INF556 -- Topological Data Analysis (2023-24)

Steve Oudot


general introduction - practical aspects - documents - schedule

General Introduction

Topological Data Analysis (TDA) is an emerging trend in exploratory data analysis and data mining. It has known a growing interest and some notable successes (such as the identification of a new type of breast cancer, or the classification of NBA players) in the recent years. Indeed, with the explosion in the amount and variety of available data, identifying, extracting and exploiting their underlying structure has become a problem of fundamental importance. Many such data come in the form of point clouds, sitting in potentially high-dimensional spaces, yet concentrated around low-dimensional geometric structures that need to be uncovered. The non-trivial topology of these structures is challenging for classical exploration techniques such as dimensionality reduction. The goal is therefore to develop novel methods that can reliably capture geometric or topological information (connectivity, loops, holes, curvature, etc) from the data without the need for an explicit mapping to lower-dimensional space. The objective of this course is to familiarize the students with these new methods, lying at the interface between pure mathematics, applied mathematics, and computer science.

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Last update: Sept. 21 2023.