Overcomplete tensor decomposition via convex optimization

Qiuwei Li; Ashley Prater; Lixin Shen; Gongguo Tang

doi:10.1109/CAMSAP.2015.7383734

Overcomplete tensor decomposition via convex optimization

Qiuwei Li, Ashley Prater, Lixin Shen, Gongguo Tang

Research output: Chapter in Book/Entry/Poem › Conference contribution

13 Scopus citations

Abstract

This work develops theories and computational methods for overcomplete, non-orthogonal tensor decomposition using convex optimization. Under an incoherence condition of the rank-one factors, we show that one can retrieve tensor decomposition by solving a convex, infinite-dimensional analog of ℓ1 minimization on the space of measures. The optimal value of this optimization defines the tensor nuclear norm. Two computational schemes are proposed to solve the infinite-dimensional optimization: semidefinite programs based on sum-of-squares relaxations and nonlinear programs that are an exact reformulation of the tensor nuclear norm. The latter exhibits superior performance compared with the state-of-the-art tensor decomposition methods.

Original language	English (US)
Title of host publication	2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	53-56
Number of pages	4
ISBN (Electronic)	9781479919635
DOIs	https://doi.org/10.1109/CAMSAP.2015.7383734
State	Published - 2015
Event	6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015 - Cancun, Mexico Duration: Dec 13 2015 → Dec 16 2015

Publication series

Name	2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015

Other

Other	6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
Country/Territory	Mexico
City	Cancun
Period	12/13/15 → 12/16/15

ASJC Scopus subject areas

Signal Processing
Computational Mathematics

Access to Document

10.1109/CAMSAP.2015.7383734

Cite this

Li, Q., Prater, A., Shen, L., & Tang, G. (2015). Overcomplete tensor decomposition via convex optimization. In 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015 (pp. 53-56). Article 7383734 (2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CAMSAP.2015.7383734

Overcomplete tensor decomposition via convex optimization. / Li, Qiuwei; Prater, Ashley; Shen, Lixin et al.
2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 53-56 7383734 (2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015).

Research output: Chapter in Book/Entry/Poem › Conference contribution

Li, Q, Prater, A, Shen, L & Tang, G 2015, Overcomplete tensor decomposition via convex optimization. in 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015., 7383734, 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015, Institute of Electrical and Electronics Engineers Inc., pp. 53-56, 6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015, Cancun, Mexico, 12/13/15. https://doi.org/10.1109/CAMSAP.2015.7383734

Li Q, Prater A, Shen L, Tang G. Overcomplete tensor decomposition via convex optimization. In 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 53-56. 7383734. (2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015). doi: 10.1109/CAMSAP.2015.7383734

Li, Qiuwei ; Prater, Ashley ; Shen, Lixin et al. / Overcomplete tensor decomposition via convex optimization. 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 53-56 (2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015).

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AB - This work develops theories and computational methods for overcomplete, non-orthogonal tensor decomposition using convex optimization. Under an incoherence condition of the rank-one factors, we show that one can retrieve tensor decomposition by solving a convex, infinite-dimensional analog of ℓ1 minimization on the space of measures. The optimal value of this optimization defines the tensor nuclear norm. Two computational schemes are proposed to solve the infinite-dimensional optimization: semidefinite programs based on sum-of-squares relaxations and nonlinear programs that are an exact reformulation of the tensor nuclear norm. The latter exhibits superior performance compared with the state-of-the-art tensor decomposition methods.

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Overcomplete tensor decomposition via convex optimization

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