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タイトル: | Reshaped tensor nuclear norms for higher order tensor completion |
著者: | Wimalawarne, Kishan Mamitsuka, Hiroshi ![]() ![]() ![]() |
著者名の別形: | 馬見塚, 拓 |
キーワード: | Tensor nuclear norm Reshaping CP rank Generalization bounds |
発行日: | Mar-2021 |
出版者: | Springer Nature |
誌名: | Machine Learning |
巻: | 110 |
開始ページ: | 507 |
終了ページ: | 531 |
抄録: | We investigate optimal conditions for inducing low-rankness of higher order tensors by using convex tensor norms with reshaped tensors. We propose the reshaped tensor nuclear norm as a generalized approach to reshape tensors to be regularized by using the tensor nuclear norm. Furthermore, we propose the reshaped latent tensor nuclear norm to combine multiple reshaped tensors using the tensor nuclear norm. We analyze the generalization bounds for tensor completion models regularized by the proposed norms and show that the novel reshaping norms lead to lower Rademacher complexities. Through simulation and real-data experiments, we show that our proposed methods are favorably compared to existing tensor norms consolidating our theoretical claims. |
著作権等: | This is a post-peer-review, pre-copyedit version of an article published in Machine Learning. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10994-020-05927-y. The full-text file will be made open to the public on 3 January 2022 in accordance with publisher's 'Terms and Conditions for Self-Archiving'. This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。 |
URI: | http://hdl.handle.net/2433/262422 |
DOI(出版社版): | 10.1007/s10994-020-05927-y |
出現コレクション: | 学術雑誌掲載論文等 |
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