This is not the latest version of this item. The latest version can be found here.
Multiresolution Low-rank Tensor Formats
Name
19m1284579.pdf
Description
Published version
Size
6.73 MB
Format
Adobe PDF
Checksum (MD5)
eb975fead345297ab0a89517b8041b77
Author(s)
Mickelin, Oscar
Karaman, Sertac
Date Issued
2020
Journal
SIAM Journal on Matrix Analysis and Applications
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
© 2020 Society for Industrial and Applied Mathematics. We describe a simple, black-box compression format for tensors with a multiscale structure. By representing the tensor as a sum of compressed tensors defined on increasingly coarse grids, we capture low-rank structures on each grid-scale, and we show how this leads to an increase in compression for a fixed accuracy. We devise an alternating algorithm to represent a given tensor in the multiresolution format and prove local convergence guarantees. In two dimensions, we provide examples that show that this approach can beat the Eckart-Young theorem, and for dimensions higher than two, we achieve higher compression than the tensor-train format on six real-world datasets. We also provide results on the closedness and stability of the tensor format and discuss how to perform common linear algebra operations on the level of the compressed tensors.
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
10.1137/19M1284579
