Convex Coupled Matrix and tensor completion

Research output: Contribution to journalLetter


Research units

  • Kyoto University
  • The Institute of Statistical Mathematics
  • Japan Science and Technological Agency


We propose a set of convex low-rank inducing norms for coupled matrices and tensors (hereafter referred to as coupled tensors), in which information is shared between thematrices and tensors through commonmodes. More specifically,we first propose a mixture of the overlapped trace norm and the latent normswith thematrix trace norm, and then, propose a completion model regularized using these norms to impute coupled tensors. A key advantage of the proposed norms is that they are convex and can be used to find a globally optimal solution, whereas existingmethods for coupled learning are nonconvex.We also analyze the excess risk bounds of the completionmodel regularized using our proposed norms and show that they can exploit the low-rankness of coupled tensors, leading to better bounds compared to those obtained using uncoupled norms. Through synthetic and real-data experiments, we show that the proposed completion model compares favorably with existing ones.


Original languageEnglish
Pages (from-to)3095-3127
Number of pages33
JournalNeural Computation
Issue number11
Publication statusPublished - 1 Nov 2018
MoE publication typeA1 Journal article-refereed

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