Persistence B-Spline Grids: Stable Vector Representation of Persistence Diagrams Based on Data Fitting. (arXiv:1909.08417v2 [cs.LG] UPDATED)

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 …

arxiv data representation spline vector