An approximation method of CP rank for third-order tensor completion

Chao Zeng; Tai Xiang Jiang; Michael K. Ng

doi:10.1007/s00211-021-01185-9

An approximation method of CP rank for third-order tensor completion

Chao Zeng^*, Tai Xiang Jiang, Michael K. Ng

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

3 Citations (Scopus)

Abstract

We study the problem of third-order tensor completion based on low CP rank recovery. Due to the NP-hardness of the calculation of CP rank, we propose an approximation method by using the sum of ranks of a few matrices as an upper bound of CP rank. We show that such upper bound is between CP rank and the square of CP rank of a tensor. This approximation would be useful when the CP rank is very small. Numerical algorithms are developed and examples are presented to demonstrate that the tensor completion performance by the proposed method is better than that of existing methods.

Original language	English
Pages (from-to)	727-757
Number of pages	31
Journal	Numerische Mathematik
Volume	147
Issue number	3
DOIs	https://doi.org/10.1007/s00211-021-01185-9
Publication status	Published - Mar 2021

Scopus Subject Areas

Computational Mathematics
Applied Mathematics

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title = "An approximation method of CP rank for third-order tensor completion",

abstract = "We study the problem of third-order tensor completion based on low CP rank recovery. Due to the NP-hardness of the calculation of CP rank, we propose an approximation method by using the sum of ranks of a few matrices as an upper bound of CP rank. We show that such upper bound is between CP rank and the square of CP rank of a tensor. This approximation would be useful when the CP rank is very small. Numerical algorithms are developed and examples are presented to demonstrate that the tensor completion performance by the proposed method is better than that of existing methods.",

author = "Chao Zeng and Jiang, {Tai Xiang} and Ng, {Michael K.}",

note = "Funding information: T.-X. Jiang{\textquoteright}s research is supported in part by the National Natural Science Foundation of China (12001446) and the Fundamental Research Funds for the Central Universities (JBK2102001). M. Ng{\textquoteright}s research is supported in part by the HKRGC GRF 12306616, 12200317, 12300218 and 12300519, and HKU 104005583. Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021",

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N1 - Funding information: T.-X. Jiang’s research is supported in part by the National Natural Science Foundation of China (12001446) and the Fundamental Research Funds for the Central Universities (JBK2102001). M. Ng’s research is supported in part by the HKRGC GRF 12306616, 12200317, 12300218 and 12300519, and HKU 104005583. Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH, DE part of Springer Nature 2021

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N2 - We study the problem of third-order tensor completion based on low CP rank recovery. Due to the NP-hardness of the calculation of CP rank, we propose an approximation method by using the sum of ranks of a few matrices as an upper bound of CP rank. We show that such upper bound is between CP rank and the square of CP rank of a tensor. This approximation would be useful when the CP rank is very small. Numerical algorithms are developed and examples are presented to demonstrate that the tensor completion performance by the proposed method is better than that of existing methods.

AB - We study the problem of third-order tensor completion based on low CP rank recovery. Due to the NP-hardness of the calculation of CP rank, we propose an approximation method by using the sum of ranks of a few matrices as an upper bound of CP rank. We show that such upper bound is between CP rank and the square of CP rank of a tensor. This approximation would be useful when the CP rank is very small. Numerical algorithms are developed and examples are presented to demonstrate that the tensor completion performance by the proposed method is better than that of existing methods.

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DO - 10.1007/s00211-021-01185-9

M3 - Journal article

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ER -

An approximation method of CP rank for third-order tensor completion

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