# An Improved Artificial Bee Colony for Feature Selection in QSAR
## 6 Experimental Results and Analysis
Overall, ABGWO achieved better performance than others with respect to both convergence speed and solution quality. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **Artemisinin** & **BZR** & **Selwood** \\ \hline PSO-PLS & \(2.5606\times 10^{-34}\) & \(1.6434\times 10^{-34}\) & \(2.1212\times 10^{-35}\) \\ WS-PSO-PLS & \(4.2026\times 10^{-33}\) & \(5.1827\times 10^{-31}\) & \(1.6109\times 10^{-27}\) \\ BEFD-PLS & \(2.6385\times 10^{-34}\) & \(2.7446\times 10^{-34}\) & \(2.1211\times 10^{-35}\) \\ ABC-PLS & \(1.4839\times 10^{-7}\) & \(1.6434\times 10^{-34}\) & \(1.5693\times 10^{-33}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Significant difference in mean \(Q^{2}\) between ABC-PLS-1 and the other four methods. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Method** & **Mean \(Q^{2}\pm\) Std** & **Mean \(RMSE\pm\) Std** & **Mean \(NUM\pm\) Std** \\ \hline \multirow{6}{*}{Artemisinin} & PLS & 0.6 & 0.99 & 89 \\  & PSO-PLS & \(0.7352\pm 0.012\) & \(0.8066\pm 0.0182\) & \(39.18\pm 4.6436\) \\  & WS-PSO-PLS & \(0.7568\pm 0.0072\) & \(0.7732\pm 0.0115\) & \(32.19\pm 4.41\) \\  & BEFD-PLS & \(0.7299\pm 0.0109\) & \(0.8147\pm 0.0164\) & \(\mathbf{22.48\pm 4.2557}\) \\  & ABC-PLS & \(0.7697\pm 0.0016\) & \(0.7524\pm 0.0026\) & \(30.77\pm 3.5358\) \\  & ABC-PLS-1 & \(\mathbf{0.7716\pm 0.002}\) & \(\mathbf{0.7493\pm 0.0032}\) & \(33.29\pm 5.3073\) \\ \hline \multirow{6}{*}{BZR} & PLS & 0.4 & 0.85 & 75 \\  & PSO-PLS & \(0.5544\pm 0.012\) & \(0.733\pm 0.0099\) & \(29.14\pm 3.6764\) \\  & WS-PSO-PLS & \(0.5595\pm 0.008\) & \(0.7288\pm 0.0066\) & \(27.4\pm 2.8955\) \\  & BFDE-PLS & \(0.5490\pm 0.0103\) & \(0.7374\pm 0.0084\) & \(\mathbf{18.9\pm 2.0865}\) \\  & ABC-PLS & \(0.4523\pm 0.0129\) & \(0.8126\pm 0.0096\) & \(38.04\pm 4.4311\) \\  & ABC-PLS-1 & \(\mathbf{0.5724\pm 0.0053}\) & \(\mathbf{0.7181\pm 0.0044}\) & \(23.26\pm 2.1112\) \\ \hline \multirow{6}{*}{Selwood} & PLS & 0.24 & 0.65 & 53 \\  & PSO-PLS & \(0.8653\pm 0.0428\) & \(0.2692\pm 0.0401\) & \(19.66\pm 3.1662\) \\ \cline{1-1}  & WS-PSO-PLS & \(0.9152\pm 0.0128\) & \(0.2153\pm 0.0163\) & \(17.02\pm 3.0977\) \\ \cline{1-1}  & BFDE-PLS & \(0.9112\pm 0.0359\) & \(0.2170\pm 0.0409\) & \(14.72\pm 2.4457\) \\ \cline{1-1}  & ABC-PLS & \(0.8187\pm 0.0887\) & \(0.3078\pm 0.0704\) & \(20.3\pm 3.9093\) \\ \cline{1-1}  & ABC-PLS-1 & \(\mathbf{0.9326\pm 0.0023}\) & \(\mathbf{0.1925\pm 0.0033}\) & \(\mathbf{13.86\pm 0.9849}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance of six QSAR methods on three datasets. Furthermore, in order to verify the validity of ABC-PLS-1, the Root Mean Square Error (RMSE) of ABC-PLS-1 is compared with that of the other four algorithms. Figure 7 presents Box-plots which show the RMES of the five algorithms on three datasets. \"+\" in figure are outliers. As can be seen from the figure, the mean line of ABC-PLS-1 is lower than PSO-PLS, WS-PSO-PLS, BFDE-PLS, and ABC-PLS on all three datasets. Therefore, the performance of ABC-PLS-1 is better and more stable than others. For a better evaluation of our proposed FS methods, not only the accuracy and the size of feature subsets but also the computational time is investigated. The computational time is presented in terms of mean values over the 100 runs in Table 5. Like as other wrapper methods, the proposed algorithm requires a high computational cost to evaluate the fitness of individuals. The CPU execution time of ABC-PLS-1 is only less than that of BFED-PLS. However, it is a remarkable fact that the accuracy of feature selection method is far more important than the computational complexity of this method in many high-precision applications, such as biological genetic engineering, medical diagnosis, drug design, and discovery. In fact, in these applications, we prefer to choose the FS method with the highest accuracy, even if it is at the cost of higher computational complexity. Although  
Figure 5: The \(Q^{2}\) obtained in 100 runs. Figure 6: The convergence curve of algorithms during 200 iterations.