# The Feature Selection Effect on Missing Value Imputation of Medical Datasets
## 4 Experiments  
### Results of Lower Dimensional Datasets  
Tables 2-4 list the classification results obtained with different combinations of feature selection methods and the MLP, KNN, and SVM imputation models over the three lower dimensional datasets with different missing rates, respectively. They are denoted as DT+MLP, GA+MLP, IG+MLP, DT+KNN, GA+KNN, IG+KNN, DT+SVM, GA+SVM, and IG+SVM. Note that the best result for each missing rate is underlined. Moreover, the number in the bracket followed by each dataset represents the classification accuracy of the SVM trained and tested by the original complete dataset. As we can see in most cases, the combined approaches perform better than the baseline models (i.e., MLP, KNN, and SVM), except for the SPECT dataset. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Missing Rates** & **DT+KNN** & **GA+KNN** & **IG+KNN** & **KNN** \\ \hline \multicolumn{5}{c}{_Lymphography (77.43)_} \\
10\% & 75.81 & 75.32 & 74.81 & 73.97 \\
20\% & 76.49 & 73.56 & 73.61 & 73.11 \\
30\% & 74.99 & 74.14 & 74.21 & 71.84 \\
40\% & 75.04 & 73.32 & 73.54 & 72.16 \\
50\% & 74.82 & 72.87 & 72.04 & 69.84 \\ \multicolumn{5}{c}{_Heart(75.11)_} \\
10\% & 77.85 & 76.89 & 76.52 & 55.56 \\
20\% & 75.70 & 75.56 & 76.74 & 55.56 \\
40\% & 75.33 & 75.93 & 76.00 & 55.56 \\
40\% & 75.70 & 74.37 & 75.48 & 56.00 \\
50\% & 74.00 & 73.41 & 74.15 & 55.70 \\ \multicolumn{5}{c}{_SPECT(75.26)_} \\
10\% & 64.85 & 72.47 & 72.61 & 73.78 \\
30\% & 65.14 & 72.4 & 72.18 & 73.33 \\
40\% & 64.93 & 71.79 & 71.11 & 73.04 \\
50\% & 64.97 & 72.39 & 71.56 & 73.63 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Classification results for the KNN imputation method. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Missing Rates** & **DT+MLP** & **GA+MLP** & **IG+MLP** & **MLP** \\ \hline \multicolumn{5}{c}{_Lymphography (77.43)_} \\
10\% & 75.53 & 76.26 & 76.2 & 73.68 \\
20\% & 74.95 & 73.93 & 73.85 & 72.87 \\
30\% & 75.22 & 74.49 & 74.15 & 73.01 \\
40\% & 74.75 & 73.02 & 73.86 & 73.17 \\
50\% & 74.06 & 72.54  
Figures 2-4 show the average classification accuracies of different combined approaches (i.e., DT/GA/IG+MLP, DT/GA/IG+KNN, and DT/GA/IG+ SVM). The baseline imputation models are MLP, KNN, and SVM, which do not have feature selection. It can be seen that the worst performance is obtained when using the baseline imputation models without performing feature selection in all cases (i.e., missing rates). In particular, using GA and IG for feature selection can make the classifier perform similarly. For the level of significance, the combined models can provide significantly better performances than the baseline imputation models (\(p<0.01\)). Table 5 shows the numbers of features that are selected by DT, GA, and IG. Among them, DT generally filters out most of the original features from the lower dimensional datasets. This indicates that DT produces \"over-selection\" results from these datasets; that is, a number of useful features are filtered out, which degrade the final classification performances. On the contrary, IG selects 80% of the original features, where most of the original features are kept. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Missing Rates** & **DT+SVM** & **GA+SVM** & **IG+SVM** & **SVM** \\ \hline \multicolumn{5}{c}{_Lymphography(77.43)_} \\ \(10\%\) & 75.5 & 76.89 & 75.94 & 75.09 \\ \(20\%\) & 74.41 & 75.76 & 74.16 & 74.48 \\ \(30\%\) & 76.01 & 76.52 & 74.7 & 73.35 \\ \(40\%\) & 75.57 & 74.6 & 74.76 & 74.45 \\ \(50\%\) & 75.05 & 75.45 & 73.6 & 69.95 \\ \multicolumn{5}{c}{_Heart(75.11)_} \\ \(10\%\) & 76.67 & 77.70 & 77.11 & 55.70 \\ \(20\%\) & 75.93 & 76.96 & 77.11 & 55.41 \\ \(30\%\) & 73.11 & 73.26 & 76.15 & 56.00 \\ \(40\%\) & 72.96 & 67.41 & 75.04 & 55.70 \\ \multicolumn{5}{c}{_SPECT(75.26)_} \\ \(10\%\) & 64.33 & 72.62 & 71.5 & 73.78 \\ \(20\%\) & 64.93 & 72.55 & 71.86 & 73.19 \\ \(30\%\) & 65.51 & 72.63 & 72.02 & 73.48 \\ \(40\%\) & 64.83 & 72.24 & 70.99 & 74.37 \\ \(50\%\) & 64.37 & 72.31 & 71.11 & 72.89 \\ \hline \hline \end{tabular}
\end{table}