# A Classification Method for Incomplete Mixed Data Using Imputation and Feature Selection
## 4 Conclusions  
In this paper, we introduce PSOFI, a novel and potent classification technique designed for handling missing data with mixed feature types. PSOFI employs distinct imputation models for quantitative and categorical features, incorporates feature selection to enhance its efficacy, and utilizes PSO to simultaneously optimize the parameters of the imputation models and the feature selection process. Furthermore, we propose a legacy learning mechanism to enhance the search capability of PSOFI by engaging additional search agents during iterations. For a comparative analysis, we employ three statistical methods and two evolutionary-algorithm-based methods, in addition to constructing two PSOFI variants, PSOIM and PSOFS, to showcase the effectiveness of our developed strategies. Moreover, a total of twelve different types of datasets are used for experiments. The experiment results lead to several conclusions: firstly, PSOFI outperforms other methods in terms of accuracy and F1 score measures in most cases. Secondly, PSOFI incurs a reasonable time cost. Thirdly, the results demonstrate the efficacy of PSOFI in leveraging both the randomness of missing values and the information of labels. Lastly, it is feasible and applicable to utilize evolutionary algorithms to integrate the data imputation and feature selection techniques. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithm** & **5\%MR** & **10\%MR** & **20\%MR** & **30\%MR** & **40\%MR** & **50\%MR** \\ \hline DEKCF & **4.3\(\times\)10\({}^{-3}\)** & **3.5\(\times\)10\({}^{-3}\)** & **3.5\(\times\)10\({}^{-3}\)** & **1.1\(\times\)10\({}^{-3}\)** & **1.1\(\times\)10\({}^{-3}\)** \\ MOGI & **3.0\(\times\)10\({}^{-2}\)** & **2.3\(\times\)10\({}^{-2}\)** & **1.9\(\times\)10\({}^{-2}\)** & **1.9\(\times\)10\({}^{-2}\)** & **1.7\(\times\)10\({}^{-2}\)** & **1.2\(\times\)10\({}^{-2}\)** \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mann–Whitney U test \(p\) value results of time costs. Figure 7: Stacked histogram of time costs. Despite its strengths, PSOFI has some limitations. It currently relies on artificial feature type determination, does not account for non-Gaussian-distributed quantitative feature values, has a mediocre performance on high-dimensional datasets, and has a higher time overhead, restricting its use in high-efficiency-demand scenarios. Additionally, as an evolutionary-algorithm-based method, PSOFI is heavily influenced by the optimization objective, yet a single classification metric is used in this study. Future work will address these limitations by developing an intelligent feature type discrimination mechanism, accommodating various data distributions, designing unique feature selection strategies for high-dimensional datasets, integrating parallel computing to reduce time overhead, expanding PSOFI to a multi-objective framework, and considering alternative metrics like balanced accuracy. Furthermore, we intend to modify PSOFI to address imbalanced, high-dimensional missing data classification problems. Conceptualization, G.L. and Y.L. ; methodology, Q.Z. and Y.L. ; software, Q.Z. and Y.L. ; validation, X.L. and Y.L. ; formal analysis, X.L. and W.Q. ; investigation, Q.Z. and Y.L. ; resources, X.L. ; data curation, Y.L. ; writing--original draft preparation, G.L. and Q.Z. ; writing--review and editing, G.L. and Y.L. ; visualization, G.L. ; supervision, X.D. ; project administration, W.Q. and X.D. ; funding acquisition, W.Q. All authors have read and agreed to the published version of the manuscript. This research was funded by National Science Foundation for Young Scientists of China (Grant No. 61802426) and Young Elite Scientists Sponsorship Program by CAST (Grant No. 2022 QNRC001). Not applicable. The original data presented in the study are openly available in UCI repository at [[https://archive.ics.uci.edu/ml/datasets](https://archive.ics.uci.edu/ml/datasets)]([https://archive.ics.uci.edu/ml/datasets](https://archive.ics.uci.edu/ml/datasets)) (accessed on 23 June 2024).