A curated list of Topological Data Analysis (TDA) tools and resources.
If you know of any other tools or resources, read the Contribution Guidelines and feel free to fork/PR or open a new issue.
- Chunk
- Mapper (brief summary)
- PHrow
- Twist
- Vineyards
- Zigzag persistent homology
- Zigzag Persistent Cohomology
- A Short Course in Computational Geometry and Topology - Herbert Edelsbrunner.
- Computational Homology - Tomasz Kaczynski, Konstantin Mischaikow, Marian 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 - Alex Fornito, Andrew Zalesky, Edward T. Bullmore.
- Geometric and Topological Inference - Jean-Daniel Boissonnat, Frédéric Chazal, Mariette Yvinec.
- 📖 Persistence Theory: From Quiver Representations to Data Analysis - Steve Y. Oudot.
- Topological and Statistical Methods for Complex Data - Janine Bennett, Fabien Vivodtzev, Valerio Pascucci.
- Topological Based Machine Learning Methods - Alex Georges.
- Topological Data Analysis for Genomics and Evolution - Raul Rabadan, Andrew J. Blumberg.
- Topological Data Analysis for Scientific Visualization - Julien Tierny.
- 📖 Topological Deep Learning - Michael T. Schaub, Yu Zhu, Jean-Baptiste Seby, T. Mitchell Roddenberry, Santiago Segarra.
- 📖 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 - Helwig Hauser, Hans Hagen, Holger Theisel.
- 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 - 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.
- Geometry Helps to Compare Persistence Diagrams - Kerber, Morozov, Nigmetov.
- Introduction to the R package TDA - Fasy, Kim, Lecci, 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 Multiparameter Persistent Homology - Harrington, 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.
- 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.
- Applied Algebraic Topology Research Network - Events, seminars, workshops, and community resources for applied topology.
- AATRN YouTube Channel - Recorded talks and seminars on applied algebraic topology and TDA.
- GUDHI Tutorials - Official tutorials for the GUDHI library.
- Scikit-TDA Tutorial - Introductory tutorial for the Scikit-TDA ecosystem.
- Topological Data Analysis - A Python Tutorial - Introductory Python tutorial.
- Hera - Software for bottleneck and Wasserstein distances between persistence diagrams.
- HomCloud - Persistent homology software with a Python interface, used especially for scientific and materials-data analysis.
- RIVET - Visualization and analysis of two-parameter persistent homology with a Python API.
- TdaToolbox - Tools that may be applied to data science in general.
- Ctl - C++11 library for building neighborhood graphs and cellular complexes, computing persistent homology over finite fields, and running parallel algorithms for homology. Can be used with C++, Python, MATLAB, and R.
- Cubical Ripser - Software for computing persistent homology of cubical complexes, especially useful for image and volume data.
- Dionysus - Computing persistent (co)homology, including persistent cohomology, vineyards, and zigzag persistent homology algorithms.
- DIPHA - Distributed persistent homology computation with MPI support.
- Flagser - Computes homology of directed flag complexes.
- PHAT - Persistent Homology Algorithm Toolbox.
- Topology ToolKit (TTK) - Efficient and generic topological data analysis and visualization.
- TDA - Some methods are provided for gridded data, such as images.
- JavaPlex - The JavaPlex library implements persistent homology and related techniques. It is designed for ease of use from MATLAB and Java-based systems.
- Eirene.jl - For homological persistence.
- JuliaTDA - Organization collecting Julia packages for topological data analysis.
- PersistenceDiagrams.jl - Types and utilities for working with persistence diagrams in Julia.
- Ripserer.jl - Flexible and efficient pure-Julia implementation of the Ripser algorithm for computing persistent homology.
- TDA.jl - Provides persistence diagrams and barcodes, nerve, and Mapper tools for topological data analysis.
- TDAmapper.jl - Mapper algorithm tools for Julia.
- ToMATo.jl - ToMATo clustering in Julia.
- Clique Top - Topological analysis of symmetric matrices.
- GDA Public - Several fundamental tools by Geometric Data Analytics Inc. geomdata.
- giotto-ph - High-performance persistent homology backend for Vietoris-Rips filtrations.
- 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). - GUDHI - Geometry Understanding in Higher Dimensions, with a Python interface.
- KeplerMapper - TDA Mapper algorithm for visualization of high-dimensional data. It can use Scikit-Learn API-compatible clustering and scaling algorithms.
- Knotter - Implementation of the Mapper algorithm for TDA.
- Mapper Implementation - Topological data analysis for high-dimensional dataset exploration.
- MoguTDA - Numerical calculation of algebraic topology for TDA, including simplicial complexes and estimates of homology and Betti numbers.
- OpenTDA
- Persim - Tools for analyzing persistence diagrams.
- pyflagser - Python API for Flagser, computing homology of directed flag complexes.
- Python Mapper - Mapper algorithm implementation with a graphical user interface.
- Qsv - Data structure visualizer.
- quaternion-monoid-algebra - Compositional monoid algebra over quaternion state packets, with machine-checked proofs that composing a configuration with a common element preserves persistence diagrams exactly; validated on TUM RGB-D and EuRoC MAV pose streams.
- Ripser.py - Lean persistent homology package.
- Scikit-TDA - Python ecosystem for topological data analysis.
- ScTDA - Tools for preprocessing, analysis, and exploration of single-cell RNA-seq data based on topological representations.
