Convex Coupled Matrix and Tensor Completion

Neural Computation
Kishan WimalawarneHiroshi Mamitsuka

Abstract

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 the matrices and tensors through common modes. More specifically, we first propose a mixture of the overlapped trace norm and the latent norms with the matrix 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 existing methods for coupled learning are nonconvex. We also analyze the excess risk bounds of the completion model 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.

References

Jan 24, 2009·Proceedings of the National Academy of Sciences of the United States of America·Thomas V Pollet, Daniel Nettle
May 15, 2013·Advances in Skin & Wound Care·Barry LadizinskiR Gary Sibbald
Aug 10, 2013·The International Journal of Tuberculosis and Lung Disease : the Official Journal of the International Union Against Tuberculosis and Lung Disease·K N OtwombeN Martinson
Jul 13, 2014·BMC Bioinformatics·Evrim AcarRasmus Bro
Feb 19, 2016·Neural Computation·Kishan WimalawarneMasashi Sugiyama

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Citations

Dec 14, 2019·Neural Computation·Kishan WimalawarneHiroshi Mamitsuka

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Methods Mentioned

BETA
nuclear magnetic resonance

Software Mentioned

Matlab
linspace
Tensorlab

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