Interpolating splines on graphs for data science applications
| Autor: | Joseph D. Ward, John Paul Ward, Francis J. Narcowich |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Ideal (set theory)
Scale (ratio) Applied Mathematics 010102 general mathematics MathematicsofComputing_NUMERICALANALYSIS Numerical Analysis (math.NA) 010103 numerical & computational mathematics Function (mathematics) 01 natural sciences 41A05 41A15 41A65 Mathematics - Classical Analysis and ODEs Kernel (statistics) ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Classical Analysis and ODEs (math.CA) FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics Exponential decay Mathematics |
| Zdroj: | Applied and Computational Harmonic Analysis. 49:540-557 |
| ISSN: | 1063-5203 |
| Popis: | 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. Comment: 17 pages |
| Databáze: | OpenAIRE |
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