Multiscale data sampling and function extension |
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Authors: | Amit Bermanis Amir Averbuch Ronald R Coifman |
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Institution: | 1. Department of Applied Mathematics, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel;2. School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel;3. Department of Mathematics, Program in Applied Mathematics, Yale University, New Haven, CT 06510, USA |
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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 Nyström 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. |
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