Zhu, Q., Wu, S., Fang, S., Wu, Q., Xie, S., & Agaian, S. (2025). Fast tensor robust principal component analysis with estimated multi-rank and Riemannian optimization. Applied Intelligence, 55(1). https://doi.org/10.1007/s10489-024-05899-9
Abstract:
Motivated by the fact that tensor robust principal component analysis (TRPCA) and its variants do not utilize the actual rank value, which limits the recovery performance, and their computational costs are always monumental for large-scale tensor recovery, a fast TRPCA is proposed to recover the low-rank tensor and sparse tensor by estimating the multi-rank vector and adopting Riemannian optimization strategy in this paper. Specifically, a fast multi-rank estimation of low-rank tensor is proposed by modifying the Gershgorin disk theorem-based matrix rank estimation. An innovative TRPCA with Estimated Multi-Rank (TRPCA-EMR) is proposed to eliminate hyperparameter tuning by imposing strictmulti-rank equality constraints. Additionally, Riemannian optimization is employed to project each frontal slice of the tensor in Fourier domain onto a low multi-rank manifold in efficiently coping with tensor Singular Value Decomposition (t-SVD) and reduce computational complexity. Experimental results on synthetic and real-world tensor datasets demonstrate TRPCA-EMR’s superior efficiency and effectiveness compared to existing methods, confirming its potential for practical applications and reassuring its reliability
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There was no specific funding for the research done
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