Tutorial on Topological Data Analysis

Written by Shizuo KAJI

This Jupyter-note book is prepared for the online event: TDA for Applications: Tutorial and Workshop being held on 18,19 June 2020.

Main Examples

Our main example runs on Google Colaboratory so that you do not have to set up a Python environment on your computer.

Open in Google Colaboratory.

This includes

• Feature extraction using persistent homology from various types of data (point cloud, graph, image, volume, time-series)
• Regression/Classification using topological features
• Dimension reduction preserving topological features
• Visualisation revealing the shape of data

Deep Learning X TDA

How Deep Learning and Persistent homology can be combined is demonstrated here.

NLP Example (vectorise and visualise)

As an example of Natural Language Processing, we look at maths papers on arXiv. This example runs only locally and not on Google Colab.

Here is an instruction

Reference

• Persistent homology - An introduction via interactive examples provides quick access to the theory of persistent homology.