# Persistence paths and signature features in topological data analysis

arXiv: https://arxiv.org/abs/1806.00381 · HTML: https://mlsanity.com/paper/1806.00381/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2018.

## Built on by (most cited first, 17 of 17)

- [Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutions](https://mlsanity.com/paper/2106.01098/) (2021)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [PCF-GAN: generating sequential data via the characteristic function of measures on the path space](https://mlsanity.com/paper/2305.12511/) (2023)
- [Cycle Registration in Persistent Homology with Applications in Topological Bootstrap](https://mlsanity.com/paper/2101.00698/) (2021)
- [Approximating Persistent Homology for Large Datasets](https://mlsanity.com/paper/2204.09155/) (2022)
- [Euler Characteristic Curves and Profiles: a stable shape invariant for big data problems](https://mlsanity.com/paper/2212.01666/) (2022)
- [The Signature Kernel](https://mlsanity.com/paper/2305.04625/) (2023)
- [Feature Engineering with Regularity Structures](https://mlsanity.com/paper/2108.05879/) (2021)
- [2-d signature of images and texture classification](https://mlsanity.com/paper/2205.11236/) (2022)
- [Global universal approximation with Brownian signatures](https://mlsanity.com/paper/2512.16396/) (2025)
- [FRUITS: Feature Extraction Using Iterated Sums for Time Series Classification](https://mlsanity.com/paper/2311.14549/) (2023)
- [Comparing the Effects of Persistence Barcodes Aggregation and Feature Concatenation on Medical Imaging](https://mlsanity.com/paper/2505.23637/) (2025)
- [From augmented microscopy to the topological transformer: a new approach in cell image analysis for Alzheimer's research](https://mlsanity.com/paper/2108.01625/) (2021)
- [A Vectorization Method Induced By Maximal Margin Classification For Persistent Diagrams](https://mlsanity.com/paper/2407.21298/) (2024)
- [A Novel Patch-Based TDA Approach for Computed Tomography Imaging](https://mlsanity.com/paper/2512.12108/) (2025)
- [Global universality via discrete-time signatures](https://mlsanity.com/paper/2603.09773/) (2026)
- [Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams](https://mlsanity.com/paper/2607.27126/) (2026)

## Abstract (arXiv)

We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in the tensor algebra of that vector space. The composition of these two operations - barcode to path, path to tensor series - results in a feature map that has several desirable properties for statistical learning, such as universality and characteristicness, and achieves state-of-the-art results on common classification benchmarks.