Geometric Data Analysis: From Correspondence Analysis to Structured Data Analysis

Abstract

- Foreword Patrick Suppes. 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. Principle Directions. 3.4. Principle 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 Interation Clouds. 6.4. Related Topics. - 7: Stability of a Euclidean Cloud. 7.1. Stability and Grouping. 7.2. Influence of aGroup of Points. 7.3. Change of Metric. 7.4. Influence of a Variable. 7.5. Basic Theorems. - 8: Inductive Data Analysis. 8.1. Influence 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. - Index. Name Index. Symbol Index. Subject Index.