## 5 Results and Discussion
### Contingency Tables  
After evaluating the clustering methods using different metrics, we compute the contingency tables for variants versus clusters for different clustering approaches. The contingency tables for different clustering methods and feature selection approaches (using \(k\)-mers and one-hot embedding) are given in Tables 4-19. In Table 4, we can observe that \(k\)-modes without applying any feature selection is outperforming \(k\)-means and also the other two clustering algorithms from Table 6. In Tables 8 and 10, we can observe that RFF is giving pure clusters for some of the variants but performing poorly on the other variants. For LASSO regression in Tables 12 and 14, we can observe that clusters started to become pure immediately when we apply LASSO regression. This shows the effectiveness of this feature selection method for the clustering of spike sequences. Similarly, in Tables 16 and 18, we can see that Boruta is not giving many pure clusters (apart from \(k\)-modes). This shows that Boruta fails to generalize over different clustering approaches and different variants. Comparing these results of contingency tables for \(k\)-mers with the results of one-hot embedding, improvement of \(k\)-mers results are obvious in terms of purity of clustering. In addition, we can see that, even with using one-hot embedding, using the feature selection methods improves the clustering purity. In addition, in Tables 5 and 7, without using any feature selection methods, we can see that \(k\)-modes is outperforming the other clustering algorithms. In Tables 9 and 11, clear clusters as a result of clustering methods and RFF can prove the effectiveness of this feature selection method. The results of applying different clustering algorithms and using LASSO feature selection method in Tables 13 and 15 also show the enhancements in terms of clustering quality, but, compared to RFF, it is not significant. The same pattern is observable in Tables 17 and 19, which are the results of using the Boruta feature selection method, showing weakness in generalization over different clustering approaches and different variants. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \multirow{3}{*}{**Embedding**} & \multirow{3}{*}{**Algorithm**} & \multicolumn{4}{c}{**Different Metrics for Different Variants**} \\ \cline{3-6}  & & **Silhouette** & **Calinski–** & **Davies–Bouldin** & **Runtime (s)** \\  & & **Coefficient** & **Harabasz Index** & **Index** & **Runtime (s)** \\ \hline \multirow{7}{*}{\(k\)-means} & \(k\)-means & 0.75 & 329,866.74 & 0.45 & 66.43 \\  & \(k\)-means + Boruta & 0.76 & 342,083.63 & 0.43 & 15.77 \\  & \(k\)-means & + & 0.42 & 17,269.34 & 1.52 & 9.56 \\  & LASSO & & & & \\  & \(k\)-means + RFF & 0.25 & 5251.93 & 1.55 & **8.65** \\ \hline \multirow{7}{*}{\(k\)-modes} & 0.05 & 10,257.1 & 7.11 & 17,580.25 \\  & \(k\)-modes + Boruta & 0.07 & 12,058.15 & 6.52 & 2965.03 \\  & \(k\)-modes & + & 0.42 & 15,704.43 & 1.54 & 784.20 \\  & LASSO & & & & \\  & \(k\)-modes + RFF & \(-\)0.15 & 13,66.91 & 1.07 & 794.56 \\ \cline{2-6}  & Fuzzy & 0.75 & 329,410.74 & 0.44 & 2358.84 \\  & Fuzzy + Boruta & **0.76** & **341,678.01** & 0.43 & 230.17 \\  & Fuzzy + LASSO & 0.41 & 15,010.79 & 2.58 & 94.36 \\  & Fuzzy + RFF & 0.19 & 13,293.96 & 0.99 & 460.82 \\ \cline{2-6}  & Hierarchical & 0.72 & 284,726.92 & 0.47 & 9934.57 \\  & Hierarchical & + & 0.73 & 280,129.56 & **0.42** & 1908.75 \\  & Boruta & & & & \\  & Hierarchical & + & 0.41 & 15,218.95 & 2.03 & 713.07 \\  & LASSO & & & & \\  & Hierarchical & + & 0.26 & 5258.43 & 1.00 & 1120.14 \\  & RFF & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._