# Genetic Algorithm-Based Optimization of Clustering Algorithms for the Healthy Aging Dataset
## 4 Results
### Analysis  
Table 2 displays the silhouette scores for several clustering methods and their corresponding versions augmented with a genetic algorithm (GA). Birch, DBSCAN, and agglomerative clustering demonstrate scores of 0.3816, 0.4653, and 0.2867, respectively, demonstrating different levels of cluster overlap and separation. Kmeans++ attains the maximum score of 0.7284, indicating the presence of distinct clusters. When the GA is used for feature selection, enhancements are observed in all algorithms. The genetic algorithm (GA) combined with the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm produces the greatest silhouette score of 0.8844, suggesting a substantial improvement in cluster separation. The genetic algorithm (GA) combined with Kmeans++ also demonstrates significant enhancement with a score of 0.9473, emphasizing the efficacy of feature selection in improving clustering performance. Furthermore, the evaluation of each clustering technique and its equivalent GA-enhanced variant is conducted using the Davies-Bouldin score. The Birch, DBSCAN, and agglomerative clustering algorithms obtain scores of 0.8433, 1.544, and 1.0995, respectively. These values indicate different levels of similarity among clusters, with larger scores suggesting worse quality clustering. Kmeans++ achieves the lowest Davies-Bouldin score of 0.474, indicating superior clustering performance compared to the other algorithms. When the GA is used for feature selection, enhancements are observed in all algorithms. The genetic algorithm (GA) combined with the Kmeans++ algorithm obtains the lowest Davies-Bouldin score of 0.1061, which indicates a substantial improvement in cluster similarity and the presence of well-defined clusters. Similarly, the Calinski-Harabasz (CH) score evaluates the quality of clustering by quantifying the ratio of dispersion between clusters to dispersion within clusters. This ratio indicates the extent to which clusters are distinct from each other in a dataset. Greater scores indicate clusters that are more distinct and tightly packed. Birch achieved a score of 68.67, indicating a moderate level of cluster separation but lower clarity compared to algorithms with higher scores. The DBSCAN algorithm achieved a score of 14.78, which suggests inadequate separation between clusters and the possibility of clusters overlapping. The agglomerative clustering algorithm achieved a score of 90.7, indicating enhanced but not yet perfect separation of clusters. Kmeans++ had superior performance compared to other methods, achieving a score of 397.46, which suggests the presence of distinct and closely packed clusters. When utilized in conjunction with a genetic algorithm (GA) for the purpose of feature selection, all methods exhibited better CH scores, which signifies improved cluster separation and density. The GA with the Kmeans++ algorithm achieved the best score of 3709.51, \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{4}{c}{**NPHA Dataset**} \\ \hline
**Model** & **Silhoutte Score** & **Davies–Bouldin Score** & **Calinski–Harabasz Score** \\ \hline Birch & 0.3816 & 0.8433 & 68.67 \\ \hline DBSCAN & 0.4653 & 1.544 & 14.78 \\ \hline Agglomerative(Agg) & 0.2867 & 1.0995 & 90.7 \\ \hline Kmeans++ & 0.7284 & 0.474 & 397.46 \\ \hline GA with Birch(GA-B) & 0.6497 & 0.6024 & 229.007 \\ \hline GA with DBSCAN(GA-DB) & 0.8844 & 1.2082 & 140.69 \\ \hline GA \& agglomerative(GA-Agg) & 0.7044 & 0.546 & 283.24 \\ \hline
**GA \& Kmeans ++(GA-KM++)** & **0.9473** & **0.1062** & **3709.51** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance evaluation metrics for the NPHA dataset. Also, the WCSS measure was computed for both the KMeans++ algorithm and the genetic algorithm with KMeans++. This measure quantifies the degree of compactness shown by clusters. The metric calculates the total of the squared distances between every data point and the centroid of its corresponding cluster.