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Many attempts have been made in recent decades to integrate machine learning(ML) and topological data analysis. A prominent problem in applying persistenthomology to ML tasks is finding a vector representation of a persistencediagram (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 techniqueof progressive-iterative approximation for least-squares B-spline functionfitting. We theoretically prove that the PBSG method is stable with respect tothe metric of 1-Wasserstein distance defined on the PD space. The proposedmethod 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 andefficiency

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