Samplets
construction and scattered data compression
Additional information
Authors
Harbrecht H.,
Multerer M.
Type
Journal Article
Year
2022
Language
English
Abstract
We introduce the concept of samplets by transferring the construction of Tausch-White wavelets to scattered data. This way, we obtain a multiresolution analysis tailored to discrete data which directly enables data compression, feature detection and adaptivity. The cost for constructing the samplet basis and for the fast samplet transform, respectively, is O(N), where N is the number of data points. Samplets with vanishing moments can be used to compress kernel matrices, arising, for instance, in kernel based learning and scattered data approximation. The result are sparse matrices with only O(N log N) remaining entries. We provide estimates for the compression error and present an algorithm that computes the compressed kernel matrix with computational cost O(N log N). The accuracy of the approximation is controlled by the number of vanishing moments. Besides the cost efficient storage of kernel matrices, the sparse representation enables the application of sparse direct solvers for the numerical solution of corresponding linear systems. In addition to a comprehensive introduction to samplets and their properties, we present numerical studies to benchmark the approach. Our results demonstrate that samplets mark a considerable step in the direction of making large scattered data sets accessible for multiresolution analysis.
Keywords
Multiresolution analysis, Unstructured data, Kernel methods, Data compression
Journal
Journal of computational physics
Volume
471
Pages (or article number)
111616
Diffusion
License
CC BY
Visibility
Public
Status open access
Hybrid
