Journal
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
Volume 34, Issue 1, Pages 15-29Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2012.03.002
Keywords
Nystrom extension; Multiscale; Subsampling; Gaussian kernel; Diffusion maps; Geometric harmonics
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Funding
- Israel Science Foundation [1041/10]
- DOE [DE-SC0002097]
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We introduce a multiscale scheme for sampling scattered data and extending functions defined on the sampled data points, which overcomes some limitations of the Nystrom 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. (C) 2012 Elsevier Inc. All rights reserved.
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