Persistence B-Spline Grids: Stable Vector Representation of Persistence Diagrams Based on Data Fitting
Abstract
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 developed 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 developed 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.
Cite
Text
Dong et al. "Persistence B-Spline Grids: Stable Vector Representation of Persistence Diagrams Based on Data Fitting." Machine Learning, 2024. doi:10.1007/S10994-023-06492-WMarkdown
[Dong et al. "Persistence B-Spline Grids: Stable Vector Representation of Persistence Diagrams Based on Data Fitting." Machine Learning, 2024.](https://mlanthology.org/mlj/2024/dong2024mlj-persistence/) doi:10.1007/S10994-023-06492-WBibTeX
@article{dong2024mlj-persistence,
title = {{Persistence B-Spline Grids: Stable Vector Representation of Persistence Diagrams Based on Data Fitting}},
author = {Dong, Zhetong and Lin, Hongwei and Zhou, Chi and Zhang, Ben and Li, Gengchen},
journal = {Machine Learning},
year = {2024},
pages = {1373-1420},
doi = {10.1007/S10994-023-06492-W},
volume = {113},
url = {https://mlanthology.org/mlj/2024/dong2024mlj-persistence/}
}