# A Classification Method for Incomplete Mixed Data Using Imputation and Feature Selection
## 3 Results
\begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Name**} & **Number of** & \multirow{2}{*}{**Number of** **Features**} & \multirow{2}{*}{**Type**} \\  & **Samples of** & & \\  & **Each Class** & & \\ \hline Breast Cancer Coimbra (BCC) & 64/52 & 10 & quantitative \\ Parkinsons (Park) & 147/48 & 23 & quantitative \\ Blood Transfusion Service Center (BTSC) & 570/178 & 4 & quantitative \\ Hill Valley (HV) & 305/301 & 100 & quantitative \\ Lymphography (Lymp) & 81/67 & 18 & categorical \\ Spectf Heart (Spec) & 212/55 & 44 & categorical \\ Monk’s Problems (Monk) & 216/216 & 7 & categorical \\ DBWorld Subjects (DBWS) & 35/29 & 242 & categorical \\ Statlog Heart (Sta) & 150/120 & 13 & mixed \\ Indian Liver Patient Dataset (ILPD) & 416/167 & 10 & mixed \\ Australian (Aus) & 383/307 & 14 & mixed \\ Gastrointestinal Lesions (GL) & 110/42 & 467 & mixed \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of twelve experiment datasets. classifier is used as the evaluation and optimization objective of PSOFI, PSOIM, and PSOFS. Besides the accuracy measure, we also take into account a classic metric commonly used for imbalanced datasets, that is, the F\({}_{1}\) score measure. Given that the F\({}_{1}\) score represents the weighted harmonic average of the precision and recall indicators, it offers a comprehensive evaluation of the performance. The accuracy and F\({}_{1}\) score measures are calculated as in (4) and (5). \[\text{accuracy}=\frac{\text{TP}+\text{TN}}{\text{TP}+\text{TN}+\text{FP}+ \text{FN}} \tag{4}\]  
\[\text{F}_{1}\text{ score}=\frac{2\times\text{TP}}{2\times\text{TP}+\text{FP}+ \text{FN}} \tag{5}\]  
where TP (True Positive) represents the number of positive samples correctly predicted as positive, TN (True Negative) represents the number of negative samples correctly predicted as negative, FP (False Positive) represents the number of negative samples incorrectly predicted as positive, and FN (False Negative) represents the number of positive samples incorrectly predicted as negative. To verify the effectiveness of the legacy learning mechanism, comparative experiments between PSOFI and PSOFI without legacy learning mechanism (PSOFIwl) are first carried out on the three different types of datasets, including BCC, Spec, and Aus. The iteration curves of the average accuracy are presented in Figure 4. As the curves show, PSOFI can obtain better solutions during or at the end of iterations under all circumstances except the Aus dataset with 20% and 50% MRs, indicating that the presented legacy learning mechanism can indeed improve the searching ability of PSOFI. The accuracy box plot results of eight algorithms on all twelve datasets with different MRs are presented in Figure 5. Based on the presented accuracy results, it is evident that evolutionary-algorithm-based methods outperformed statistics-based methods. This can be attributed to the fact that statistics-based approaches only utilize the information provided by features while evolutionary-algorithm-based algorithms utilize both feature and label information, resulting in better imputation outcomes. Among the methods, PSOFI demonstrates consistent performance across each dataset for various MRs. PSOFI's performance is slightly lower than that of DEKCF for Park and Lymp datasets with a 5% MR, and for the Aus dataset with 30% and 50% MRs. Additionally, DEKCF has better performance on Spec, HV, DBWS, and GL datasets at different MRs; this can be due to the high-dimensional features in the dataset, which lead to a comparatively large search space of PSOFI. With the exception of the aforementioned instances, PSOFI outperforms DEKCF on all other datasets. As for the comparison between MOGI and PSOFI, PSOFI has lower performance on the HV dataset with different MRs, BTSC and ILPD datasets with 10%, 20%, 30%, 40%, and 50% MRs, Monk dataset with 30%, 40%, and 50% MRs, Spec dataset with 40% and 50% MRs, Aus dataset with 30% and 50% MRs, and GL dataset with a 50% MR.