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Hengrui Luo - Generalized Penalty for Circular Coordinate Representation

Offered By: Applied Algebraic Topology Network via YouTube

Tags

Topological Data Analysis Courses Data Visualization Courses High-Dimensional Data Analysis Courses Dimension Reduction Courses

Course Description

Overview

Explore a 21-minute conference talk on adapting circular coordinate representation for high-dimensional datasets using generalized penalty functions in Topological Data Analysis. Delve into dimension reduction techniques, topological concepts, and the application of persistent cohomology for data visualization on a torus. Learn how this approach accommodates sparsity while preserving topological structures, supported by simulation experiments and real data analysis. Examine the two-loop example revisited and a high-dimensional example, based on joint research with Alice Pantania, Jisu Kim, and Mikael Vejdemo-Johansson.

Syllabus

Intro
Dimension reduction - a linear approach
Dimension reduction - a non-linear approach
Topological Concepts
Circular coordinates
Generalized Penalty Functions
Two-loop example revisited
A high-dimensional example IV


Taught by

Applied Algebraic Topology Network

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