Algebraic Foundations of Topological Data Analysis [2 ECTS, MAT/02]

Supervisor
Magnus Botnan - Vrije Universiteit Amsterdam
Date and time
Wednesday, May 26, 2021 - online, live lectures
Programme Director
Lidia Angeleri
External reference
Publication date
April 29, 2021
Department
Computer Science  

Summary

The course (12 hours) will be held by Magnus Botnan and will consist of online lectures and exercise classes.

​Schedule: always 10-12 a.m. on the following days
Wednesday 26/5/2021  
Thursday 27/5/2021
Friday 28/5/2021
Tuesday 1/6/2021
Thursday 3/6 /2021
Friday  4/6/2021

Abstract:
Topological Data Analysis (TDA) is a recent approach to data analysis
in which tools from (algebraic) topology are applied to gain a
qualitative understanding of data - or in other words - to infer
properties of the shape of the data. The ‘’simplest’’ of the
topological invariants considered is the number of connected
components of a data set. Translated into the language of traditional
data analysis this would correspond to the task of clustering the
data, i.e. the process of grouping data points together such that
points in the same cluster are comparatively closer to each other than
pairs formed from different clusters. We will see how tools from
(algebraic) topology can be used to detect other types of non-linear
structure in data. The second half of the course will focus on
multiparameter persistent homology and its connection to quiver
representations.

Most of the material can be found in my lecture notes:
https://www.few.vu.nl/~botnan/lecture_notes.pdf

Background:
The student should be familiar with basic notions from linear algebra and topology.
Some familiarity with Python will be helpful for running your own computations but it is not necessary. 





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