Topological Data Analysis for Machine Learning

The goal of this tutorial is to give an introduction to the nascent field of topological machine learning, with the express purpose of being accessible to all audiences. The tutorial will discuss state-of-the art algorithms and provide the audience with the necessary competences to apply such techniques to their own research problems.

Requirements

This tutorial targets machine leaning researchers of any background. It is helpful if you already have some some knowledge about concepts from undergraduate mathematics, such as vector spaces and groups. If not, do not worry—I will provide intuitive descriptions for all of them during the tutorial.

To make the most of this session, I would recommend the following things:

  • Some way of taking notes; the slides will be available (see below), so you could also annotate them along the way.
  • A laptop with either Linux or Mac OS X will be helpful in order to try out some of the packages for computing persistent homology. This is not a necessity, though.

Course materials

  • Lecture 1: Algebraic Topology
    In which we discuss an introduction to computational topology, the utility of Betti numbers, simplicial homology (with examples) and simplicial complexes, as well as how to compute all of this manually.

  • Lecture 2: Computational Topology
    In which we discuss a multi-scale variant of simplicial homology, viz. persistent homology, provide copious examples, and show that everything—once again—boils down to neat linear algebra calculations.

  • Lecture 3: Topological Descriptors & How to Use Them
    In which we take a look at the landscape of existing topological descriptors, present their respective properties, and provide some guidance about their usage.

  • Lecture 4: Recent Advances in Topological Machine Learning
    In which we discuss recent research in topology-driven graph classification, as well as how to successfully integrate topological features into modern neural network architectures.

Schedule
Date Monday, 14 September 2020
Time 14:00–18:00
Lecture 1 14:00–14:45
Lecture 2 14:45–15:30
Q & A 15:30–16:00
Lecture 3 16:00–16:45
Lecture 4 16:45–17:30
Q & A 17:00–18:00

Please consult your official Whova schedule for details about the Zoom links that are required to join the tutorial. Feel free to drop in or out at any point!

  • DIPHA, a distributed persistent homology algorithm. This is our fork of the original project, with a slightly simplified installation. dipha supports different scenarios, such as the calculation of persistent homology of structured data sets.

  • math3ma, the website of Tai-Danae Bradley. Her articles provide exceptionally well-written explanations of many of the concepts discussed in this course. While her main focus is the wonderful field of category theory, numerous other concepts from linear algebra are also discussed.

  • Ripser, arguably the fastest software currently available for calculating a Vietoris–Rips filtration.