# An Empirical Study of Cluster-Based MOEA/D Bare Bones PSO for Data Clustering +
## 4 Results
### MOO Comparisons

Table 2: Performance of CM-BBPSO and other clustering algorithms on CMC dataset with the best result produced by the algorithm presented in bold. \begin{table}
\begin{tabular}{l c c c c c c} \hline
**Clus Algo** & **Accuracy** & **F1** & **Kappa** & **BSS** & **WSS** & **QE** \\ \hline CM-BBPSO & \(0.402\pm 0.02\) & \(0.371\pm 0.04\) & \(0.089\pm 0.05\) & \(6590\pm 1540\) & \(4150\pm 186\) & \(2.88\pm 0.25\) \\ IB-Fuzzy & \(0.393\pm 0.02\) & \(0.368\pm 0.04\) & \(0.081\pm 0.05\) & \(5650\pm 1380\) & \(4260\pm 194\) & \(2.9\pm 0.14\) \\ IB-QPSO & \(0.401\pm 0.02\) & \(0.321\pm 0.05\) & \(0.056\pm 0.05\) & \(3980\pm 1130\) & \(4120\pm 157\) & \(2.97\pm 0.29\) \\ M-Fuzzy & \(\mathbf{0.404\pm 0.02}\) & \(\mathbf{0.383\pm 0.03}\) & \(\mathbf{0.100\pm 0.04}\) & \(5310\pm 1280\) & \(\mathbf{3950\pm 174}\) & \(\mathbf{2.72\pm 0.15}\) \\ M-QPSO & \(0.402\pm 0.01\) & \(0.356\pm 0.04\) & \(0.069\pm 0.04\) & \(5820\pm 1370\) & \(4050\pm 129\) & \(2.86\pm 0.23\) \\ M-BBPSO & \(0.400\pm 0.02\) & \(0.352\pm 0.03\) & \(0.063\pm 0.04\) & \(523 Using the averages of the six evaluation metrics, we performed sum rank of each algorithm across the 13 datasets. For algorithms with no results for certain datasets, we gave a rank of 6 (middle rank). The sum rank table is presented in Table 5. We placed MG algorithms at the end of the table, as they had issues in two or more datasets and the sum rank may not fully reflect their performance. In these three challenging datasets, CM-BBPSO was found to be very competitive. Overall, M-Fuzzy outperformed all other techniques, acquiring the smallest sum rank across most of the evaluation metrics, followed by M-BBPSO and M-QPSO. CM-BBPSO was ranked sixth. In Table 6, we calculate the sum rank for clustering performance on two datasets only, CMC and Sonar. Based on the external metrics of accuracy, F1 and Kappa, we can observe that CM-BBPSO performed best in CMC and Sonar. We placed MG-QPSO and MG-BBPSO, which had issues, at the end of the table as reference. The reason for isolating the two datasets is to identify the clustering techniques that performed well on the two datasets. Here, we observe that CM-BBPSO was the second best. In Table 7, we study which are the best two performing algorithms for the respective datasets based on the six evaluation metrics, highlighted in bold. M-Fuzzy was the top 2 best for 7 out of 13 datasets, while M-BBPSO was top 2 for 5 datasets. Previously, without the results from CMC, Segment and Vehicle, M-BBPSO was found to be best. CM-BBPSO was top 2 for one dataset only, CMC. \begin{table}
\begin{tabular}{l c c c c c c} \hline \hline
**Clus Algo** & **Accuracy** & **F1** & **Kappa** & **QE** & **WSS** & **BSS** & **Total** \\ \hline M-Fuzzy & **5** & **5** & **5** & **4** & **3** & 13 & 35 \\ CM-BBPSO & **6** & **5** & **5** & 11 & 15 & **4** & 46 \\ MG-Fuzzy & 10 & **5** & **4** & **9** & 13 & 9 & 50 \\ IB-Fuzzy & 9 & **5** & 6 & 7 & 11 & 13 & 51 \\ M-QPSO & 11 & 10 & **10** & 11 & 12 & 7 & 61 \\ M-BBPSO & 13 & 13 & 13 & 8 & 10 & 12 & 69 \\ IB-QPSO & 10 & 16 & 15 & 17 & 15 & 12 & 85 \\ SP-QPSO & 13 & 19 & 19 & 12 & **6** & 19 & 88 \\ BBPSO & 17 & 14 & 15 & 20 & 20 & **2** & 88 \\ \hline MG-BBPSO * & 12 & 15 & 14 & 10 & 7 & 17 & 75 \\ MG-QPSO * & 16 & 16 & 16 & 14 & 10 & 15 & 87 \\ \hline \hline \end{tabular}  
* No results for CMC.  
\end{table} 
Table 6: Sum rank of algorithms based on performances on 6 metrics on CMC and Sonar datasets with best two sum rank values presented in bold.