Computational topology | Homology theory | Applied mathematics
In applied mathematics, topological based data analysis (TDA) is an approach to the analysis of datasets using techniques from topology. Extraction of information from datasets that are high-dimensional, incomplete and noisy is generally challenging. TDA provides a general framework to analyze such data in a manner that is insensitive to the particular metric chosen and provides dimensionality reduction and robustness to noise. Beyond this, it inherits functoriality, a fundamental concept of modern mathematics, from its topological nature, which allows it to adapt to new mathematical tools. The initial motivation is to study the shape of data. TDA has combined algebraic topology and other tools from pure mathematics to allow mathematically rigorous study of "shape". The main tool is persistent homology, an adaptation of homology to point cloud data. Persistent homology has been applied to many types of data across many fields. Moreover, its mathematical foundation is also of theoretical importance. The unique features of TDA make it a promising bridge between topology and geometry. (Wikipedia).
Peter Bubenik (6/2/20): Topological data analysis for biological images
Title: Topological data analysis for biological images Abstract: I will introduce topological data analysis and show how it may be combined with machine learning to analyze certain biological images. Using a small collection of high-resolution images of a cell's actin cytoskeleton, we are
From playlist SIAM Topological Image Analysis 2020
Aras Asaad (6/2/20): Topological data analysis to detect fake faces from images and videos
Title: Topological data analysis to detect fake faces from images and videos Abstract: The aim of Topological data analysis (TDA) is to provide new topological and geometric tools to analyse complex and high-dimensional data. This talk will cover a brief introduction to TDA and its applic
From playlist SIAM Topological Image Analysis 2020
Vasileios Maroulas (12/1/21): Statistics, Topology and Data Analysis
Abstract: In this talk, I will discuss how statistics and topological data analysis are beautifully complement each other to solve real data problems. As a paradigm, I will discuss supervised learning, and present a classification approach using a novel Bayesian framework for persistent ho
From playlist AATRN 2021
Anne Marie Svane (12/14/2022): Analyzing point processes using topological data analysis
Abstract: Topological data analysis has become a popular tool in spatial statistics for analyzing point processes. This talk will introduce some of the standard models for point processes and indicate how topological data analysis can be used to distinguish between different types of model
From playlist AATRN 2022
Topological Data Analysis and Persistent Homology -
Michael Lesnick Stanford University; Member, School of Mathematics September 28, 2012 For more videos, visit http://video.ias.edu
From playlist Mathematics
Hengrui Luo (4/22/20): Lower dimensional topological information: Theory and applications
Title: Lower dimensional topological information: Theory and applications Abstract: Topological data analysis (TDA) allows us to explore the topological features of a dataset. Among topological features, lower dimensional ones are of growing interest in mathematics and statistics due to t
From playlist AATRN 2020
Christian Lehn (3/26/19): Limit theorems in topological data analysis
Title: Limit theorems in topological data analysis Abstract: In a joint work with S. Kališnik Verošek and V. Limic we generalize the notion of barcodes in topological data analysis in order to prove limit theorems for point clouds sampled from an unknown distribution as the number of poin
From playlist AATRN 2019
Sarah Tymochko (02/22/23): Topological Time Series Analysis for Hurricanes and Dynamical Systems
Title: Applications of Topological Time Series Analysis to Hurricanes and Dynamical Systems Abstract: Topological data analysis (TDA) is a fairly new field with tools to quantify the shape of data in a manner that is concise and robust using concepts from algebraic topology. Persistent ho
From playlist AATRN 2023
Quantum Topological Data Analysis (Part 1) [Péguy Kem-Meka]
Quantum Topological Data Analysis is about how quantum computers and quantum information processors can learn pattern in data that cannot be learn by classical TDA algorithms. Quantum computers are becoming available to general public. They can dramatically reduce both execution time and e
From playlist Tutorials
Patrizio Frosini (8/30/21): On the role of group equivariant non-expansive operators in TDA
Group equivariant non-expansive operators (GENEOs) have been recently introduced as mathematical tools for approximating data observers, when data are represented by real-valued or vector-valued functions. The use of these operators is based on the assumption that the interpretation of dat
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
The shape of data: Ulrike Tillmann, FRS, University of Oxford
Ulrike Tillmann (Turing Fellow and University of Oxford, UK) Prof. Ulrike Tillmann FRS has been at the University of Oxford since 1992. She is an algebraic topologist, known in particular for her work on Riemann surfaces and the homology of their moduli spaces. She has long standing rese
From playlist Women in data science conference
Jose Perea - LatMath 2022 - IPAM's Latinx in the Mathematical Sciences Conference
Recorded 08 July 2022. Jose Perea presents at IPAM's Latinx in the Mathematical Sciences Conference. Learn more online at: http://www.ipam.ucla.edu/programs/special-events-and-conferences/latinx-in-the-mathematical-sciences-conference-2022/
From playlist LatMath 2022 - IPAM's Latinx in the Mathematical Sciences Conference
Stéphane Béreux: Identifying and Assessing Damage in Infrastructure Using TDA and Machine Learning
Title: Identifying and Assessing Damage inInfrastructure Using Topological Data Analysis and Machine Learning Abstract: Assessing the damage of concrete damage in infrastructure is an important task as many constructions are nearing the end of their service life. Currently, the technique
From playlist AATRN 2021
Professor Gunnar Carlsson , Stanford University, USA
From playlist Public Lectures
Elizabeth Munch (6/2/20): Topological data analysis for quantifying plant morphology
Title: Topological data analysis for quantifying plant morphology Abstract: Persistent homology is a powerful tool from topological data analysis (TDA) for measuring shape and structure in data. One method for interfacing with persistent homology is to provide input data in the form of an
From playlist SIAM Topological Image Analysis 2020