Weighted Robust Tensor Principal Component Analysis for the Recovery of Complex Corrupted Data in a 5G-Enabled Internet of Things †
Abstract
:1. Introduction
- This work presents an enhanced method for multivariate data reconstruction in 5G-operating IoTs. A TRPCA is combined with TC to enhance the method’s ability to handle missing data, noise, or missing values. This unique approach leverages correlations among multiple attributes to improve reconstruction performance.
- This study introduces a weighted approach to TC and the TRPCA, offering a means of handling singular values. In contrast to traditional methods, the proposed approach uses weighted tensor singular value thresholding (WTSVT) to shrink singular values based on their importance, potentially boosting reconstruction accuracy.
- The proposed approach effectively tackles complex types of corrupted data, such as mixture noise, outliers, and missing values, and stands out in comparison to other models.
2. Related Work
2.1. Data Reconstruction with Missing Values
2.2. Noise and Outlier Reduction Using Robust Principal Component Analysis
2.3. Primary Challenges in 5G-Enabled IoTs
3. Preliminaries
3.1. Introduction to Tensors
Algorithm 1 Tensor singular value decomposition (t-SVD). |
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3.2. Tensor Robust Principal Component Analysis with Weighted Tensor Nuclear Norm Minimization
3.3. Tensor Completion with Weighted Tensor Nuclear Norm Minimization
4. The Proposed Model
Algorithm 2 Weighted tensor singular value thresholding method (). |
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Algorithm 3 Weighted tensor completion. |
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Algorithm 4 Weighted robust tensor principal component analysis integrated with weighted tensor completion. |
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5. Experiments and Results
5.1. Dataset
5.2. Low-Rank Structures and Correlation in Multi-Attribute Sensing Data
5.3. Experiment Setup
5.4. Metrics
5.5. Results and Analysis
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Paper | Year | Multivariate | Univariate | Corrupted Type | Weighted | Method | |||
---|---|---|---|---|---|---|---|---|---|
Missing Value | Noise | Outlier | |||||||
Gaussian | Impulsive | ||||||||
[11] | 2021 | X | X | X | TRPCA | ||||
[12] | 2021 | X | X | X | TRPCA-TNN | ||||
[13] | 2022 | X | X | X | X | WRPCA | |||
Our | 2024 | X | X | X | X | X | X | WRTPCA-WTNN |
Notation | Definition |
---|---|
g, g, G, | scalar, vector, matrix, and tensor formats |
ith singular value | |
, , | ith horizontal slice, ith lateral slice, and ith frontal slice |
, ith frontal slice | |
Fourier transformation of , | |
Frobenius norm | |
nuclear norm | |
weighted nuclear norm | |
tensor Frobenius norm | |
tensor nuclear norm | |
weighted tensor nuclear norm | |
rank of matrix G | |
tubal rank of tensor | |
t-SVD | tensor singular value decomposition |
ADMM | alternative direction method of multipliers |
WTNN | weighted tensor nuclear norm |
position of missing elements in | |
projection on |
NDBC-TAO | U.S. Climate Normal | |
---|---|---|
No. of nodes | 8 | 89 |
Period of observation | 1 October 2020 00:00:00 –3 October 2020 23:50:00 | 1 December 2022 00:00:00 –15 December 2022 23:00:00 |
Measured attribute | Temperature, density, and salinity | Dew, temperature, and wind |
Sampling period | 10 min | 1 h |
Tensor dimension | 8 × 3 × 432 | 89 × 3 × 360 |
Corruption Type | Parameter | Range | Step Size |
---|---|---|---|
Gaussian noise | 11 to 20 | 1 | |
Impulsive noise | 0.1 to 0.55 | 0.05 | |
Outlier | k | 6 to 15 | 1 |
Missing value | 0.1 to 0.55 | 0.05 |
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Vo, H.H.-P.; Nguyen, T.M.; Yoo, M. Weighted Robust Tensor Principal Component Analysis for the Recovery of Complex Corrupted Data in a 5G-Enabled Internet of Things. Appl. Sci. 2024, 14, 4239. https://doi.org/10.3390/app14104239
Vo HH-P, Nguyen TM, Yoo M. Weighted Robust Tensor Principal Component Analysis for the Recovery of Complex Corrupted Data in a 5G-Enabled Internet of Things. Applied Sciences. 2024; 14(10):4239. https://doi.org/10.3390/app14104239
Chicago/Turabian StyleVo, Hanh Hong-Phuc, Thuan Minh Nguyen, and Myungsik Yoo. 2024. "Weighted Robust Tensor Principal Component Analysis for the Recovery of Complex Corrupted Data in a 5G-Enabled Internet of Things" Applied Sciences 14, no. 10: 4239. https://doi.org/10.3390/app14104239
APA StyleVo, H. H.-P., Nguyen, T. M., & Yoo, M. (2024). Weighted Robust Tensor Principal Component Analysis for the Recovery of Complex Corrupted Data in a 5G-Enabled Internet of Things. Applied Sciences, 14(10), 4239. https://doi.org/10.3390/app14104239