TY - JOUR
T1 - Interpolating splines on graphs for data science applications
AU - Ward, John P
AU - Narcowich, Francis J.
AU - Ward, John P
PY - 2020/9/1
Y1 - 2020/9/1
N2 - 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.
AB - 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.
KW - Interpolation
KW - Kernel-based machine learning
KW - Lagrange functions
KW - Local basis functions
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85086071954&origin=inward
UR - https://www.scopus.com/inward/citedby.uri?partnerID=HzOxMe3b&scp=85086071954&origin=inward
U2 - 10.1016/j.acha.2020.06.001
DO - 10.1016/j.acha.2020.06.001
M3 - Article
SN - 1063-5203
VL - 49
SP - 540
EP - 557
JO - Applied and Computational Harmonic Analysis
JF - Applied and Computational Harmonic Analysis
IS - 2
ER -