Thinking Ultrametrically: Understanding Massive Data Sets and Navigating Information Spaces

Inaugural Lecture: Professor Fionn Murtagh
Thursday 22nd February 2007 (Main Lecture Theatre, 5.30pm)

Abstract:
Hierarchy is one of the central structural schemes that the architect of complexity uses" (H.A. Simon). An ultrametric or tree distance is used in hierarchical clustering. P-adic algebra, expressing ultrametric topology, is used in the physics of the early Universe, and in quantum statistics. In semantic analysis, spherically complete ultrametric spaces play an important role in the proof of computability of recursive systems.

Recent applications to data analysis have included: (i) computational implications of pervasive ultrametricity resulting from sparse and possibly high-dimensional spaces; (ii) textual analysis based on inherent, local hierarchical structure; (iii) time series analysis, again based on inherent, local hierarchical structure; (iv) new algorithms for search and matching in high dimensional massive data sets.

We will review recent progress in this interface area and show how it leads to new insights on information and computation.

Streamed video of the presentation, and of the lecture, and text of the vote of thanks.