Geometric Data Analysis

Cover -- Contents -- Foreword -- Preface -- 1 Overview of Geometric Data Analysis -- 1.1 CA of a Historical Data Set -- 1.2 The Three Key Ideas of GDA -- 1.3 Three Paradigms of GDA -- 1.4 Historical Sketch -- 1.5 Methodological Strong Points -- 1.6 From Descriptive to Inductive Analysis -- 1.7 Organization of the Book -- 2 Correspondence Analysis (CA) -- 2.1 Measure vs Variable Duality -- 2.2 Measure over a Cartesian Product -- 2.3 Correspondence Analysis -- 2.4 Extensions and Concluding Comments -- Exercises -- 3 Euclidean Cloud -- 3.1 Basic Statistics -- 3.2 Projected Clouds -- 3.3 Principal Directions -- 3.4 Principal Hyperellipsoids -- 3.5 Between and Within Clouds -- 3.6 Euclidean Classification -- 3.7 Matrix Formulas -- 4 Principal Component Analysis (PCA) -- 4.1 Biweighted PCA -- 4.2 Simple PCA -- 4.3 Standard PCA -- 4.4 General PCA -- 4.5 PCA of a Table of Measures -- 4.6 Methodology of PCA -- 5 Multiple Correspondence Analysis (MCA) -- 5.1 Standard MCA -- 5.2 Specific MCA -- 5.3 Methodology of MCA -- 5.4 The Culture Example -- Exercises -- 6 Structured Data Analysis -- 6.1 Structuring Factors -- 6.2 Analysis of Comparisons -- 6.3 Additive and Interaction Clouds -- 6.4 Related Topics -- 7 Stability of a Euclidean Cloud -- 7.1 Stability and Grouping -- 7.2 Influence of a Group of Points -- 7.3 Change of Metric -- 7.4 Influence of a Variable -- 7.5 Basic Theorems -- 8 Inductive Data Analysis -- 8.1 Inference in Multivariate Statistics -- 8.2 Univariate Effects -- 8.3 Combinatorial Inference -- 8.4 Bayesian Data Analysis -- 8.5 Inductive GDA -- 8.6 Guidelines for Inductive Analysis -- 9 Research Case Studies -- 9.1 Parkinson Study -- 9.2 French Political Space -- 9.3 EPGY Study -- 9.4 About Software -- 10 Mathematical Bases -- 10.1 Matrix Operations -- 10.2 Finite ... dimensional Vector Space -- 10.3 Euclidean Vector Space -- 10.4 Multidimensional Geometry -- 10.5 Spectral Theorem -- Bibliography -- Name Index -- Symbol Index.