Tutorial on Topological Data Analysis

Written by Shizuo Kaji

Overview

This repository provides hands-on tutorials for topological data analysis (TDA), with notebooks that run in Google Colaboratory so no local Python setup is required.

Main Notebooks

Notebook	Description	Colab
TopologicalDataAnalysisWithPython.ipynb	End-to-end TDA workflow with examples across multiple data types and machine learning tasks.	Open in Colab
PersistentHomology_Interactive.ipynb	Interactive examples focused on persistent homology concepts.	Open in Colab

What You Will Learn

The tutorial notebook includes:

• Interactive intuition-building for persistent homology of Vietoris-Rips and cubical complexes
• Feature extraction using persistent homology from point clouds, graphs, images, volumes, and time-series data
• Representative cycles that locate the loops behind persistence intervals in images
• Zigzag persistence for tracking components and holes through time-varying images
• Regression and classification using topological features
• Dimension reduction while preserving topological features
• Visualisation to reveal the shape of data

Background

This tutorial was originally prepared for the online event: TDA for Applications: Tutorial and Workshop (18-19 June 2020).

Legacy Demo

The following example is no longer maintained and is not compatible with Google Colaboratory:

• NLP Example: Vectorisation and Visualisation Analyse mathematics papers from arXiv and visualise the data using mapper. Setup instructions: NLP_example.md

Reference

• Persistent Homology - An Introduction via Interactive Examples: A quick and interactive introduction to persistent homology theory.