A Weighted Nuclear Norm Method for Tensor Completion

Geng, Juan; Wang, Lai-Sheng; Xu, Yitian; Wang, Xiuyu

doi:10.14257/ijsip.2014.7.1.01

Cited by 4 publications

(5 citation statements)

References 16 publications

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“…Similarly, the weighted nuclear norm has been applied to unfolded tensors for TC to recover lost data from remote sensing images [25,26]. The weighted tensor nuclear norm for TC uses reconstruction loss data as image data [27].…”

Section: Data Reconstruction With Missing Valuesmentioning

confidence: 99%

Weighted Robust Tensor Principal Component Analysis for the Recovery of Complex Corrupted Data in a 5G-Enabled Internet of Things

Vo,

Nguyen,

Yoo

2024

Applied Sciences

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Technological developments coupled with socioeconomic changes are driving a rapid transformation of the fifth-generation (5G) cellular network landscape. This evolution has led to versatile applications with fast data-transfer capabilities. The integration of 5G with wireless sensor networks (WSNs) has rendered the Internet of Things (IoTs) crucial for measurement and sensing. Although 5G-enabled IoTs are vital, they face challenges in data integrity, such as mixed noise, outliers, and missing values, owing to various transmission issues. Traditional methods such as the tensor robust principal component analysis (TRPCA) have limitations in preserving essential data. This study introduces an enhanced approach, the weighted robust tensor principal component analysis (WRTPCA), combined with weighted tensor completion (WTC). The new method enhances data recovery using tensor singular value decomposition (t-SVD) to separate regular and abnormal data, preserve significant components, and robustly address complex data corruption issues, such as mixed noise, outliers, and missing data, with the globally optimal solution determined through the alternating direction method of multipliers (ADMM). Our study is the first to address complex corruption in multivariate data using the WTRPCA. The proposed approach outperforms current techniques. In all corrupted scenarios, the normalized mean absolute error (NMAE) of the proposed method is typically less than 0.2, demonstrating strong performance even in the most challenging conditions in which other models struggle. This highlights the effectiveness of the proposed approach in real-world 5G-enabled IoTs.

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Section: Data Reconstruction With Missing Valuesmentioning

confidence: 99%

Weighted Robust Tensor Principal Component Analysis for the Recovery of Complex Corrupted Data in a 5G-Enabled Internet of Things

Vo,

Nguyen,

Yoo

2024

Applied Sciences

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“…In previous work, the model ( 17) has successfully imputed missing tensor data. Recent studies suggest that the results can be significantly improved, using certain nonconvex functions [35][36][37].…”

Section: Low N-rank Tensor Completion Problemmentioning

confidence: 99%

A Novel Log-Based Tensor Completion Algorithm

Geng¹,

Liang²,

Liu³

2020

ISI

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In recent years, tensor completion problem, as a higher order generalization of matrix completion, has received much attention from scholars engaged in computer vision, data mining, and neuroscience. The problem is often solved by convex relaxation, which minimizes the tensor nuclear norm instead of the n-rank of the tensor. However, tensor nuclear minimizes all the singular value at the same level, which is unfair to large singular values. To solve the problem, this paper defines a log function of tensor, and uses it as an approximation of tensor rank function. Then, a simple yet efficient log-based algorithm for tensor completion (Log-TC) was proposed to recover an underlying low n-rank tensor. The Log-TC was verified through experiments on randomly generated tensors and color image inpainting, in comparison with two tensor completion algorithms: fixed point iterative method for low-rank tensor completion (FP-LRTC) and fast low rank tensor completion algorithm (FaLRTC). The results show that our algorithm greatly outperformed the two contrastive methods.

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“…where X * is the tensor trace norm (tensor nuclear norm) defined as: Geng et al [10] introduced the weighted nuclear norm minimization to tensor completion, and the main problem is to solve the following model:…”

Section: Low N-rank Tensor Completion Problemmentioning

confidence: 99%

“…Signoretto et al [9] introduced a proper extension of the concept of Shatten-q norm for matrices and studied a general class of non-smooth convex optimization problem. Geng et al [10] generalized the weighted nuclear norm of matrices to the tensors and develop a majorization-minimization weighted soft thresholding algorithm for solving the weighted nuclear norm model of the low-rank tensor completion problem. Rauhut et al [11] proposed an extension of the iterative hard thresholding algorithm which used for recovery of low-rank matrices [12] and introduced the iterative hard thresholding algorithm (TIHT) for the higher order singular value decomposition.…”

Section: Introductionmentioning

confidence: 99%

An Accelerated Iterative Hard Thresholding Method for Tensor Completion

Geng

Yang

Wang

et al. 2015

Journal of Interdisciplinary Mathematics

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Tensor completion aims to recover an unknown low-rank or approximately low-rank tensor from a sampling set of its entries. It is shown that this problem can be solved via iterative hard thresholding method. However the orthogonality of the current step and the previous step leads to its slow convergence speed. In this paper, we propose an accelerated iterative hard thresholding method for tensor completion (ATIHT) by combining the current gradient and directions of several previous iterative steps as new search direction. *We make some comparison between numerical tests of our algorithm and TIHT, FP-LRTC and HaLRTC algorithms on randomly generated tensors and low-rank color image recovery problem. The results suggest that our method is more effective and promising.

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A Weighted Nuclear Norm Method for Tensor Completion

Cited by 4 publications

References 16 publications

Weighted Robust Tensor Principal Component Analysis for the Recovery of Complex Corrupted Data in a 5G-Enabled Internet of Things

Weighted Robust Tensor Principal Component Analysis for the Recovery of Complex Corrupted Data in a 5G-Enabled Internet of Things

A Novel Log-Based Tensor Completion Algorithm

An Accelerated Iterative Hard Thresholding Method for Tensor Completion

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