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Exploring the Foundations and Techniques of Geometrical Data Analysis

This document provides a comprehensive overview of geometrical data analysis, highlighting key algorithms, methodologies, and applications in the field. The discourse covers both statistical and hypothesis-driven approaches, including parametric model fitting and feature extraction techniques. Contributions from notable figures such as Roger Shepard and Michael Kirby emphasize the intersection of cognitive science and mathematics in understanding spatial relations and dimensionality reduction. The evolution of clustering methods and their importance in modern data analysis is also explored, underscoring this ever-expanding field's relevance.

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Exploring the Foundations and Techniques of Geometrical Data Analysis

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  1. Plato, 427-347 BC Geometrical Data Analysis

  2. Algorithms for Geometrical Data Analysis N. Laskaris Geometrical Data Analysis

  3. What isn’t Geometrical Data Analysis ? Statistical Data Analysis Hypothesis Driven methodologies A-priori (Top-Down) Data Modeling Parametric (model fitting) approaches Geometrical Data Analysis

  4. A little Motivation Geometrical Data Analysis

  5. Information-Geometry vs. Informative - Geometry Geometrical Data Analysis

  6. Roger Shepard (1929 - ) Prof. Emeritus of Social Science, Stanford University A cognitive scientist (Ph.D. in psychology 1955)and author of ‘‘Toward a Universal Law of Generalization for Psychological Science ’’ He is considered the father of spatial relations Geometrical Data Analysis

  7. Science, vol. 237, Sept.1987 Does psychological science have any hope of achieving a law that is comparable in generality (if not in predictive accuracy) to Neuton’s universal law of gravitation ? Geometrical Data Analysis

  8. Science, vol. 237, Sept.1987 Geometrical Data Analysis

  9. Michael KirbyProfessor of Mathematics and Computer Science Graduate Program Director, Colorado State University An Empirical Approach to Dimensionality Reduction and the Study of Patterns Geometrical Data Analysis

  10. (1890-1962) Sir Ronald Aylmer Fisher ‘‘Let the Data Speak for itself ’’ Geometrical Data Analysis

  11. Feature Extraction Distance measure Embedding in Feature-Space Structure description Geometrical Data Analysis

  12. Outlier Partitional Clustering Geometrical Data Analysis

  13. Hierarchical Clustering Geometrical Data Analysis

  14. Graph-theoretic Clustering Geometrical Data Analysis

  15. Feature-selection Geometrical Data Analysis

  16. Feature-normalization Geometrical Data Analysis

  17. It’s an Ever Expanding field # 33 issue Geometrical Data Analysis

  18. Geometrical Data Analysis

  19. Clustering Ensembles Geometrical Data Analysis

  20. Clustering Dynamics 1. Raw-data. 2. Feature-space. 3. Models Geometrical Data Analysis

  21. Randomization Kernel-based Clustering Geometrical Data Analysis

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