Topological Methods in Machine Learning: A Tutorial for Practitioners

Authors: Baris Coskunuzer (University of Texas at Dallas, USA) , Cuneyt Gurcan Akcora (University of Central Florida, USA)

This repository contains the code and resources for the tutorial "Topological Methods in Machine Learning: A Tutorial for Practitioners" This tutorial provides an introduction to topological data analysis (TDA) techniques, focusing on Persistent Homology and the Mapper algorithm, with practical applications in machine learning.

Table of Contents

• Persistent Homology
• Mapper Algorithm
• Applications
• References

Introduction

As datasets become increasingly complex, traditional machine learning methods may not capture critical topological structures inherent in the data. Topological Machine Learning (TML) leverages concepts from algebraic topology to analyze complex data structures at multiple scales.

In this tutorial, we cover two main tools of TML:

• Persistent Homology: This technique detects and quantifies clusters, loops, and voids across different scales of data.
• Mapper Algorithm: This algorithm constructs an interpretable graph to summarize high-dimensional data.

Key Features

• A hands-on introduction to Persistent Homology and Mapper.
• Step-by-step examples for applying these techniques to real-world data.
• Practical implementations using Python libraries.

Entry Points

If you do not have any experience with Python, first install an IDE such as PyCharm. If you have a university email, you can download and use the professional version of PyCharm. Next, clone this GitHub repo using PyCharm. Python is used within a project workspace (as was common in the CS in the old days) or in a notebook. We follow the notebook approach because it allows us to see the outputs quickly.

There are a few popular notebooks, such as Jupyter and Google Colab. PyCharm should ask to install the Jupyter notebook plugin within itself once the *.ipynb files are encountered. You can follow the on-screen tips from PyCharm to install the notebook. Once installed: There are two main entry points in this repository:

• The Persistent Homology tutorial can be found in the notebook persistentHomology.ipynb.

• The Mapper Algorithm tutorial can be found in the notebook mapper.ipynb.

Setup

Whenever the code uses a Python library, we have provided the command to install the necessary libraries. For example,

!pip install numpy matplotlib gudhi persim

will install all these libraries. If you know Python well, you can create virtual environments, but we assumed the worst case and used simple pip commands.

Applications

We provide case studies from several domains that demonstrate how Topological Data Analysis techniques can be applied to practical problems, such as:

• Shape Recognition: Using Persistent Homology to detect shapes in point clouds.
• Cancer Diagnosis: Employing topological techniques to improve cancer diagnosis from histopathological images.
• Drug Discovery: Applying Multiparameter Persistence to drug discovery tasks.

Slides

We do not yet have the slides for the tutorial, but we used this slide deck for a previous tutorial on Topology and Graphs.

References

For further reading, please refer to:

@misc{coskunuzer2024tml,
  author = {Baris Coskunuzer and C{\"u}neyt G{\"u}rcan Ak{\c{c}}ora},
  title = {Topological Methods in Machine Learning: A Tutorial for Practitioners},
  year = {2024},
  eprint = {5833867},
  archivePrefix = {arXiv},
  primaryClass = {cs.LG},
  url = {https://github.com/cakcora/TopologyForML},
  comment = {54 pages, 35 figures},
  license = {http://creativecommons.org/licenses/by/4.0/}
}