## 4 Results and Discussion
### Real-World Multiplex Networks
#### 4.2.1 Real-World Multiplex Networks Clustering  
In this section, the experimental results of the proposed **Mx-CRTSA** method on real multiplex networks are presented and compared to other well-known methods in clustering multiplex networks through several clustering quality measures. These quality measures include ACC, NMI, AR and F-score. The comparison results are summarized in Table 4, where the best performance is in bold font. The evaluation metrics results reported in Table 4 illustrate that the proposed method achieves the best performance across the different networks. For instance, **Mx-CRTSA** is the only method that detects the correct community structure, with a score of 1 in the different quality metrics in both **CKM** and **Cora** networks. In particular, the proposed **Mx-CRTSA** enhances the performance by 3.7%, 98.3%, 17.9%, 4.2%, 17.9%, 96.8%, 5.2%, 52.8% and 22.2% in the **CKM** network in terms of NMI over the **CSNMTF**, **CPNMF**, **CSNMF**, **SCML**, **RMSC**, **PM**, **CentroidCoreg**, **DiMMA** and **2 CMV**, respectively, whereas in **Cora**, the performance is boosted by 49.2%, 55.8%, 39.7%, 2.1%, 49.7%, 2.1%, 1.8%, 54.5% and 49.3% in terms of ACC over the **CSNMTF**, **CPNMF**, **CSNMF**, **SCML**, **RMSC**, **PM**, **CentroidCoreg**, **DiMMA** and **2 CMV**, respectively. Another example is the **NRC** network, where **Mx-CRTSA** improves the performance by 26.9%, 39.6%, 21.1%, 15.7%, 17.3%, 17.6%, 19.2%, 24.7% and 20.8% in terms of the NMI over **CSNMTF**, **CPNMF**, **CSNMF**, **SCML**, **RMSC**, **PM**, **CentroidCoreg**, **DiMMA** and **2 CMV**, respectively. In the **C. Elegans** network, the **Mx-CRTSA** algorithm improves the quality of the detected structure by approximately 4.8%, 12.7%, 6.7%, 6.1%, 20.6%, 8.2%, 7.7%, 16.8% and 17.5% in terms of the NMI over the **CSNMTF**, **CPNMF**, **CSNMF**, **SCML**, **RMSC**, **PM**, **CentroidCoreg**, **DiMMA** and **2 CMV** method, respectively. Furthermore, **Mx-CRTSA** performs better than **CSNMTF**, **CPNMF**, **CSNMF**, **SCML**, **RMSC**, **PM**, **CentroidCoreg**, **DiMMA** and **2 CMV** by 70.4%, 75.3%, 71.7%, 25.4%, 9.4%, 46.9%, 22.8%, 53.7% and 27.5% in the **BBCSport** network in terms of ACC, respectively. For the 100**leaves** network, the proposed **Mx-CRTSA** improves the performance by 53.8%, 71.7%, 13.9%, 3.3%, 16.6%, 28.8%, 5.1%, 35.2% and 11.7% in terms of the F-score over the **CSNMTF**, **CPNMF**, **CSNMF**, **SCML**, **RMSC**, **PM**, **CentroidCoreg**, **DiMMA** and 2 CMV**, respectively. The improvement in performance of the proposed approach with respect to the other algorithms and the different metrics is presented in Table 5. These results demonstrate the enhancement achieved by the proposed algorithm with respect to the other methods, where estimating a clean adjacency tensor and employing it to discover the communities by optimizing the contribution of the individual subspaces to the common subspace boosts the accuracy of the detected community structure. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Network** & **Nodes** & **Layers** & **Clusters** \\ \hline
**NRC** & 136 & 3 & 8 \\
**CKM** & 246 & 3 & 4 \\
**C. Elegans** & 279 & 3 & 12 \\
**Cora** & 292 & 3 & 3 \\
**BBCSPORT** & 544 & 2 & 5 \\
**Wikipedia** & 693 & 2 & 10 \\
**COIL20** & 1440 & 3 & 20 \\
100**Leaves** & 1600 & 3 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Description of the real-world multiplex networks.