Tensor completion using geodesics on Segre manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866909233246633984 |
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| author | Swijsen, Lars Van der Veken, Joeri Vannieuwenhoven, Nick |
| author_facet | Swijsen, Lars Van der Veken, Joeri Vannieuwenhoven, Nick |
| contents | We propose a Riemannian conjugate gradient (CG) optimization method for finding low rank approximations of incomplete tensors. Our main contribution consists of an explicit expression of the geodesics on the Segre manifold. These are exploited in our algorithm to perform the retractions. We apply our method to movie rating predictions in a recommender system for the MovieLens dataset, and identification of pure fluorophores via fluorescent spectroscopy with missing data. In this last application, we recover the tensor decomposition from less than $10\%$ of the data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_00735 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Tensor completion using geodesics on Segre manifolds Swijsen, Lars Van der Veken, Joeri Vannieuwenhoven, Nick Differential Geometry Information Retrieval Machine Learning 15A69, 53C22, 53C30, 65K05, 90C30, 14P10, 15A83 We propose a Riemannian conjugate gradient (CG) optimization method for finding low rank approximations of incomplete tensors. Our main contribution consists of an explicit expression of the geodesics on the Segre manifold. These are exploited in our algorithm to perform the retractions. We apply our method to movie rating predictions in a recommender system for the MovieLens dataset, and identification of pure fluorophores via fluorescent spectroscopy with missing data. In this last application, we recover the tensor decomposition from less than $10\%$ of the data. |
| title | Tensor completion using geodesics on Segre manifolds |
| topic | Differential Geometry Information Retrieval Machine Learning 15A69, 53C22, 53C30, 65K05, 90C30, 14P10, 15A83 |
| url | https://arxiv.org/abs/2108.00735 |