Scaled coupled norms and coupled higher-order tensor completion

Kishan Wimalawarne, Makoto Yamada, Hiroshi Mamitsuka*

*Corresponding author for this work

Research output: Contribution to journalLetterScientificpeer-review

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Recently, a set of tensor norms known as coupled norms has been proposed as a convex solution to coupled tensor completion. Coupled norms have been designed by combining low-rank inducing tensor norms with the matrix trace norm. Though coupled norms have shown good performances, they have two major limitations: they do not have a method to control the regularization of coupled modes and uncoupled modes, and they are not optimal for couplings among higher-order tensors. In this letter, we propose a method that scales the regularization of coupled components against uncoupled components to properly induce the low-rankness on the coupled mode. We also propose coupled norms for higher-order tensors by combining the square norm to coupled norms. Using the excess risk-bound analysis, we demonstrate that our proposed methods lead to lower risk bounds compared to existing coupled norms. We demonstrate the robustness of our methods through simulation and real-data experiments.

Original languageEnglish
Pages (from-to)447-484
Number of pages38
JournalNeural Computation
Issue number2
Publication statusPublished - 1 Feb 2020
MoE publication typeA1 Journal article-refereed


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