Topological Data Analysis

Overview

1. Simplicial complexes
2. PL functions
3. Simplicial homology
4. Filtrations and barcodes
5. Matrix reduction
6. The Mapper Algorithm
7. Learning with topological descriptors
8. Statistics with topological descriptors

Learning Objectives

It is intended that students shall, on successful completion of the module, demonstrate knowledge and confidence in applying key ideas and concepts of topological data analysis, such as simplicial complexes, simplicial homology, barcodes, matrix reduction and the analysis of topological descriptors.

In addition, students should be able to use standard software (e.g. the freely available R package TDA) to analyse simple data sets.

Skills

Knowing and applying basic techniques of topological data analysis. In particular, this includes the analysis and interpretation of topological invariants of data sets; the production of graphical representations of such descriptors; and basic computational aspects of linear algebra.

Assessment

None