## 3 Case Study
### Data Prediction and Analysis  
In the case of random missing, the time series of the Shuizhuyuan landslide is predicted for 300 days after data missing processing is performed with a missing ratio of 40%. The time series of four sensors numbered SZY-02, SZY-03, SZY-06 and SZY-08 are analyzed separately, and the prediction results are shown in Figure 8. The analysis shows that the prediction results are ultimately consistent with the original displacement data in the case of the 40% missing data ratio. The MLATC model realizes well the deformation trend feature fitting of displacement, and effectively predicts the displacement data. Similarly, after processing the dataset of the Shuizhuyuan landslide with 40% non-random missing, the data completion effect is shown in Figure 9. The prediction results of MLATC model are also ultimately close to the original displacement data. Although there are some fluctuations in the prediction data, the overall effective fitting of displacement is still achieved. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **TRMF** & **HALRTC** & **MLATC** \\ \hline RM 5\% & 11.8535/14.0634 & 0.8087/2.7628 & 0.7676/0.9880 \\ RM 10\% & 10.2782/16.5925 & 0.9729/3.0545 & 0.7263/1.0339 \\ RM 20\% & 11.7037/18.1142 & 11.7976/25.2256 & 0.9494/1.7648 \\ RM 40\% & 13.8347/25.9556 & 15.0777/38.6958 & 1.4817/1.8889 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Evaluation metrics for data completion in the RM case (MAPE/RMSE). Figure 8: Prediction of displacement data (RM40%). (**a**) Point SZY-02; (**b**) point SZY-03; (**c**) point SZY-06; (**d**) point SZY-08. The blue curve represents the measured data and the red curve represents the predicted data. The prediction effect of MLATC model under random and non-random missing is shown in Tables 3 and 4. By analyzing the prediction results of each model, it can be proven that the prediction accuracy of the time series model is effectively improved after converting the original time series into a tensor structure in this method. The prediction accuracy of both HALRTC model and MLATC model has improved significantly over the prediction accuracy of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **TRMF** & **HALRTC** & **MLATC** \\ \hline NM5\% & 39.4527/102.047 & 14.9328/38.9776 & 1.1079/3.6676 \\ NM10\% & 42.7754/110.746 & 14.2427/37.2552 & 1.1037/3.6588 \\ NM20\% & 49.9770/126.921 & 12.6523/33.3975 & 1.1099/3.6785 \\ NM40\% & 83.7004/212.867 & 11.5458/30.6736 & 1.1694/3.8755 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Evaluation metrics for data prediction in the NM case (MAPE/RMSE). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **TRMF** & **HALRTC** & **MLATC** \\ \hline RM5\% & 39.6023/102.415 & 15.2062/39.8024 & 1.1084/3.6774 \\ RM10\% & 41.1064/106.681 & 14.8872/39.0352 & 1.0792/3.6587 \\ RM20\% & 50.2660/127.588 & 14.8241/39.1718 & 1.1120/3.7032 \\ RM40\% & 83.7915/213.040 & 13.8827/37.1245 & 1.1012/3.6665 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Evaluation metrics for data prediction in the RM case (MAPE/RMSE). Figure 9: Prediction of displacement data (NM40%). (**a**) Point SZY-02; (**b**) point SZY-03; (**c**) point SZY-06; (**d**) point SZY-08. The blue curve represents the measured data and the red curve represents the predicted data. TRMF. This indicates that although the TRMF model captures the global consistency of the time series, the model mainly acts on the latent layer matrix data, which may cause the local trend feature information between different sensors to be ignored, thus affecting the prediction accuracy. Due to the intervention of the autoregressive norm, the prediction of HALRTC and MLATC models is significantly better than that of TRMF model, and the MAPE and RMSE accuracy of the models are higher.