README.md

Awesome TDA

A curated list of Topological Data Analysis (TDA) tools and resources.

If you know of any other tools or resources, read Contribution Guidelines and feel free to fork/PR or open a new issue.

Contents

• Theory
  • Algorithms
  • Books
  • Articles
  • Courses
• Tools
• Frameworks and Libs
  • C++
  • Go
  • Haskell
  • Java
  • Julia
  • Matlab
  • Python
  • R
  • Spark
• Useful Links
  • Bioinformatics
  • Brain Network Analysis
  • Computing Homology
  • Computer Vision
  • Data Professionals
  • Deep Learning
  • Machine Learning
  • Persistent Homology
  • Use Python
  • Use R
  • Theory and applications of TDA
• Event

Theory

Algorithms

• Chunk
• Mapper (brief summary)
• PHrow
• Twist
• Vineyards
• Zigzag persistent homology
• Zigzag Persistent Cohomology

Books

• A Short Course in Computational Geometry and Topology - Edelsbrunner, Herbert.

• Computational Homology (Applied Mathematical Sciences) - Kaczynski, Mischaikow, Mrozek.

• 📖 Computational Topology: An Introduction - Herbert Edelsbrunner, John L Harer.

• 📖 Computational Topology for Data Analysis - Tamal Krishna Dey, Yusu Wang.

• 📖 Elementary Applied Topology - Robert Ghrist.

• Fundamentals of Brain Network Analysis - Fundamentals of Brain Network Analysis.

• Geometric and Topological Inference - Boissonnat, Chazal, Yvinec.

• 📖 Persistence Theory: From Quiver Representations to Data Analysis - Steve Y Oudot.

• Topological and Statistical Methods for Complex Data: Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces - Bennett, Janine, Vivodtzev, Fabien, Pascucci, Valerio.

• Topological Based Machine Learning Methods - Alex Georges.

• Topological Data Analysis for Genomics and Evolution: Topology in Biology - Raul Rabadan, Andrew J Blumberg.

• Topological Data Analysis for Scientific Visualization - Tierny, Julien.

• 📖 Topological Methods for 3D Point Cloud Processing - William Joseph Beksi.

• 📖 Topology for Computing - AFRA J ZOMORODIAN.

• Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications

• Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications II

• Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications III

• Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications IV

• Topology-based Methods in Visualization - Hauser, Helwig, Hagen, Hans, Theisel, Holger (Eds.)

Articles

• A Fuzzy Clustering Algorithm for the Mode Seeking Framework - Bonis, Oudot.

• A topological data analysis based classification method for multiple measurements - Riihimäki, Chachólski, Theorell, Hillert, Ramanujam.

• A User's Guide to Topological Data Analysis - Elizabeth Munch.

• An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists - Chazal, Michel.

• Barcodes: The Persistent Topology of Data - Robert Ghrist.

• Computing Persistent Homology (Discrete and Computational Geometry) - Zomorodian, Carlsson.

• Deep Learning with Topological Signatures - Hofer, Kwitt, Niethammer, Uhl.

• Designing machine learning workflows with an application to topological data analysis - Cawi, La Rosa, Nehorai.

• Introduction to the R package TDA - Fasy, Jisu Kim, Lecci, Clément Maria, Millman, Rouvreau.

• Homological Algebra and Data - Robert Ghrist.

• Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport - Lacombe, Cuturi, OUDOT.

• Sampling real algebraic varieties for topological data analysis - Dufresne, Edwards, Harrington, Hauenstein.

• Stratifying Multiparmeter Persistent Homology - Harriington, Otter, Schenck, Tillmann.

• Text Mining using Topological Data Analysis. An introduction - Carrazana, Chong.

• Topology and Data - Gunnar Carlsson.

• Topological Data Analysis - Larry Wasserman.

• Topological Data Analysis and Its Application to Time-Series Data Analysis - Umeda, Kaneko, Kikuchi.

• Topological Data Analysis and Machine Learning Theory - Carlsson , Jardine, Feichtner-Kozlov, Morozov.

• Topological Data Analysis for Object Data - Patrangenaru, Bubenik, Paige, Osborne .

• Two-Tier Mapper: a user-independent clustering method for global gene expression analysis based on topology - Jeitziner, Carrière, Rougemont, Oudot, Hess, Brisken.

• Why Topology for Machine Learning and Knowledge Extraction? - Massimo Ferri.

Courses

• Applied Algebraic Topology Seminars

• Computational Topology and Data Analysis - Course is not active, but the course notes are useful.

• Topological Data Analysis - Course is not active, but the course notes are useful.

• Topics in topology: Scientific and engineering applications of algebraic topology - 2013 lecture series.

Tools

• Ctl - (C++11 library) A set of generic tools for Building Neighborhood Graphs and Cellular Complexes, Computing (persistent) homology over finite fields, Parallel algorithms for homology. an be used with c++, Python, MATLAB and R.

• Knotter - Implementation of Mapper algorithm for TDA.

• RIVET - For the visualization and analysis of two-parameter persistent homology with Python API.

• TdaToolbox - Some tools that may be applied to data science in general.

• TTk - Topological data analysis in scientific visualization. Can be used with C++, python.

