Reshaped tensor nuclear norms for higher order tensor completion

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2021-03
Major/Subject
Mcode
Degree programme
Language
en
Pages
25
Series
Machine Learning
Abstract
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.
Description
Keywords
CP rank, Generalization bounds, Reshaping, Tensor nuclear norm
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Citation
Wimalawarne , K & Mamitsuka , H 2021 , ' Reshaped tensor nuclear norms for higher order tensor completion ' , Machine Learning , vol. 110 , no. 3 , pp. 507-531 . https://doi.org/10.1007/s10994-020-05927-y