# Persistence Bag-of-Words for Topological Data Analysis

## TL;DR

This paper introduces persistence bag-of-words, a new stable vectorized representation of persistence diagrams that enhances integration with machine learning and achieves state-of-the-art results efficiently.

## Contribution

The paper proposes a novel persistence bag-of-words method that simplifies and stabilizes the use of persistence diagrams in machine learning workflows.

## Key findings

- Achieves state-of-the-art performance on benchmark tasks.
- Provides a computationally efficient alternative to existing methods.
- Ensures stability and robustness of the representation.

## Abstract

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine learning workflows. This paper introduces persistence bag-of-words: a novel and stable vectorized representation of PDs that enables the seamless integration with machine learning. Comprehensive experiments show that the new representation achieves state-of-the-art performance and beyond in much less time than alternative approaches.