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. | |
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dc.identifier.uri | ||
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 | ||
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 |