Reshaped tensor nuclear norms for higher order tensor completion

Kishan Wimalawarne*, Hiroshi Mamitsuka

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


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.

Original languageEnglish
Pages (from-to)507-531
Number of pages25
JournalMachine Learning
Issue number3
Early online date2021
Publication statusPublished - Mar 2021
MoE publication typeA1 Journal article-refereed


  • CP rank
  • Generalization bounds
  • Reshaping
  • Tensor nuclear norm


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