# Topological Machine Learning with Persistence Indicator Functions

arXiv: https://arxiv.org/abs/1907.13496 · HTML: https://mlsanity.com/paper/1907.13496/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2019.

## Built on by (most cited first, 11 of 11)

- [Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions](https://mlsanity.com/paper/2106.01098/) (2021)
- [Curvature Filtrations for Graph Generative Model Evaluation](https://mlsanity.com/paper/2301.12906/) (2023)
- [On the Expressivity of Persistent Homology in Graph Learning](https://mlsanity.com/paper/2302.09826/) (2023)
- [Characterizing and Measuring the Similarity of Neural Networks with Persistent Homology](https://mlsanity.com/paper/2101.07752/) (2021)
- [The magnitude vector of images](https://mlsanity.com/paper/2110.15188/) (2021)
- [A computationally efficient framework for vector representation of persistence diagrams](https://mlsanity.com/paper/2109.08239/) (2021)
- [A Review of Topological Data Analysis for Cybersecurity](https://mlsanity.com/paper/2202.08037/) (2022)
- [A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces for Clustering](https://mlsanity.com/paper/2105.12208/) (2021)
- [Image Classification using Combination of Topological Features and Neural Networks](https://mlsanity.com/paper/2311.06375/) (2023)
- [Higher-order topological kernels via quantum computation](https://mlsanity.com/paper/2307.07383/) (2023)
- [Visualizing Topological Importance: A Class-Driven Approach](https://mlsanity.com/paper/2309.13185/) (2023)

## Abstract (arXiv)

Techniques from computational topology, in particular persistent homology, are becoming increasingly relevant for data analysis. Their stable metrics permit the use of many distance-based data analysis methods, such as multidimensional scaling, while providing a firm theoretical ground. Many modern machine learning algorithms, however, are based on kernels. This paper presents persistence indicator functions (PIFs), which summarize persistence diagrams, i.e., feature descriptors in topological data analysis. PIFs can be calculated and compared in linear time and have many beneficial properties, such as the availability of a kernel-based similarity measure. We demonstrate their usage in common data analysis scenarios, such as confidence set estimation and classification of complex structured data.