plato, 427-347 bc

Geometrical Data Analysis

Plato, 427-347 BCPlato, 427-347 BC

Geometrical Data Analysis N. LaskarisN. Laskaris

Algorithms for Algorithms for Geometrical Data AnalysisGeometrical Data Analysis

Geometrical Data Analysis

What isn’t What isn’t Geometrical Data Analysis Geometrical Data Analysis

??

Statistical Data Analysis

Hypothesis Driven methodologies

A-priori (Top-Down) Data Modeling

Parametric (model fitting) approaches

Geometrical Data Analysis

A little Motivation A little Motivation

Geometrical Data Analysis

Information-Geometry

vs. Informative - Geometry

Geometrical Data Analysis

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

Science, vol. 237, Sept.1987 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

Science, vol. 237, Sept.1987 Science, vol. 237, Sept.1987

Geometrical Data Analysis

Michael KirbyMichael 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

(1890-1962)

Sir Ronald Aylmer Fisher

‘‘Let the Data Speak for itself ’’

Geometrical Data Analysis

Feature

Extraction

Distance measure

Structure description

Embedding in Feature-Space

Geometrical Data Analysis

Partitional ClusteringPartitional Clustering

Outlier

Geometrical Data Analysis

Hierarchical ClusteringHierarchical Clustering

Geometrical Data Analysis

Graph-theoretic Graph-theoretic ClusteringClustering

Geometrical Data Analysis

Feature-selectionFeature-selection

Geometrical Data Analysis

Feature-normalizationFeature-normalization

Geometrical Data Analysis

It’s an Ever Expanding field It’s an Ever Expanding field

# 33 issue

Geometrical Data Analysis

Geometrical Data Analysis

Clustering Ensembles Clustering Ensembles

Geometrical Data Analysis

Clustering Dynamics Clustering Dynamics

1. Raw-data. 2. Feature-space. 3. Models

Geometrical Data Analysis

Kernel-based ClusteringRandomization