Persistence Images

Explore persistent homology and persistence images in this comprehensive lecture from the Applied Algebraic Topology Network. Dive into the world of topological data analysis, learning how to characterize the underlying structure of noisy data sets. Discover the concept of persistence diagrams (PDs) and their transformation into persistence images (PIs). Understand the stability of this transformation and its advantages in machine learning tasks. Compare the discriminatory power of PIs against existing methods and explore their application with vector-based machine learning tools. Examine real-world applications, including parameter inference from dynamic systems and partial differential equations. Follow the lecture's progression through topics such as metric spaces, persistence landscapes, implementation techniques, and classification methods.

Introduction
Overview
Persistent homology
Persistence pipeline
metric space
different approaches
persistence landscapes
Persistence images
Parameters
Implementation
Examples
Stability
Data
Distance matrices
Resolution and variance
Classification