Interpolating splines on graphs for data science applications Academic Article

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.

authors

• Narcowich, Francis

published proceedings

• APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS

author list (cited authors)

• Ward, J. P., Narcowich, F. J., & Ward, J. D.

citation count

• 5

complete list of authors

• Ward, John Paul||Narcowich, Francis J||Ward, Joseph D

publication date

• September 2020

publisher

• Elsevier  Publisher

published in

• Applied and Computational Harmonic Analysis  Journal

keywords

• Interpolation
• Kernel-based Machine Learning
• Lagrange Functions
• Local Basis Functions

Digital Object Identifier (DOI)

• 10.1016/j.acha.2020.06.001

start page

• 540

end page

• 557

volume

• 49

issue

• 2

URL

• http://dx.doi.org/10.1016/j.acha.2020.06.001