On Spatio-Temporal Data Modelling and Uncertainty Quantification Using Machine Learning and Information Theory (Springer Theses)

Supervisor’s Foreword
Acknowledgements
Contents
Abbreviations
1 Introduction
	1.1 Sketch of the Thesis
	1.2 Spatio-Temporal Data Modelling and Analysis
		1.2.1 Statistical Interpolation for Spatio-Temporal Data
		1.2.2 Machine Learning for Spatial Data
		1.2.3 Uncertainty Quantification
		1.2.4 Information Theory as an Advanced Exploratory Tool
	1.3 Objectives
	1.4 Contributions
	1.5 Thesis Organisation
	References
2 Study Area and Data Sets
	2.1 Switzerland and Its Topography
	2.2 MeteoSwiss Wind Speed Data
		2.2.1 Data Wrangling, Cleaning and Missing Values
		2.2.2 Exploratory Data Analysis
	2.3 MoTUS High-Frequency Wind Speed Data
		2.3.1 Data Wrangling, Cleaning and Missing Values
		2.3.2 Exploratory Data Analysis
	2.4 Summary
	References
3 Advanced Exploratory Data Analysis
	3.1 Empirical Orthogonal Functions
		3.1.1 Spatial Formulation
		3.1.2 Temporal Formulation
		3.1.3 Singular Value Decomposition
	3.2 Variography
	3.3 Wavelet Variance Analysis
		3.3.1 Multiresolution Wavelet Analysis
		3.3.2 The Wavelet Variance
		3.3.3 Application to the MoTUS Data
	3.4 Summary
	References
4 Fisher-Shannon Analysis
	4.1 Related Work
	4.2 Fisher-Shannon Analysis
		4.2.1 Shannon Entropy Power and Fisher Information Measure
		4.2.2 Properties
		4.2.3 Fisher-Shannon Complexity
		4.2.4 Fisher-Shannon Information Plane
	4.3 Analytical Solutions for Some Distributions
		4.3.1 Gamma Distribution
		4.3.2 Weibull Distribution
		4.3.3 Log-Normal Distribution
	4.4 Data-Driven Non-parametric Estimation
	4.5 Experiments and Case Studies
		4.5.1 Logistic Map
		4.5.2 Normal Mixtures Densities
		4.5.3 MoTUS Data: Advanced EDA
		4.5.4 MoTUS Data: Complexity Discrimination
		4.5.5 Other Applications
	4.6 Summary
	References
5 Spatio-Temporal Prediction with Machine Learning
	5.1 Motivation
	5.2 Machine-Learning-Based Framework for Spatio-Temporal Interpolation
		5.2.1 Decomposition of Spatio-Temporal Data Using EOFs
		5.2.2 Spatial Modelling of the Coefficients
	5.3 Simulated Data Case Study
	5.4 Experiment on Temperature Monitoring Network
	5.5 Experiment on the MeteoSwiss Data
	5.6 Summary
	References
6 Uncertainty Quantification with Extreme Learning Machine
	6.1 Related Work and Motivation
	6.2 Background and Notations
		6.2.1 Extreme Learning Machine
		6.2.2 Regularised ELM
		6.2.3 ELM Ensemble
	6.3 Analytical Developments
		6.3.1 Bias and Variance for a Single ELM
		6.3.2 Bias and Variance for ELM Ensemble
		6.3.3 Use of Random Variable Quadratic Forms
		6.3.4 Correlation Between Two ELMs
	6.4 Variance Estimation of ELM Ensemble
		6.4.1 Estimation of the Least-Squares Bias Variation
		6.4.2 Estimation Under Independence and Homoskedastic Assumptions
		6.4.3 Estimation Under Independence and Heteroskedastic Assumptions
	6.5 Synthetic Experiments
		6.5.1 One-Dimensional Case
		6.5.2 Multi-dimensional Case
		6.5.3 Towards Confidence Intervals
	6.6 Summary
	References
7 Spatio-Temporal Modelling Using Extreme Learning Machine
	7.1 Spatio-Temporal ELM Model
		7.1.1 ELM Modelling of the Spatial Coefficients
		7.1.2 Model Variance Estimation
		7.1.3 Prediction Variance Estimation
	7.2 Application to the MeteoSwiss Data
		7.2.1 Wind Speed Modelling
		7.2.2 Residual Analysis
	7.3 Aeolian Energy Potential Estimation
		7.3.1 Wind Speed Conversion and Uncertainty Propagation
		7.3.2 Power Estimation for Switzerland
	7.4 Summary
	References
8 Conclusions, Perspectives  and Recommendations
	8.1 Fisher-Shannon Analysis and Complexity Quantification
		8.1.1 Thesis Achievements
		8.1.2 Implications and Future Challenges
	8.2 Spatio-Temporal Interpolation with Machine Learning
		8.2.1 Thesis Achievements
		8.2.2 Implications and Future Challenges
	8.3 Uncertainty Quantification with Extreme Learning Machine
		8.3.1 Thesis Achievements
		8.3.2 Implications and Future Challenges
	8.4 Application on Wind Phenomenon and Wind Energy Potential Estimation
		8.4.1 Thesis Achievements
		8.4.2 Implications and Future Challenges
	References