# A Classification Method for Incomplete Mixed Data Using Imputation and Feature Selection
## 3 Results
The significance level is set to \(\alpha=0.05\), the mean values of indicators on each dataset with different MRs are used, and the results are shown in Table 2. It can be seen that, except for DEKCF in two indicators, all other comparison algorithms reject the null hypothesis for both accuracy and F1 score indicators. The findings suggest that PSOFI outperforms the majority of the algorithms under comparison, with the exception of DEKCF. This discrepancy can mainly be attributed to PSOFI's lower performance on high-dimensional datasets. Further analyzing the results presented above, we conclude some points as follows. * The performance of PSOFI and DEKCF is usually within a small range, while MOGI's advantage or disadvantage is typically of a larger magnitude, reflecting the instability of MOGI's performance. * The indicator values show no significant decline with increasing MRs, and, in some cases, such as BCC and Monk, demonstrate an improvement. This can be attributed to the datasets' strong discriminative features, where missing values have minimal impact on classification performance. * The MOGI algorithm exhibits improved performance with increasing MRs on each dataset. We speculate that the original values may not be discriminative enough for learning algorithms, and thus MOGI searches for an optimal value for each missing position to ensure a better fit to the algorithm. This explanation supports the fact that MOGI performs better, particularly when other algorithms demonstrate relatively low accuracy. * PSOFI, DEKCF, and PSOFS present comparatively better performance on some datasets, such as the BCC, Monk, and Sta datasets, whereas PSOIM performs poorly. This highlights the essential role that the feature selection technique plays in improving the methods' performance. * When focusing on the results obtained from mixed feature datasets, PSOFI demonstrates overall superiority, which illustrates the efficacy of our strategy for imputing mixed data. PSOFI utilizes Gaussian distribution to impute missing quantitative feature values and selecting probabilities to impute missing categorical feature values, leading to better outcomes by effectively leveraging the randomness of mixed missing values. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Indicator** & **PSOIM** & **PSOFS** & **DEKCF** & **MOGI** & **MI** & **KNN** & **REM** \\ \hline Accuracy & **2.01 \(\times\)10\({}^{-6}\)** & **9.27 \(\times\)10\({}^{-9}\)** & 3.23 \(\times\)10\({}^{-1}\) & **2.83 \(\times\)10\({}^{-3}\)** & **3.14 \(\times\)10\({}^{-15}\)** & **2.59 \(\times\)10\({}^{-15}\)** & **3.92 \(\times\)10\({}^{-15}\)** \\ F1 score & **1.70 \(\times\)10\({}^{-3}\)** & **2.22 \(\times\)10\({}^{-5}\)** & 3.49 \(\times\)10\({}^{-1}\) & **4.86 \(\times\)10\({}^{-2}\)** & **1.56 \(\times\)10\({}^{-11}\)** & **5.89 \(\times\)10\({}^{-12}\)** & **1.15 \(\times\)10\({}^{-11}\)** \\ \hline \hline \end{tabular} Results in bold font represent that they are lower than the significance level.  
\end{table} 
Table 2: Mann–Whitney U test \(p\) value results of performance. * PSOFI obtains mediocre results on high-dimensional datasets while DEKCF shows stronger performance on these datasets. This indicates that PSOFI may not be as competitive as DEKCF in terms of feature selection, as we have used a relatively simple strategy to implement feature selection. Now, we analyze the time complexity of the PSOFI algorithm. Obviously, the time complexity of statistics-based methods is smaller than that of evolutionary-algorithm-based methods. Therefore, only PSOFI, DEKCF, and MOGI are compared in detail here. Figure 6: F\({}_{1}\) score box plot results on datasets with different MRs, where different colors represent different MRs: (**a**) on BCC dataset; (**b**) on Park dataset; (**c**) on BTSC dataset; (**d**) on HV dataset; (**e**) on Lymp dataset; (**f**) on Spec dataset; (**g**) on Monk dataset; (**h**) on DBWS dataset; (**i**) on Sta dataset; (**j**) on ILPD dataset; (**k**) on Aus dataset; (**l**) on GL dataset; (**m**) figure legend.