Skip to content
Henry Adams edited this page Jul 26, 2018 · 7 revisions

Introduction

This tutorial accompanies the TRIPODS Summer Bootcamp: Topology and Machine Learning, https://icerm.brown.edu/tripods/tri18-2-tml/

If you code up a cool related example, please let us know and we may add it to this repository!

Python

The code in this repository is written in python.

Installing and running new code is annoying, especially if it is in a language (perhaps python) that is unfamiliar to you. Nevertheless, we believe that it is extremely important for all practitioners of machine learning to have some exposure to python. For this reason, the time you spend getting python running on your machine is time well spent, even though this can feel like a frustrating investment of time.

Persistent homology

We will be using Ripser in this tutorial. The code for Ripser is available at https://github.com/Ripser/ripser, and you can also run a live demo in a browser at http://live.ripser.org/.

Machine learning

Open a terminal on your machine, and change directories to the `machine-learning' folder.

In the terminal, try typing the following command.

python classifier_compare.py

Topological feature vectors

Bibliography

M. A. Armstrong. Basic Topology. Springer, New York, Berlin, 1983.

G. Carlson, T. Ishkhanov, V. de Silva, and A. Zomorodian. On the local behavior of spaces of natural images. Int. J. Computer Vision, 76:1-12, 2008.

F. Chazal, V. de Silva, and S. Oudot. Persistence stability for geometric complexes. Geometriae Dedicata, pages 1-22, 2013.

H. Edelsbrunner and J. Harer. Computational Topology: An Introduction. American Mathematical Society, Providence, 2010.

H. Edelsbrunner, D. Letscher, and A. Zomorodian. Topological persistence and simplification. Discrete Comput. Geom., 28:511-533, 2002.

A. Hatcher. Algebraic Topology. Cambridge University Press, Cambridge, 2002.

S. Martin and J. P. Watson. Non-manifold surface reconstruction from high-dimensional point cloud data. Computational Geometry, 44:427-441, 2011.

S. Martin, A. Thompson, E. A. Coutsias, and J. P. Watson. Topology of cyclo-octane energy landscape. Journal of Chemical Physics, 132: 234115, 2010.

A. Zomorodian. Advances in Applied and Computational Topology. American Mathematical Society, 2012.

A. Zomorodian and G. Carlsson. Computing persistent homology. Discrete Comput. Geom., 33:249-274, 2005.

Clone this wiki locally