Efficient construction of tensor ring representations from sampling

dc.contributor.author

Khoo, Y

dc.contributor.author

Lu, J

dc.contributor.author

Ying, L

dc.date.accessioned

2017-11-30T21:56:25Z

dc.date.available

2017-11-30T21:56:25Z

dc.date.issued

2017-11-30

dc.description.abstract

In this note we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least-squares (ALS). Since the function has size exponential in $d$ where $d$ is the number of dimensions, we propose efficient sampling scheme to obtain $O(d)$ important samples in order to learn the tensor ring. Furthermore, we devise an initialization method for ALS that allows fast convergence in practice. Numerical examples show that to approximate a function with similar accuracy, the tensor ring format provided by the proposed method has less parameters than tensor-train format and also better respects the structure of the original function.

dc.identifier

http://arxiv.org/abs/1711.00954v1

dc.identifier.uri

https://hdl.handle.net/10161/15779

dc.publisher

Society for Industrial & Applied Mathematics (SIAM)

dc.subject

math.NA

dc.subject

math.NA

dc.subject

65D15, 33F05, 15A69

dc.subject

G.1.3; G.1.10

dc.title

Efficient construction of tensor ring representations from sampling

dc.type

Journal article

duke.contributor.orcid

Lu, J|0000-0001-6255-5165

pubs.author-url

http://arxiv.org/abs/1711.00954v1

pubs.organisational-group

Chemistry

pubs.organisational-group

Duke

pubs.organisational-group

Mathematics

pubs.organisational-group

Physics

pubs.organisational-group

Temp group - logins allowed

pubs.organisational-group

Trinity College of Arts & Sciences

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