Interpolating splines on graphs for data science applications
Numerical Analysis
2020-04-21 v3 Numerical Analysis
Classical Analysis and ODEs
Abstract
We introduce intrinsic interpolatory bases for data structured on graphs and derive properties of those bases. Polyharmonic Lagrange functions are shown to satisfy exponential decay away from their centers. The decay depends on the density of the zeros of the Lagrange function, showing that they scale with the density of the data. These results indicate that Lagrange-type bases are ideal building blocks for analyzing data on graphs, and we illustrate their use in kernel-based machine learning applications.
Cite
@article{arxiv.1806.10695,
title = {Interpolating splines on graphs for data science applications},
author = {John Paul Ward and Francis J. Narcowich and Joseph D. Ward},
journal= {arXiv preprint arXiv:1806.10695},
year = {2020}
}
Comments
17 pages