## 5 Experiments and Results
### Experiment Setup  
This section outlines a series of experiments conducted to confirm the efficacy of WRTPCA_WTNN, the proposed method. Its performance was compared with that of three other methods: the TRPCA [22], WTC [24], and the TRPCA combined with TC using the weighted sum tensor nuclear norm (TRPCA_TNN) [11]. This study used two real-world IoT datasets, namely the U.S. Climate Normal and NDBC-TAO datasets, to analyze their recovery under various conditions, including sparse mixed noise, outliers, and missing values. Various methods were used in these experiments to achieve optimal visual results.  
All methods were carefully fine-tuned and tested repeatedly, 20 times in total, for all corrupted cases. The average values were calculated to obtain the results. Data corruption was characterized using four factors: Gaussian noise, impulsive noise, outliers, and missing values.  
In extensive experiments, we assessed the performance of our model using different types of corrupted data. For Gaussian noise, we chose a zero mean and investigated ten variance levels (\(\sigma^{2}\)) ranging from 11 to 20 in increments of one. Impulsive noise was examined at ten percentage levels (\(\rho_{n}\)) from 0.1 to 0.55, with a step size of 0.05. Outliers were studied at ten magnitudes (\(k\)) ranging from 6 to 15 with a step size of 1, each being k times the standard deviation (\(\sigma\)) of each attribute. Missing values were explored at ten ratio levels (\(\rho_{m}\)) from 0.1 to 0.55, with a step size of 0.05. Table 4 presents detailed parameters of the four corruption types.  
In each experimental case, we varied only the type of corruption across the levels and held the other parameters constant. The fixed values for the experiment were a Gaussian noise variance (\(\sigma^{2}\)) set at 15, an impulsive noise percentage (\(\rho_{n}\)) set at 0.3, an outlier magnitude (\(k\)) set at 15, and a missing ratio (\(\rho_{m}\)) set at 0.3. For instance, in the Gaussian noise experiment, we altered the Gaussian noise variances (\(\sigma^{2}\)) from 11 to 20 in steps of 1 while maintaining an impulsive noise percentage (\(\rho_{n}\)) of 0.3, an outlier magnitude (\(k\)) of 15, and a missing ratio (\(\rho_{m}\)) of 0.3.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Corruption Type** & **Parameter** & **Range** & **Step Size** \\ \hline Gaussian noise & \(\sigma^{2}\) & 11 to 20 & 1 \\ Impulsive noise & \(\rho_{n}\) & 0.1 to 0.55 & 0.05 \\ Outlier & \(k\) & 6 to 15 & 1 \\ Missing value & \(\rho_{m}\) & 0.1 to 0.55 & 0.05 \\ \hline \end{tabular}
\end{table}
Table 4: Detail parameters of each corruption type.  
Figure 7: Low-rank structure within sensing data utilizing the singular values of the core tensor’s block diagonal matrices.  
Two algorithms, labeled Algorithms 3 and 4, were initialized with different WTSVT weight values. Specifically, \(\mathbf{\omega}=(1;1.9;2.1)\) was used in Algorithm 4, whereas \(\mathbf{\omega}=(1;1;1.6)\) was used in Algorithm 3. It was necessary to select appropriate values for \(\mu_{0}\), \(\mu_{\max}\), \(\epsilon\), and \(\rho\), which were the characteristics of the sensing data. In this study, the values of \(\mu_{0}\), \(\mu_{\max}\), \(\epsilon\), and \(\rho\) were set to \(1\times 10^{-1}\), \(1\times 10^{10}\), \(1\times 10^{-8}\), and \(1.1\), respectively. The experimental results showed promising outcomes.  
The experimental results were averaged across 20 replicates. All simulations used MATLAB R2021a on an Intel(R) Core(TM) i7-10700K CPU 3.80 GHz (Intel, Santa Clara, CA, USA).