# An Empirical Study of Cluster-Based MOEA/D Bare Bones PSO for Data Clustering +
## 5 Discussion  
From the various comparative analysis, it is evident that CM-BBPSO does not perform better than the other algorithms on datasets with well-separated or a small number of clusters, such as Iris, Wine, WOBC and WDBC. Instead, it performs well on highly overlapping clusters, such as Sonar and CMC. Although other MOC results, both from our previous work and from other reported work, outperform CM-BBPSO on Sonar and CMC, we consider the CM-BBPSO to be promising. It used a simple clustering with two clusters for MOEA, and the results are not a lot worse. There was also no setting of parameters apart from the number of clusters, swarm size and maximum iteration. Excluding population size, maximum k and total generations, HT-MOC requires the parameters of neighborhood size, upper limit, branching factor and length of minimum spanning tree links. Excluding the number of objects, total generation and crossover, MOF-TMS requires the degree of the membrane system.  
With the 2-cluster K-means cluster-based approach in MOEA/D, the local search is introduced such that the evolved candidate is evaluated with the cluster closest to it during the dominance check. This brought on the effect of balancing the compactness and well-separatedness of the cluster as shown in Table 1. Further experimentation is required to study the effects of clustering on solution selection and whether such effects are consistent across other MOC algorithms.  
From Tables 2-4, we observed that M-Fuzzy works well with the WSS as one of the objectives to achieve good accuracy. Examining all WSS and accuracy results of MOC algorithms from the previous and current work, those with best accuracy also produce the  
Figure 3: Convergence plot of particles \(p\) and their _pbest_ where \(p\) dominates _pbest_ in line 9 in Algorithm 1 on Appendicitis dataset using different swarm size (s) and maximum iterations (i), labeled as s-i in (**a–d**).  
best WSS for 7 out of 13 datasets. Two thoughts came to mind: first, the objective functions in Fuzzy and BBPSO clustering. All BBPSO objective functions are based on [23]. Using the same objective function as that of Fuzzy clustering on BBPSO clustering may improve it. Second is the objective functions in MOEA. The objective functions WSS and Connectivity in MOEA may not be the best combination for all datasets, and more objective functions can be considered. There is consideration to study the same framework, but with different objective functions [34]. HT-MOC used variance and connectivity, while MOFC-TMS used \(J_{m}\), XB-index and Sym-index. With three objective functions, MOFC-TMS produced good results for challenging datasets, such as CMC and Glass. To test on datasets with highly overlapping clusters, HT-MOC was tested on CoverType and Shuttle datasets. This will be considered in our further investigations.  
So far, we applied the cluster-based approach only on MOEA/D BBPSO clustering. From Table 5, despite having issues on the CMC dataset, M-Fuzzy was found to produce good results; further investigation of applications of the cluster-based technique on it can be considered. The latest cluster-based MOEA techniques were investigated in non-convex clusters in objective space, which is of interest to our future investigation in clustering problems. Furthermore, we would like to investigate adding the cluster representatives in our reproduction pool to guide the evolution of new candidates, which was conducted in [13], but we did not apply it in this manner. By including cluster representatives, this can increase diversity while applying local search in the objective space during the dominance check. The results from the current work is promising, and this work has opened up potential research directions in applying cluster-based MOEA techniques for data clustering, using as few parameters as possible.