YoVDO

An Intrinsic Persistent Homology Transform

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Topological Data Analysis Courses Euclidean Spaces Courses Algebraic Topology Courses

Course Description

Overview

Explore an in-depth lecture on the Intrinsic Persistent Homology Transform (IPHT) and its applications in topological data analysis. Delve into the origins of the Persistent Homology Transform (PHT) and Euler Characteristic Transform (ECT), understanding their significance as the first TDA invariants proven to be injective on shapes embedded in Euclidean space. Examine recent developments in the field, including new proofs, finiteness results, and practical applications. Focus on joint research with Steve Oudot, investigating an analogue of these constructions for intrinsic metric spaces, particularly metric graphs. Discover the unique properties of the IPHT, including its lack of injectivity in certain cases and its generic injectivity in appropriate topologies. Gain insights into the evolving landscape of algebraic topology and its implications for shape analysis and data science.

Syllabus

Elchanan Solomon (10/16/18): An intrinsic persistent homology transform


Taught by

Applied Algebraic Topology Network

Related Courses

Topological Data Analysis - New Perspectives on Machine Learning - by Jesse Johnson
Open Data Science via YouTube
Analyzing Point Processes Using Topological Data Analysis
Applied Algebraic Topology Network via YouTube
MD Simulations and Machine Learning to Quantify Interfacial Hydrophobicity
Applied Algebraic Topology Network via YouTube
Topological Data Analysis of Plant-Pollinator Resource Complexes - Melinda Kleczynski
Applied Algebraic Topology Network via YouTube
Hubert Wagner - Topological Data Analysis in Non-Euclidean Spaces
Applied Algebraic Topology Network via YouTube