# Persistence B-Spline Grids: Stable Vector Representation of Persistence Diagrams Based on Data Fitting

arXiv: https://arxiv.org/abs/1909.08417 · HTML: https://mlsanity.com/paper/1909.08417/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2019.

## Built on by (most cited first, 3 of 3)

- [A Vectorization Method Induced By Maximal Margin Classification For Persistent Diagrams](https://mlsanity.com/paper/2407.21298/) (2024)
- [G-LoG Bi-filtration for Medical Image Classification](https://mlsanity.com/paper/2602.18329/) (2026)
- [Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagrams](https://mlsanity.com/paper/2607.27126/) (2026)

## Abstract (arXiv)

Many attempts have been made in recent decades to integrate machine learning (ML) and topological data analysis. A prominent problem in applying persistent homology to ML tasks is finding a vector representation of a persistence diagram (PD), which is a summary diagram for representing topological features. From the perspective of data fitting, a stable vector representation, namely, persistence B-spline grid (PBSG), is proposed based on the efficient technique of progressive-iterative approximation for least-squares B-spline function fitting. We theoretically prove that the PBSG method is stable with respect to the metric of 1-Wasserstein distance defined on the PD space. The proposed method was tested on a synthetic data set, data sets of randomly generated PDs, data of a dynamical system, and 3D CAD models, showing its effectiveness and efficiency