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 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
Cite
@article{arxiv.1909.08417,
title = {Persistence B-Spline Grids: Stable Vector Representation of Persistence Diagrams Based on Data Fitting},
author = {Zhetong Dong and Hongwei Lin and Chi Zhou},
journal= {arXiv preprint arXiv:1909.08417},
year = {2022}
}