ABSTRACT. This work is concerned with pattern recognition, knowledge discovery, computer learning and statistics. I address how geometry and topology can uncover and empower the semantics of data. In addition to the semantics of data that can be explored using Correspondence Analysis and related multivariate data analyses, hierarchy is a fundamental concept in this work. I address not only low dimensional projection for display purposes, but carry out search and pattern recognition, whenever useful, in very high dimensional spaces. High dimensional spaces present very different characteristics from low dimensions. It can be shown that in a particular sense very high dimensional space becomes, as dimensionality increases, hierarchical. It is also shown how in hierarchy, and hence in an ultrametric topological mapping of information space, we track change or anomaly or rupture.

Lectures:

• 1) An Introduction to Multivariate Data Analysis with a Focus on Hierarchical Clustering, and Correspondence Analysis - a "tale of three metrics", chi squared, Euclidean and ultrametric.
• 2) Data Analytics of Narrative: Pattern Recognition in Text, and Text Synthesis, Supported by the Correspondence Analysis Platform.
• 3) The Future of Search and Discovery in Big Data Analytics: Ultrametric Information Spaces.
• 4) Hierarchy and Symmetry in Data Analysis -- Thinking Ultrametrically.