Frameworks and Libs

C++

• Dionysus - Computing persistent (co)homology, Implementation of the Persistent (co)homology computation, Vineyards, Zigzag persistent homology algorithms.

• PHAT - Persistent Homology Algorithm Toolbox.

• Topology ToolKit (TTK) - Efficient, generic and easy and Topological data analysis and visualization

Go

• TDA - Some methods are provided for gridded data (images).

Haskell

• Persistence

Java

• JavaPlex - The JavaPlex library implements persistent homology and related techniques. It designed for ease of use from Matlab and java-based systems.

Julia

• Eirene.jl - For homological persistence.
• TDA.jl - This package provides Persistence Diagram & Barcode, Nerve, Mapper tools for topological data analysis.

Matlab

• Clique Top - Doing topological analysis of symmetric matrices.

Python

• GDA Public - Several fundamental tools by Geometric Data Analytics Inc. geomdata

• Giotto TDA(GTDA) - A high-performance topological machine learning toolbox

• GUDHI - Geometry Understanding in Higher Dimensional with a Python interface.

• KeplerMapper - TDA Mapper algorithm for visualization of high-dimensional data. it can make use of Scikit-Learn API compatible cluster and scaling algorithms.

• Kohonen - Kohonen-style vector quantizers: Self-Organizing Map (SOM), Neural Gas, and Growing Neural Gas.

• Mapper Implementation - Topological Data Analysis for high dimensional dataset exploration.

• MoguTDA - Numerical calculation of algebraic topology in an application to topological data analysis: implicial complex, and the estimation of homology and Betti numbers.

• OpenTDA

• Persim - package for many tools used in analyzing Persistence Diagrams

• Python Mapper - Mapper algorithm implementation + graphical user interface.

• Qsv - Data structure visualizer.

• Ripser - lean persistent homology package.

• Scikit-TDA - For non-topologists.

• Giotto-TDA - A scikit-learn - compatible library for end-to-end topological machine learning including Mapper, persistent homology, vectorization methods for persistence diagrams, and preprocessing components for time series, graphs, images, and point clouds (paper).

• ScTDA - It includes tools for the preprocessing, analysis, and exploration of single-cell RNA-seq data based on topological representations.

• Topology ToolKit (TTK) - Efficient, generic and easy and Topological data analysis and visualization

• TMAP - Population-scale microbiome data analysis.

R

• TDA - Tools for the statistical analysis of persistent homology and for density clustering.

• TDAmapper - An R package for using discrete Morse theory to analyze a data set using the Mapper algorithm described in G. Singh, F. Memoli, G. Carlsson (2007).

• TDAstats - Computing persistent homology.

Spark

• Spark Mapper - Estimating a lower dimensional simplicial complex from a dataset.

• Spark TDA - Scalable topological data analysis package.

Useful Links

Bioinformatics

• List of Resources for Topological Data Analysis in Bioinformatics

Brain Network Analysis

• An algebraic topological method for multimodal brain networks comparisons

• Complex Brain Network Analysis and Its Applications to Brain Disorders: A Survey

• Functional Brain Network Topology Discriminates between Patients with Minimally Conscious State and Unresponsive Wakefulness Syndrome

• Graph theory methods: applications in brain networks

• Topological Methods in Brain Network Analysis

Computing Homology

• Computing Homology

Computer Vision

• Topological Data Analysis in Computer Vision

Data Professionals

• Topological Data Analysis for Data Professionals

Deep Learning

• Applied Topological Data Analysis to Deep Learning? Hands-on Arrhythmia Classification!

• From Topological Data Analysis to Deep Learning: No Pain No Gain

• On Characterizing the Capacity of Neural Networks Using Algebraic Topology

• Using Topological Data Analysis to Understand the Behavior of Convolutional Neural Networks

Machine Learning

• How TDA and Machine Learning Enhance Each Other

• Machine Learning Explanations with Topological Data Analysis

• Topological Methods for Machine Learning

• Topological Machine Learning

Persistent Homology

• A roadmap for the computation of persistent homology

• Practical Guide to Persistent Homology

Use Python

• Python Tutorial on Topological Data Analysis

• Topological Data Analysis - A Python tutorial

Use R

• A Mathematician's Perspective on Topological Data Analysis and R

Theory and applications of TDA

• A concrete application of Topological Data Analysis

• A Guide to Data Science from mathematics

• An Algebraic Geometry Perspective on Topological Data Analysis

• Topological Data Analysis - A Very Short Introduction

• Topological Data Analysis - UFL.

• Topological Data Analysis - IBM.

• Theory and applications of topological data analysis

Event

• Conferences and workshops

• International Conference on Computational Topology and Topological Data Analysis

2024

• Jan. 30 - Feb. 2 | The 4th POSTECH MINDS Workshop on Topological Data Analysis and Machine Learning | Korea

• Feb. 7 - Apr. 1 | self-study group for textbook: "Computational Topology for Data Analysis" | zoom

• Mar. 21 - Mar. 22 | Workshop on Topological Data Analysis | India

2025

• Jan. 8 | AMS Special Session on Topological Data Analysis: Theory and Applications

• Jun. 30 - Jul. 4 | EWM-EMS Summer School: Stability in Topological Data Analysis | Sweden