# Adaptive template systems: Data-driven feature selection for learning with persistence diagrams

arXiv: https://arxiv.org/abs/1910.06741 · HTML: https://mlsanity.com/paper/1910.06741/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Oct 2019.

## Built on by (most cited first, 4 of 4)

- [A Pipeline for Data-Driven Learning of Topological Features with Applications to Protein Stability Prediction](https://mlsanity.com/paper/2408.04847/) (2024)
- [Learning on Persistence Diagrams as Radon Measures](https://mlsanity.com/paper/2212.08295/) (2022)
- [Sleep Staging from Airflow Signals Using Fourier Approximations of Persistence Curves](https://mlsanity.com/paper/2411.07964/) (2024)
- [Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams](https://mlsanity.com/paper/2607.27126/) (2026)

## Abstract (arXiv)

Feature extraction from persistence diagrams, as a tool to enrich machine learning techniques, has received increasing attention in recent years. In this paper we explore an adaptive methodology to localize features in persistent diagrams, which are then used in learning tasks. Specifically, we investigate three algorithms, CDER, GMM and HDBSCAN, to obtain adaptive template functions/features. Said features are evaluated in three classification experiments with persistence diagrams. Namely, manifold, human shapes and protein classification. The main conclusion of our analysis is that adaptive template systems, as a feature extraction technique, yield competitive and often superior results in the studied examples. Moreover, from the adaptive algorithms here studied, CDER consistently provides the most reliable and robust adaptive featurization.