Robust Low-Tubal-Rank Tensor Completion Based on Tensor Factorization and Maximum Correntopy Criterion

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low tubal rank was shown to give a valuable characterization of the inherent low-rank structure of a tensor. While some l...

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Veröffentlicht in:IEEE transaction on neural networks and learning systems Jg. 35; H. 10; S. 14603 - 14617
Hauptverfasser: He, Yicong, Atia, George K.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: United States IEEE 01.10.2024
Schlagworte:
Alternating minimization
Computational modeling
correntropy
half-quadratic (HQ)
Linear programming
Matrix decomposition
Measurement uncertainty
Minimization
Signal processing algorithms
tensor completion
tensor factorization
Tensors
ISSN:2162-237X, 2162-2388, 2162-2388
Online-Zugang:Volltext
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Zusammenfassung:The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low tubal rank was shown to give a valuable characterization of the inherent low-rank structure of a tensor. While some low-tubal-rank tensor completion algorithms with favorable performance have been recently proposed, these algorithms utilize second-order statistics to measure the error residual, which may not work well when the observed entries contain large outliers. In this article, we propose a new objective function for low-tubal-rank tensor completion, which uses correntropy as the error measure to mitigate the effect of the outliers. To efficiently optimize the proposed objective, we leverage a half-quadratic minimization technique whereby the optimization is transformed to a weighted low-tubal-rank tensor factorization problem. Subsequently, we propose two simple and efficient algorithms to obtain the solution and provide their convergence and complexity analysis. Numerical results using both synthetic and real data demonstrate the robust and superior performance of the proposed algorithms.
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ISSN:2162-237X
2162-2388
2162-2388
DOI:10.1109/TNNLS.2023.3280086