Some applications of local operators

Hrushikesh Mhaskar^*

In recent years, we have developed quadrature formulas and localized operators for approximation of functions on unknown, data defined manifolds. We describe some applications of this theory to the analysis of some standard data sets. In particular, we describe an interesting application of approximation on the Euclidean unit sphere S4 to the question of drusen classification in retinal images, an important tool in the diagnosis of age related macular disease. This is joint work with M. Ehler and F. Filbir.

Mathematics Subject Classification: 65D15

Keywords: machine learning, localized kernels, quadrature formulas, drusen classification in retina

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