# Vectorization of Persistence Diagrams for Topological Data Analysis in R and Python Using TDAvec Package

arXiv: https://arxiv.org/abs/2411.17340 · HTML: https://mlsanity.com/paper/2411.17340/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 22 references that are in the map.
- First posted on arXiv 26 Nov 2024.

## Builds on (most cited first, 7 of 7)

- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration](https://mlsanity.com/paper/2004.02551/) (2020)
- [Persistence Curves: A canonical framework for summarizing persistence diagrams](https://mlsanity.com/paper/1904.07768/) (2019)
- [Approximating Continuous Functions on Persistence Diagrams Using Template Functions](https://mlsanity.com/paper/1902.07190/) (2019)
- [A computationally efficient framework for vector representation of persistence diagrams](https://mlsanity.com/paper/2109.08239/) (2021)

## Abstract (arXiv)

Persistent homology is a widely-used tool in topological data analysis (TDA) for understanding the underlying shape of complex data. By constructing a filtration of simplicial complexes from data points, it captures topological features such as connected components, loops, and voids across multiple scales. These features are encoded in persistence diagrams (PDs), which provide a concise summary of the data's topological structure. However, the non-Hilbert nature of the space of PDs poses challenges for their direct use in machine learning applications. To address this, kernel methods and vectorization techniques have been developed to transform PDs into machine-learning-compatible formats. In this paper, we introduce a new software package designed to streamline the vectorization of PDs, offering an intuitive workflow and advanced functionalities. We demonstrate the necessity of the package through practical examples and provide a detailed discussion on its contributions to applied TDA. Definitions of all vectorization summaries used in the package are included in the appendix.