Geometrical Data Analysis Plato, 427-347 BC Geometrical Data Analysis

Algorithms for Geometrical Data Analysis N. Laskaris Geometrical Data Analysis

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

Geometrical Data Analysis A little Motivation Geometrical Data Analysis

Information-Geometry vs. Informative - Geometry Geometrical Data Analysis

He is considered the father of spatial relations 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

Geometrical Data Analysis 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

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

Geometrical Data Analysis Michael Kirby Professor 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

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

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

Partitional Clustering Outlier Geometrical Data Analysis

Hierarchical Clustering Geometrical Data Analysis

Graph-theoretic Clustering Geometrical Data Analysis

Geometrical Data Analysis Feature-selection Geometrical Data Analysis

Feature-normalization Geometrical Data Analysis

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

Geometrical Data Analysis

Geometrical Data Analysis Clustering Ensembles Geometrical Data Analysis

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

Geometrical Data Analysis Randomization Kernel-based Clustering Geometrical Data Analysis