# An Empirical Study of Cluster-Based MOEA/D Bare Bones PSO for Data Clustering +
## 4 Results
### Visual Examination of CM-BBPSO Clustering  
We visually inspect CM-BBPSO clustering by comparing T-SNE biplots with the ground truth. The biplots are generated using R package _rtsne_, and a perplexity value of 40 is applied to all datasets presented. In Figure 1a,e, we observe that clusters of CMC and Sonar highly overlap, but CM-BBPSO was able to cluster correctly some data points located between clusters. In Figure 2a-f, the ground truth and CM-BBPSO clustering biplots of challenging datasets, Glass, Segment and Vehicle, are presented. For contrast, we present the biplot for Iris in Figure 2h to show that CM-BBPSO can easily find the clusters. Where clusters do not overlap, CM-BBPSO performs with no issues, though its strength is in highly overlapping clusters. In Figure 3, convergence plots of connectedness values of particles and their _pbest_ against the number of iterations for particles using CM-BBPSO on the Appendicitis dataset are presented to show the convergence and, thus, the stability of CM-BBPSO. We observe that the connectedness values of particles and their _pbest_ converge on all four experiment settings. It is interesting to note that fewer particles dominate the _pbest_ value as the algorithm reaches near the maximum iteration. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Appendicitis**} & \multicolumn{2}{c}{**CMC**} & \multicolumn{2}{c}{**Dermatology**} & \multicolumn{2}{c}{**Ecoli**} \\ \hline
**s-i** & **Accuracy** & **QE** & **Accuracy** & **QE** & **Accuracy** & **QE** & **Accuracy** & **QE** \\ \hline
20-100 & 0.771 \(\pm\) 0.08 & 2.56 \(\pm\) 0.43 & 0.402 \(\pm\) 0.02 & **2.88 \(\pm\) 0.25** & **0.651 \(\pm\) 0.07** & 5.31 \(\pm\) 0.31 & 0.499 \(\pm\) 0.07 & 1.97 \(\pm\) 0.33 \\
30-100 & 0.775 \(\pm\) 0.08 & 2.61 \(\pm\) 0.38 & 0.396 \(\pm\) 0.02 & 3.00 \(\pm\) 0.24 & 0.619 \(\pm\) 0.09 & 5.35 \(\pm\) 0.34 & 0.501 \(\pm\) 0.06 & 2.10 \(\pm\) 0.42 \\
30-200 & **0.781 \(\pm\) 0.07** & 2.57 \(\pm\) 0.50 & 0.402 \(\pm\) 0.02 & 2.94 \(\pm\) 0.18 & 0.632 \(\pm\) 0.09 & 5.38 \(\pm\) 0.36 & 0.497 \(\pm\) 0.08 & **1.92 \(\pm\) 0.19** \\
40-100 & 0.750 \(\pm\) 0.11 & **2.49 \(\pm\) 0.30** & **0.405 \(\pm\) 0.02** & 2.94 \(\pm\) 0.24 & 0.623 \(\pm\) 0.08 & **5.30 \(\pm\) 0.347** & **0.514 \(\pm\) 0.06** & 2.00 \(\pm\) 0.19 \\ \hline  & \multicolumn{2}{c}{**Glass**} & \multicolumn{2}{c}{**Iris**} & \multicolumn{2}{c}{**Seeds**} & \multicolumn{2}{c}{**Segment**} \\ \hline
**s-i** & **Accuracy** & **QE** & **Accuracy** & **QE** & **Accuracy** & **QE** & **Accuracy** & **QE** \\ \hline
20-100 & 0.429 \(\pm\) 0.04 & 2.75 \(\pm\) 0.45 & 0.721 \(\pm\) 0.10 & **1.41 \(\pm\) 0.29** & 0.727 \(\pm\) 0.12 & 2.1 \(\pm\) 0.38 & 0.547 \(\pm\) 0.06 & 3.15 \(\pm\) 0.41 \\
30-100 & **0.431 \(\pm\) 0.04** & 2.72 \(\pm\) 0.48 & 0.704 \(\pm\) 0.12 & 1.49 \(\pm\) 0.30 & 0.707 \(\pm\) 0.13 & 2.14 \(\pm\) 0.41 & 0.542 \(\pm\) 0.07 & **3.08 \(\pm\) 0.35** \\
30-200 & 0.419 \(\pm\) 0.04 & **2.65 \(\pm\) 0.40** & 0.706 \(\pm\) 0.09 & 1.51 \(\pm\) 0.32 & 0.721 \(\pm\) 0.11 & 2.11 \(\pm\) 0.39 & 0.546 \(\pm\) 0.06 & 3.17 \(\pm\) 0.45 \\
40-100 & 0.412 \(\pm\) 0.05 & 2.80 \(\pm\) 0.43 & **0.746 \(\pm\) 0.11** & 1.45 \(\pm\) 0.30 & **0.750 \(\pm\) 0.13** & **2.05 \(\pm\) 0.38** & **0.553 \(\pm\) 0.05** & 3.12 \(\pm\) 0.44 \\ \hline  & \multicolumn{2}{c}{**Sonar**} & \multicolumn{2}{c}{**Vehicle**} & \multicolumn{2}{c}{**WDBC**} & \multicolumn{2}{c}{**Wine**} \\ \hline
**s-i** & **Accuracy** & **QE** & **Accuracy** & **QE** & **Accuracy** & **QE** & **Accuracy** & **QE** \\ \hline
20-100 & 0.552 \(\pm\) 0.05 & 9.13 \(\pm\) 0.70 & 0.374 \(\pm\) 0.019 & **3.66 \(\pm\) 0.59** & 0.782 \(\pm\) 0.13 & 6.08 \(\pm\) 1.07 & **0.719 \(\pm\) 0.15** & **3.5 \(\pm\) 0.25** \\
30-100 & 0.553 \(\pm\) 0.05 & **9.05 \(\pm\) 0.63** & **0.385 \(\pm\) 0.02** & 3.86 \(\pm\) 0.89 & **0.811 \(\pm\) 0.11** & **5.92 \(\pm\) 0.92** & 0.712 \(\pm\) 0.13 Figure 1: T-SNE biplots of CM-BBPSO best performing datasets.