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TDA (topological data analysis) is a relatively new area of research related to importing classical ideas from topology into the realm of data analysis. Under the umbrella term TDA, there falls, in particular, the notion of persistent…

Algebraic Topology · Mathematics 2019-06-03 Facundo Memoli , Kritika Singhal

Over the last two decades, topological data analysis (TDA) has emerged as a very powerful data analytic approach which can deal with various data modalities of varying complexities. One of the most commonly used tools in TDA is persistent…

Methodology · Statistics 2025-12-08 Anass El Yaagoubi Bourakna , Moo K. Chung , Hernando Ombao

Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected…

Machine Learning · Statistics 2025-11-18 Ioannis Diamantis

This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we…

Machine Learning · Computer Science 2021-10-12 Mustafa Hajij , Ghada Zamzmi , Xuanting Cai

Topological data analysis (TDA) is gaining prominence across a wide spectrum of machine learning tasks that spans from manifold learning to graph classification. A pivotal technique within TDA is persistent homology (PH), which furnishes an…

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of…

Topological Data Analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. This includes: clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation…

Methodology · Statistics 2016-09-28 Larry Wasserman

Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…

Machine Learning · Statistics 2023-07-10 Yueqi Cao , Athanasios Vlontzos , Luca Schmidtke , Bernhard Kainz , Anthea Monod

TopoDetect is a Python package that allows the user to investigate if important topological features, such as the Degree of the nodes, their Triangle Count, or their Local Clustering Score, are preserved in the embeddings of graph…

Machine Learning · Computer Science 2021-10-11 Maroun Haddad , Mohamed Bouguessa

Topological Data Analysis (TDA) offers a suite of computational tools that provide quantified shape features in high dimensional data that can be used by modern statistical and predictive machine learning (ML) models. In particular,…

Cryptography and Security · Computer Science 2023-07-06 Dominic Gold , Koray Karabina , Francis C. Motta

Topological Data Analysis (TDA) is the collection of mathematical tools that capture the structure of shapes in data. Despite computational topology and computational geometry, the utilization of TDA in time series and signal processing is…

Information Retrieval · Computer Science 2018-10-23 Shafie Gholizadeh , Wlodek Zadrozny

Surface roughness plays an important role in analyzing engineering surfaces. It quantifies the surface topography and can be used to determine whether the resulting surface finish is acceptable or not. Nevertheless, while several existing…

Signal Processing · Electrical Eng. & Systems 2021-10-20 Melih C. Yesilli , Firas A. Khasawneh

Identifying molecular signatures from complex disease patients with underlying symptomatic similarities is a significant challenge in the analysis of high dimensional multi-omics data. Topological data analysis (TDA) provides a way of…

Genomics · Quantitative Biology 2024-04-23 Davide Gurnari , Aldo Guzmán-Sáenz , Filippo Utro , Aritra Bose , Saugata Basu , Laxmi Parida

Topological data analysis (TDA) is an active field of mathematics for quantifying shape in complex data. Standard methods in TDA such as persistent homology (PH) are typically focused on the analysis of data consisting of a single entity…

Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…

Machine Learning · Computer Science 2021-02-09 Rolando Kindelan , José Frías , Mauricio Cerda , Nancy Hitschfeld

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…

Graphics · Computer Science 2017-10-04 Mustafa Hajij , Bei Wang , Carlos Scheidegger , Paul Rosen

Topological Data Analysis (TDA) is a modern approach to Data Analysis focusing on the topological features of data; it has been widely studied in recent years and used extensively in Biology, Physics, and many other areas. However,…

Mathematical Finance · Quantitative Finance 2023-07-11 Miguel A. Ruiz-Ortiz , José Carlos Gómez-Larrañaga , Jesús Rodríguez-Viorato

Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two…

Applications · Statistics 2020-03-04 Sarit Agami

Topological Data Analysis (TDA) is a novel, and relatively new approach to analysing high-dimensional data sets. It does this by focussing on global properties like the shape and connectivity of the data giving it a significant advantage…

Instrumentation and Methods for Astrophysics · Physics 2019-04-26 Jeff Murugan , Duncan Robertson

Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the "shape" of such complex high-dimensional data. Research in this…

Algebraic Topology · Mathematics 2022-04-15 R. W. R. Darling , John A. Emanuello , Emilie Purvine , Ahmad Ridley