## 5 Case Studies
### Comparison with Other Data-Level Methods  
In this section, the DSEC method is compared with some state-of-the-art data-level methods for imbalanced TSSP problem, including random oversampling (ROS) [14], random undersampling (RUS) [20], the synthetic minority over-sampling technique (SMOTE) [26], ADASYN, cluster-based undersampling (CUS) [27], and EasyEnsemble [20]. The detailed processes using these methods for the imbalanced data problem of TSSP are described as follows:  
1. ROS: A new unstable set \(U_{\text{ROS}}\) is sampled with replacement from the original unstable set \(U\), so that \(|U_{\text{ROS}}|=N_{S}\). Then the unstable set \(\text{U}_{\text{ROS}}\) is combined with stable set \(S\) to form a new training set.
2. RUS: A new stable set, \(S_{\text{RUS}}\), is sampled with replacement from the original stable set, \(S\), so that \(|S_{\text{ROS}}|=N_{U}\). Then the stable set \(S_{\text{RUS}}\) is combined with stable set \(U\) to form a new training set.
3. SMOTE: New \(N_{S}\)-\(N_{U}\) unstable samples are generated by using SMOTE. Then, these unstable samples are added into the original training set, so that \(|U_{\text{SMOTE}}|=N_{S}\) in the new training set.
4. ADASYN: New \(N_{S}\)-\(N_{U}\) unstable samples are generated by using ADASYN. Then, these unstable samples are added into the original training set, so that \(|U_{\text{ADASYN}}|=N_{S}\) in the new training set.
5. CUS: The _k-mediods_ algorithm is used for clustering the stable samples with \(N_{U}\) clusters. A new unstable set \(U_{\text{CUS}}\) is constructed with the \(N_{U}\) samples from cluster center, so that \(|U_{\text{CUS}}|=N_{S}\). Then the unstable set \(U_{\text{CUS}}\) is combined with stable set \(S\) to form a new training set.
6. EasyEnsemble: Randomly sample a stable subset \(S_{\text{Easy}}\) from the original stable set \(S\), so that \(|S_{\text{Easy}}|=N_{U}\). Then the stable set \(S_{\text{Easy}}\) is combined with stable set \(U\) to form a new training subset. Repeat above process \(T_{\text{Easy}}\) times and obtain \(T_{\text{Easy}}\) training subsets. Here, \(T_{\text{Easy}}\) is set to 5.  
The AdaBoost classifier is employed for data-level methods hereinbefore, and considering the randomness of these methods, the average results of 10 repeated experiments are taken for comparison. The training time and classification results of these methods are compared and shown in Table 6.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Training Time (s)** & **TSR (\%)** & **TUR (\%)** & **GM (\%)** \\ \hline ROS & 32.53 & 98.35 & 85.55 & 91.73 \\ RUS & 3.46 & 91.98 & 95.89 & 93.91 \\ SMOTE & 32.85 & 97.40 & 89.84 & 93.54 \\ ADASYN & 45.28 & 96.95 & 90.94 & 93.90 \\ CUS & 51.36 & 95.41 & 92.13 & 93.75 \\ EasyEnsemble & 17.16 & 92.13 & 96.26 & 94.17 \\ DSEC & 16.57 & 92.28 & 97.03 & 94.62 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Results comparison of imbalanced data process methods.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Parameters** & **TSR (\%)** & **TUR (\%)** & **GM (\%)** \\ \hline SVM & C = 16; \(\gamma=1\) & 98.14 & 82.09 & 89.76 \\ ELM & L = 850 & 98.15 & 77.99 & 87.49 \\ AdaBoost & R = 40 & 98.37 & 85.02 & 91.45 \\ CART & – & 96.36 & 81.69 & 88.72 \\ DSEC & R = 40 & 92.28 & 97.03 & 94.62 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Results comparison with traditional machine learning methods.  
From Table 6, the DSEC method has higher TUR and GM values than other imbalanced data process methods, which means that the proposed method has a better classification performance both in unstable samples and overall samples and costs relatively less training time than other methods, except RUS. Therefore, the DSEC method is superior for TSSP with imbalanced data. Furthermore, the total time cost of DSEC method on testing data is 0.20 s, i.e., the computation time of one sample, is about 0.06 ms, which demonstrates the feasibility of applying the method for online application.