of expert-designed fault indicators for smart-buildings, I-V curves for photovoltaic systems and acoustic signals for Li-ion batteries.
1 Data science context.- 1.1 Data in a metric space.- 1.1.1 Measuring dissimilarities and similarities .- 1.1.2 Neighbourhood ranks.- 1.1.3 Embedding space notations.- 1.1.4 Multidimensional data .- 1.1.5 Sequence data.- 1.1.6 Network data.- 1.1.7 A few multidimensional datasets .- 1.2 Automated tasks.- 1.2.1 Underlying distribution.- 1.2.2 Category identification.- 1.2.3 Data manifold analysis.- 1.2.4 Model learning.- 1.2.5 Regression.- 1.3 Visual exploration.- 1.3.1 Human in the loop using graphic variables.- 1.3.2 Spatialization and Gestalt principles.- 1.3.3 Scatter plots.- 1.3.4 Parallel coordinates.- 1.3.5 Colour coding.- 1.3.6 Multiple coordinated views and visual interaction.- 1.3.7 Graph drawing.- 2 Intrinsic dimensionality.- 2.1 Curse of dimensionality.- 2.1.1 Data sparsity.- 2.1.2 Norm concentration.- 2.2 ID estimation.- 2.2.1 Covariance-based approaches.- 2.2.2 Fractal approaches.- 2.2.3 Towards local estimation.- 2.3 TIDLE .- 2.3.1 Gaussian mixture modelling.- 2.3.2 Test of TIDLE on a two clusters case.- 3 Map evaluation.- 3.1 Objective and practical indicators.- 3.1.1 Subjectivity of indicators.- 3.1.2 User studies on specific tasks.- 3.2 Unsupervised global evaluation.- 3.2.1 Types of distortions.- 3.2.2 Link between distortions and mapping continuity.- 3.2.3 Reasons of distortions ubiquity.- 3.2.4 Scalar indicators.- 3.2.5 Aggregation.- 3.2.6 Diagrams.- 3.3 Class-aware indicators.- 3.3.1 Class separation and aggregation.- 3.3.2 Comparing scores between the two spaces.- 3.3.3 Class cohesion and distinction.- 3.3.4 The case of one cluster per class.- 4 Map interpretation.- 4.1 Axes recovery.- 4.1.1 Linear case: biplots .- 4.1.2 Non-linear case.- 4.2 Local evaluation.- 4.2.1 Point-wise aggregation.- 4.2.2 One to many relations with focus point.- 4.2.3 Many to many relations.- 4.3 MING.- 4.3.1 Uniform formulation of rank-based indicator.- 4.3.2 MING graphs.- 4.3.3 MING analysis for a toy dataset.- 4.3.4 Impact of MING parameters.- 4.3.5 Visual clutter.- 4.3.6 Oil flow.- 4.3.7 COIL-20 dataset.- 4.3.8 MING perspectives.- 5 Unsupervised DR.- 5.1 Spectral projections.- 5.1.1 Principal Component Analysis.- 5.1.2 Classical MultiDimensional Scaling.- 5.1.3 Kernel methods: Isompap, KPCA, LE.- 5.2 Non-linear MDS.- 5.2.1 Metric MultiDimensional Scaling.- 5.2.2 Non-metric MultiDimensional Scaling.- 5.3 Neighbourhood Embedding.- 5.3.1 General principle: SNE.- 5.3.2 Scale setting.- 5.3.3 Divergence choice: NeRV and JSE.- 5.3.4 Symmetrization.- 5.3.5 Solving the crowding problem: tSNE.- 5.3.6 Kernel choice.- 5.3.7 Adaptive Student Kernel Imbedding.- 5.4 Graph layout.- 5.4.1 Force directed graph layout: Elastic Embedding.- 5.4.2 Probabilistic graph layout: LargeVis.- 5.4.3 Topological method UMAP.- 5.5 Artificial neural networks.- 5.5.1 Auto-encoders.- 5.5.2 IVIS.- 6 Supervised DR.- 6.1 Types of supervision.- 6.1.1 Full supervision.- 6.1.2 Weak supervision.- 6.1.3 Semi-supervision.- 6.2 Parametric with class purity.- 6.2.1 Linear Discriminant Analysis.- 6.2.2 Neighbourhood Component Analysis.- 6.3 Metric learning.- 6.3.1 Mahalanobis distances.- 6.3.2 Riemannian metric.- 6.3.3 Direct distances transformation.- 6.3.4 Similarities learning.- 6.3.5 Metric learning limitations.- 6.4 Class adaptive scale.- 6.5 Classimap.- 6.6 CGNE.- 6.6.1 ClassNeRV stress.- 6.6.2 Flexibility of the supervision.- 6.6.3 Ablation study.- 6.6.4 Isolet 5 case study.- 6.6.5 Robustness to class misinformation.- 6.6.6 Extension to the type 2 mixture: ClassJSE.- 6.6.7 Extension to semi-supervision and weak-supervision.- 6.6.8 Extension to soft labels.- 7 Mapping construction.- 7.1 Optimization.- 7.1.1 Global and local optima.- 7.1.2 Descent algorithms.- 7.1.3 Initialization.- 7.1.4 Multi-scale optimization.- 7.1.5 Force-directed placement interpretation.- 7.2 Acceleration strategies.- 7.2
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