# Persistence Diagrams with Linear Machine Learning Models

arXiv: https://arxiv.org/abs/1706.10082 · HTML: https://mlsanity.com/paper/1706.10082/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2017.

## Built on by (most cited first, 7 of 7)

- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [Euler Characteristic Tools For Topological Data Analysis](https://mlsanity.com/paper/2303.14040/) (2023)
- [Statistical learning on measures: an application to persistence diagrams](https://mlsanity.com/paper/2303.08456/) (2023)
- [A Multi-parameter Persistence Framework for Mathematical Morphology](https://mlsanity.com/paper/2103.13013/) (2021)
- [Persistent homology-based descriptor for machine-learning potential of amorphous structures](https://mlsanity.com/paper/2206.13727/) (2022)
- [Statistical embedding: Beyond principal components](https://mlsanity.com/paper/2106.01858/) (2021)
- [Topology-Informed Machine Learning for Efficient Prediction of Solid Oxide Fuel Cell Electrode Polarization](https://mlsanity.com/paper/2410.05307/) (2024)

## Abstract (arXiv)

Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be extracted by applying machine learnings. In particular, the ability for explicitly analyzing the inverse in the original data space from those statistical features of persistence diagrams is significantly important for practical applications. In this paper, we propose a unified method for the inverse analysis by combining linear machine learning models with persistence images. The method is applied to point clouds and cubical sets, showing the ability of the statistical inverse analysis and its advantages.