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.
- Chunk
- Mapper (brief summary)
- PHrow
- Twist
- Vineyards
- Zigzag persistent homology
- Zigzag Persistent Cohomology
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A Short Course in Computational Geometry and Topology - Edelsbrunner, Herbert.
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Computational Homology (Applied Mathematical Sciences) - Kaczynski, Mischaikow, Mrozek.
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📖 Computational Topology: An Introduction - Herbert Edelsbrunner, John L Harer.
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📖 Computational Topology for Data Analysis - Tamal Krishna Dey, Yusu Wang.
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📖 Elementary Applied Topology - Robert Ghrist.
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Fundamentals of Brain Network Analysis - Fundamentals of Brain Network Analysis.
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Geometric and Topological Inference - Boissonnat, Chazal, Yvinec.
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📖 Persistence Theory: From Quiver Representations to Data Analysis - Steve Y Oudot.
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Topological and Statistical Methods for Complex Data: Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces - Bennett, Janine, Vivodtzev, Fabien, Pascucci, Valerio.
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Topological Based Machine Learning Methods - Alex Georges.
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Topological Data Analysis for Genomics and Evolution: Topology in Biology - Raul Rabadan, Andrew J Blumberg.
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Topological Data Analysis for Scientific Visualization - Tierny, Julien.
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📖 Topological Methods for 3D Point Cloud Processing - William Joseph Beksi.
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📖 Topology for Computing - AFRA J ZOMORODIAN.
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Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications
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Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications II
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Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications III
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Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications IV
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Topology-based Methods in Visualization - Hauser, Helwig, Hagen, Hans, Theisel, Holger (Eds.)
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A Fuzzy Clustering Algorithm for the Mode Seeking Framework - Bonis, Oudot.
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A topological data analysis based classification method for multiple measurements - Riihimäki, Chachólski, Theorell, Hillert, Ramanujam.
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A User's Guide to Topological Data Analysis - Elizabeth Munch.
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An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists - Chazal, Michel.
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Barcodes: The Persistent Topology of Data - Robert Ghrist.
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Computing Persistent Homology (Discrete and Computational Geometry) - Zomorodian, Carlsson.
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Deep Learning with Topological Signatures - Hofer, Kwitt, Niethammer, Uhl.
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Designing machine learning workflows with an application to topological data analysis - Cawi, La Rosa, Nehorai.
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Introduction to the R package TDA - Fasy, Jisu Kim, Lecci, Clément Maria, Millman, Rouvreau.
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Homological Algebra and Data - Robert Ghrist.
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Large Scale computation of Means and Clusters for Persistence Diagrams using Optimal Transport - Lacombe, Cuturi, OUDOT.
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Sampling real algebraic varieties for topological data analysis - Dufresne, Edwards, Harrington, Hauenstein.
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Stratifying Multiparmeter Persistent Homology - Harriington, Otter, Schenck, Tillmann.
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Text Mining using Topological Data Analysis. An introduction - Carrazana, Chong.
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Topology and Data - Gunnar Carlsson.
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Topological Data Analysis - Larry Wasserman.
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Topological Data Analysis and Its Application to Time-Series Data Analysis - Umeda, Kaneko, Kikuchi.
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Topological Data Analysis and Machine Learning Theory - Carlsson , Jardine, Feichtner-Kozlov, Morozov.
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Topological Data Analysis for Object Data - Patrangenaru, Bubenik, Paige, Osborne .
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Two-Tier Mapper: a user-independent clustering method for global gene expression analysis based on topology - Jeitziner, Carrière, Rougemont, Oudot, Hess, Brisken.
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Why Topology for Machine Learning and Knowledge Extraction? - Massimo Ferri.
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Computational Topology and Data Analysis - Course is not active, but the course notes are useful.
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Topological Data Analysis - Course is not active, but the course notes are useful.
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Topics in topology: Scientific and engineering applications of algebraic topology - 2013 lecture series.
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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.
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Knotter - Implementation of Mapper algorithm for TDA.
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RIVET - For the visualization and analysis of two-parameter persistent homology with Python API.
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TdaToolbox - Some tools that may be applied to data science in general.
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TTk - Topological data analysis in scientific visualization. Can be used with C , python.
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Dionysus - Computing persistent (co)homology, Implementation of the Persistent (co)homology computation, Vineyards, Zigzag persistent homology algorithms.
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PHAT - Persistent Homology Algorithm Toolbox.
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Topology ToolKit (TTK) - Efficient, generic and easy and Topological data analysis and visualization
- TDA - Some methods are provided for gridded data (images).
- JavaPlex - The JavaPlex library implements persistent homology and related techniques. It designed for ease of use from Matlab and java-based systems.
- Eirene.jl - For homological persistence.
- TDA.jl - This package provides Persistence Diagram & Barcode, Nerve, Mapper tools for topological data analysis.
- Clique Top - Doing topological analysis of symmetric matrices.
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GDA Public - Several fundamental tools by Geometric Data Analytics Inc. geomdata
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Giotto TDA(GTDA) - A high-performance topological machine learning toolbox
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GUDHI - Geometry Understanding in Higher Dimensional with a Python interface.
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KeplerMapper - TDA Mapper algorithm for visualization of high-dimensional data. it can make use of Scikit-Learn API compatible cluster and scaling algorithms.
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Kohonen - Kohonen-style vector quantizers: Self-Organizing Map (SOM), Neural Gas, and Growing Neural Gas.
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Mapper Implementation - Topological Data Analysis for high dimensional dataset exploration.
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MoguTDA - Numerical calculation of algebraic topology in an application to topological data analysis: implicial complex, and the estimation of homology and Betti numbers.
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Persim - package for many tools used in analyzing Persistence Diagrams
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Python Mapper - Mapper algorithm implementation graphical user interface.
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Qsv - Data structure visualizer.
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Ripser - lean persistent homology package.
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Scikit-TDA - For non-topologists.
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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.
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Topology ToolKit (TTK) - Efficient, generic and easy and Topological data analysis and visualization
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TMAP - Population-scale microbiome data analysis.
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TDA - Tools for the statistical analysis of persistent homology and for density clustering.
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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).
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TDAstats - Computing persistent homology.
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Spark Mapper - Estimating a lower dimensional simplicial complex from a dataset.
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Spark TDA - Scalable topological data analysis package.
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An algebraic topological method for multimodal brain networks comparisons
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Complex Brain Network Analysis and Its Applications to Brain Disorders: A Survey
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Applied Topological Data Analysis to Deep Learning? Hands-on Arrhythmia Classification!
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From Topological Data Analysis to Deep Learning: No Pain No Gain
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On Characterizing the Capacity of Neural Networks Using Algebraic Topology
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Using Topological Data Analysis to Understand the Behavior of Convolutional Neural Networks
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An Algebraic Geometry Perspective on Topological Data Analysis
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Topological Data Analysis - UFL.
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Topological Data Analysis - IBM.
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Feb. 7 - Apr. 1 | self-study group for textbook: "Computational Topology for Data Analysis" | zoom
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Mar. 21 - Mar. 22 | Workshop on Topological Data Analysis | India
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Aug. 7 - Aug. 9 | the 4th annual Centre for Topological Data Analysis conference | Oxford, UK
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Oct. 13 - Oct. 18 | TopoInVis 2024 - Topological Data Analysis and Visualization | Florida, USA