# An Improved Artificial Bee Colony for Feature Selection in QSAR
## 6 Experimental Results and Analysis  
Table 3 shows the experimental results of six QSAR methods.The best results are identified in boldface. Without introducing intelligent algorithms, the PLS model selects all features in each dataset, and the mean \(Q^{2}\) and root mean square error are respectively 0.6 and 0.99 on the Artemisinin dataset, 0.4 and 0.85 on the BZR dataset, and 0.24 and 0.65 on the Selwood dataset. However, the performance of PLS is improved when the intelligent algorithm is introduced into the model. The experimental results show that the intelligent algorithm can eliminate the irrelevant features in the datasets by using global search or local search. The following comparison results can be obtained from Table 3: on the Artemisinin dataset, the mean \(Q^{2}\) of ABC-PLS-1 is 3.64% larger than that of PSO-PLS and 1.48% larger than that of WS-PSO-PLS, the root mean square error of ABC-PLS-1 is 5.73% smaller than that of PSO-PLS and 2.39% smaller than WS-PSO-PLS. On the BZR dataset, the mean \(Q^{2}\) of ABC-PLS-1 is 1.8% larger than that of PSO-PLS and 1.29% larger than that of WS-PSO-PLS, the root mean square error of ABC-PLS-1 is 1.49% smaller than that of PSO-PLS and 1.07% smaller than that of WS-PSO-PLS, and the features selected by ABC-PLS-1 are 5.88 less than that selected by PSO-PLS and 4.14 less than that selected by WS-PSO-PLS. On the Selwood dataset, the mean \(Q^{2}\) of ABC-PLS-1 is 6.73% larger than that of PSO-PLS and 1.74% larger than that of WS-PSO-PLS, the root mean square error of ABC-PLS-1 is 7.67% smaller than that of PSO-PLS and 2.28% smaller than that of WS-PSO-PLS, and the features selected by ABC-PLS-1 are 5.8 less than that selected by PSO-PLS and 3.16 less than that selected by WS-PSO-PLS. The mean \(Q^{2}\) of ABC-PLS-1 is larger than that of BFDE-PLS and the root mean square error of ABC-PLS-1 is smaller than that of BFDE-PLS on all the three datasets. However, the features selected by ABC-PLS-1 is more than that selected by BFDE-PLS in the Artemisinin dataset and the BZR dataset. ABC-PLS-1 selects more features than ABC-PLS on the Artemisinin dataset, but it is superior to the ABC-PLS on the other two datasets. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **Learning Rate \(\alpha\)** & **Limit** & **learning Rate \(\beta\)** & **Weight Coefficient** \\ \hline PSO-PLS & 0.5 & / & / & / \\ WS-PSO-PLS & 0.5 & / & 0.8 & 0.5 \\ BFDE-PLS & / & / & / & / \\ ABC-PLS & / & 100 & / & / \\ ABC-PLS-1 & / & 100 & / & / \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental parameters and settings. In conclusion, although the number of selected features of ABC-PLS-1 is not smaller than that of BEFD-PLS on Artemisinin and BZR, the prediction accuracy and the root mean square error of ABC-PLS-1 is obviously better than ABC-PLS, PSO-PLS, WS-PSO-PLS, and BEFD-PLS on all the three datasets. A rank sum test method at a significance level of 0.05 is used to compare mean \(Q^{2}\) on three datasets to determine whether ABC-PLS-1 is significantly different from PSO-PLS, WS-PSO-PLS, BEFD-PLS, and ABC-PLS. As shown in Table 4, ABC-PLS-1 is significantly better than others in the mean \(Q^{2}\) on all datasets. Figure 5 shows the \(Q^{2}\) obtained by each algorithm used by running 100 times on three datasets. It is obvious that the \(Q^{2}\) of ABC-PLS-1 is generally higher than that of the other four algorithms on the Artemisinin dataset and the Selwood dataset. In the last subfigure, the \(Q^{2}\) of ABC-PLS-1 is higher than PSO-PLS, WS-PSO-PLS, and ABC-PLS, and it is stable. Convergence curves of the algorithms on three datasets are shown in Figure 6. Each curve is an average result of 100 runs in each iteration. ABC-PLS-1 converges faster with a good quality of solution compared to other state of-the-art methods on Artemisinin and BZR datasets. Although BEFD-PLS finally converges to a higher quality solution than ABC-PLS-1 on the Selwood dataset, it is greatly inferior to others on Artemisinin and BZR datasets and its convergence speed is slow.