Persistent Entropy, a Tool for Topologically Summarizing Data

Explore persistent entropy as a tool for topologically summarizing data in this 52-minute conference talk. Delve into the properties and applications of this entropy-based summarization of persistence barcodes, including its stability to small perturbations in input data. Learn about its usefulness in machine learning and pattern recognition. Discover diverse applications such as emotion recognition in talking-face videos, summarizing cell organization in epithelial tissues, and characterizing literary styles of poets. Gain insights into the persistent entropy formula, normalization techniques, and stability properties. Examine practical examples in emotion recognition, epithelial tissue analysis, and philology using word embeddings. Conclude with a summary of applications and engage in a Q&A session addressing intuitive interpretations of persistent entropy.

Introduction
Persistent homology
Example
What is persistent entropy
Persistent entropy formula
Computing persistent entropy separately
Normalized persistent entropy
Stability of persistent entropy
Scaling variant
Emotion Recognition
Epithelial tissues
Persistent entropy
Philology
Word embedding
Congo
Applications
Summarize
Thank you
Audio content
Question
Audience questions
Is there any intuitive way to interpret this number