@article{4aa56a5039ce42169787ffe6d64f8458,
title = "Multiscale data sampling and function extension",
abstract = "We introduce a multiscale scheme for sampling scattered data and extending functions defined on the sampled data points, which overcomes some limitations of the Nystr{\"o}m interpolation method. The multiscale extension (MSE) method is based on mutual distances between data points. It uses a coarse-to-fine hierarchy of the multiscale decomposition of a Gaussian kernel. It generates a sequence of subsamples, which we refer to as adaptive grids, and a sequence of approximations to a given empirical function on the data, as well as their extensions to any newly-arrived data point. The subsampling is done by a special decomposition of the associated Gaussian kernel matrix in each scale in the hierarchical procedure.",
keywords = "Diffusion maps, Gaussian kernel, Geometric harmonics, Multiscale, Nystr{\"o}m extension, Subsampling",
author = "Amit Bermanis and Amir Averbuch and Coifman, {Ronald R.}",
note = "Funding Information: This research was partially supported by the Israel Science Foundation (Grant No. 1041/10). Ronald R. Coifman and Amit Bermanis were partially supported by DOE grant DE-SC0002097. We would like to thank Yoel Shkolnisky for helpful discussions.",
year = "2013",
month = jan,
doi = "10.1016/j.acha.2012.03.002",
language = "אנגלית",
volume = "34",
pages = "15--29",
journal = "Applied and Computational Harmonic Analysis",
issn = "1063-5203",
publisher = "Academic Press Inc.",
number = "1",
}