# Kernel method for persistence diagrams via kernel embedding and weight factor

arXiv: https://arxiv.org/abs/1706.03472 · HTML: https://mlsanity.com/paper/1706.03472/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2017.

## Built on by (most cited first, 20 of 20)

- [Generalized Shape Metrics on Neural Representations](https://mlsanity.com/paper/2110.14739/) (2021)
- [Persformer: A Transformer Architecture for Topological Machine Learning](https://mlsanity.com/paper/2112.15210/) (2021)
- [Sobolev Transport: A Scalable Metric for Probability Measures with Graph Metrics](https://mlsanity.com/paper/2202.10723/) (2022)
- [Entropy Partial Transport with Tree Metrics: Theory and Practice](https://mlsanity.com/paper/2101.09756/) (2021)
- [Approximating Persistent Homology for Large Datasets](https://mlsanity.com/paper/2204.09155/) (2022)
- [Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds](https://mlsanity.com/paper/2307.09259/) (2023)
- [Optimal Transport for Measures with Noisy Tree Metric](https://mlsanity.com/paper/2310.13653/) (2023)
- [A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces for Clustering](https://mlsanity.com/paper/2105.12208/) (2021)
- [Do Neural Networks Trained with Topological Features Learn Different Internal Representations?](https://mlsanity.com/paper/2211.07697/) (2022)
- [Reliable Malware Analysis and Detection using Topology Data Analysis](https://mlsanity.com/paper/2211.01535/) (2022)
- [Scalable Sobolev IPM for Probability Measures on a Graph](https://mlsanity.com/paper/2502.00737/) (2025)
- [Beyond Means: Topological Causal Effects under Persistent-Homology Ignorability](https://mlsanity.com/paper/2603.14169/) (2026)
- [A Mathematical Framework for Topological Causal Data Analysis](https://mlsanity.com/paper/2607.28161/) (2026)
- [Sparse Portfolio Selection via Topological Data Analysis based Clustering](https://mlsanity.com/paper/2401.16920/) (2024)
- [Persistence kernels for classification: A comparative study](https://mlsanity.com/paper/2408.07090/) (2024)
- [PI-Att: Topology Attention for Segmentation Networks through Adaptive Persistence Image Representation](https://mlsanity.com/paper/2408.08038/) (2024)
- [Topology-Informed Machine Learning for Efficient Prediction of Solid Oxide Fuel Cell Electrode Polarization](https://mlsanity.com/paper/2410.05307/) (2024)
- [Persistence Spheres: Bi-continuous Representations of Persistence Diagrams](https://mlsanity.com/paper/2509.16999/) (2025)
- [Revisiting the Sliced Wasserstein Kernel for persistence diagrams: a Figalli-Gigli approach](https://mlsanity.com/paper/2602.06539/) (2026)
- [Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams](https://mlsanity.com/paper/2607.27126/) (2026)

## Abstract (arXiv)

Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy topological properties. Nowadays, it is highly desired to develop a statistical framework on persistence diagrams to deal with practical data. This paper proposes a kernel method on persistence diagrams. A theoretical contribution of our method is that the proposed kernel allows one to control the effect of persistence, and, if necessary, noisy topological properties can be discounted in data analysis. Furthermore, the method provides a fast approximation technique. The method is applied into several problems including practical data in physics, and the results show the advantage compared to the existing kernel method on persistence diagrams.