Geometric data analysis from correspondence analysis to structured data analysis

Geometric Data Analysis (GDA) is the name suggested by P. Suppes (Stanford University) to designate the approach to Multivariate Statistics initiated by Benzécri as Correspondence Analysis, an approach that has become more and more used and appreciated over the years. This book presents the full formalization of GDA in terms of linear algebra - the most original and far-reaching consequential feature of the approach - and shows also how to integrate the standard statistical tools such as Analysis of Variance, including Bayesian methods. Chapter 9, Research Case Studies, is nearly a book in itself, it presents the methodology in action on three extensive applications, one for medicine, one from political science, and one from education (data borrowed from the Stanford computer-based Educational Program for Gifted Youth ). Thus the readership of the book concerns both mathematicians interested in the applications of mathematics, and researchers willing to master an exceptionally powerful approach of statistical data analysis.

- 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 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. 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.