- TMAP - Population-scale microbiome data analysis.
- TopoDrift - Open benchmark for topological drift detection: evaluates persistent homology against KS/MMD/PSI on 7 regime types invisible to classical statistics.
- torch_topological - Topological machine learning tools for PyTorch.
- torch-tda - Automatic differentiation utilities for topological data analysis.
- torchph - PyTorch extensions for persistent homology and differentiable persistent homology computations.
- TopologyLayer - PyTorch-compatible persistent homology layers and featurization tools.
- ggtda -
ggplot2layers for visualizing constructions and statistics from topological data analysis. - phutil - Utilities and common data structures for persistence data analysis in R.
- ripserr - R interface to Ripser and Cubical Ripser for persistent homology of point-cloud, image, and volume data.
- TDA - Tools for statistical analysis of persistent homology and density clustering.
- TDAmapper - R package for using discrete Morse theory to analyze a dataset with the Mapper algorithm described in Singh, Mémoli, and Carlsson (2007).
- TDAstats - Computing persistent homology.
- TDAvec - Vector summaries of persistence diagrams for use in statistical and machine-learning workflows.
- tdaverse - Collection of R packages for topological data analysis.
- Spark Mapper - Estimating a lower-dimensional simplicial complex from a dataset.
- Spark TDA - Scalable topological data analysis package.
- 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
- From Topological Data Analysis to Deep Learning: No Pain No Gain
- On Characterizing the Capacity of Neural Networks Using Algebraic Topology
- A Topology Layer for Machine Learning
- Using Topological Data Analysis to Understand the Behavior of Convolutional Neural Networks
- Topological Machine Learning for Graphs - Research resources on topological approaches to machine learning and graphs.
- How TDA and Machine Learning Enhance Each Other
- Machine Learning Explanations with Topological Data Analysis
- Topological Methods for Machine Learning
- Topological Machine Learning
- A concrete application of Topological Data Analysis
- A Guide to Data Science from mathematics
- An Algebraic Geometry Perspective on Topological Data Analysis
- AwesomeTDA4NLP - Resources for topological data analysis in NLP.
- Topological Data Analysis - A Very Short Introduction
- Topological Data Analysis - UFL.
- Topological Data Analysis - IBM.
- Theory and applications of topological data analysis
- Applied Algebraic Topology Research Network Calendar - Community announcements for applied topology, TDA, workshops, schools, and related opportunities.
- Conferences and workshops - Curated list of TDA, applied topology, and computational topology events.
- CG Week / Symposium on Computational Geometry - Annual computational geometry conference series; includes computational topology, topological data analysis, and related workshops.
- Jan. 19 - Jan. 22 | Topological Data Analysis and Industrial Mathematics | Kyushu University, Japan
- Jan. 24 - Jan. 29 | Bridging Topology and Machine Learning for Data Science | BIRS, Banff, Canada
- Jun. | CG Week / SoCG 2027 | Bangalore, India
- Aug. 22 - Aug. 27 | Interactions of Topological Data Analysis and Combinatorial Topological Dynamics | BIRS, Banff, Canada
- Jan. 4 - Jan. 7 | TDA @ JMM 2026 | Washington, DC, USA
- Feb. 2 - Feb. 6 | Topological Statistics, Data and Intelligence | Beijing, China
- Feb. 12 - Feb. 13 | Topological Data Analysis and Representation Theory 2026 | Tohoku University, Japan / Hybrid
- Feb. 20 - Feb. 28 | OneMath World School: Topological Data Analysis and Applications | Chennai Mathematical Institute, India
- Mar. 30 - Mar. 31 | H2O: Higher-Order Pattern-Discovery in High-Dimensional Data | Aarhus University, Denmark
- May. 18 - May. 21 | Foundations of Computational Geometry and Topology | ICERM, Providence, RI, USA
- May. 18 - May. 22 | Geometry, Topology and Machine Learning | Paris, France
- Jun. 2 - Jun. 5 | CG Week / SoCG 2026 | Rutgers University, New Brunswick, NJ, USA
- Jun. 4 - Jun. 5 | Theory and Applications of Topological Data Analysis | Rutgers University, New Brunswick, NJ, USA
- Jun. 8 - Jun. 12 | Jardine-Fest: Homotopy Theory, K-theory, and Topological Data Analysis | University of Western Ontario, Canada
- Jul. 9 - Jul. 18 | FoCM 2026 | Vienna, Austria
- Jul. 9 - Jul. 11 | FoCM Workshop: Computational Geometry and Topology | Vienna, Austria
- Sep. 28 - Oct. 2 | Persistent Homology and Applications in Topological Data | University of Bonn, Germany
- Jan. 8 | AMS Special Session on Topological Data Analysis: Theory and Applications
- Jun. 22 - Jun. 28 | Dynamics, Topology and Computations | Poland
- Jun. 30 - Jul. 4 | EWM-EMS Summer School: Stability in Topological Data Analysis | Sweden
- Aug. 25 - Aug. 29 | Workshop on Topological Data Analysis | Canada
- Nov. 2 | IEEE Workshop on Topological Data Analysis and Visualization | Austria
- Nov. 10 - Nov. 14 | Workshop on Geometry, Topology, and Machine Learning (GTML) | Germany
- 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
- Sep. 7 - Dec. 18 | Dual Trimester Program: Geometric Statistics: theory, application, and computation | Germany