dc.contributor.author | Mickelin, Oscar | |
dc.contributor.author | Karaman, Sertac | |
dc.date.accessioned | 2021-10-27T20:30:05Z | |
dc.date.available | 2021-10-27T20:30:05Z | |
dc.date.issued | 2020 | |
dc.identifier.uri | https://hdl.handle.net/1721.1/135948 | |
dc.description.abstract | © 2020 John Wiley & Sons, Ltd. Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension instead of exponential scaling. In this paper, we investigate even lower storage-cost representations in the tensor ring format, which is an extension of the tensor train format with variable end-ranks. Firstly, we introduce two algorithms for converting a tensor in full format to tensor ring format with low storage cost. Secondly, we detail a rounding operation for tensor rings and show how this requires new definitions of common linear algebra operations in the format to obtain storage-cost savings. Lastly, we introduce algorithms for transforming the graph structure of graph-based tensor formats, with orders of magnitude lower complexity than existing literature. The efficiency of all algorithms is demonstrated on a number of numerical examples, and in certain cases, we demonstrate significantly higher compression ratios when compared to previous approaches to using the tensor ring format. | |
dc.language.iso | en | |
dc.publisher | Wiley | |
dc.relation.isversionof | 10.1002/NLA.2289 | |
dc.rights | Creative Commons Attribution-Noncommercial-Share Alike | |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
dc.source | arXiv | |
dc.title | On algorithms for and computing with the tensor ring decomposition | |
dc.type | Article | |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | |
dc.contributor.department | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics | |
dc.relation.journal | Numerical Linear Algebra with Applications | |
dc.eprint.version | Author's final manuscript | |
dc.type.uri | http://purl.org/eprint/type/JournalArticle | |
eprint.status | http://purl.org/eprint/status/PeerReviewed | |
dc.date.updated | 2021-04-30T17:43:49Z | |
dspace.orderedauthors | Mickelin, O; Karaman, S | |
dspace.date.submission | 2021-04-30T17:43:50Z | |
mit.journal.volume | 27 | |
mit.journal.issue | 3 | |
mit.license | OPEN_ACCESS_POLICY | |
mit.metadata.status | Authority Work and Publication Information Needed | |