# A Classification Method for Incomplete Mixed Data Using Imputation and Feature Selection
###### Abstract
For example, the Multi-Objective Genetic algorithm for data Imputation (MOGI) [20] uses Nondominated Sorting Genetic Algorithm-II (NSGA-II) to find the optimal imputation values. These methods utilize the strong search ability of evolutionary algorithms to search for imputation values, and the large population of search agents can guarantee effectiveness and randomness simultaneously. Despite this, these methods are inadequate in utilizing both feature and label information, thereby constraining their performance. Furthermore, real-world datasets often contain quantitative features and categorical features at the same time. The distribution of these two types of features is probably different, yet most data imputation methods do not take this into consideration and regard all features the same. In this data-proliferating era of big data, the data produced and stored by different fields have significantly increased. As a consequence, the dimensionality of datasets increases, thus aggravating the \"curse of dimensionality\" problem in many real-world applications [21]. Feature selection is one key technique for solving this. It selects a small subset of relevant features from the original feature set to maximize the evaluation criteria. By removing irrelevant and redundant features, feature selection can reduce the time taken to obtain the original data and the storage space of the data, diminish the training time of classification models, and improve the interpretability and performance of the classification models [22; 23]. Feature selection is a Nondeterministic Polynomial (NP) hard problem with a large search space, and there are three main types of feature selection approaches, namely, filter, wrapper, and embedded methods. Among these, the evolutionary-algorithm-based wrapper methods have shown a great capability of searching the optimal feature subset, therefore attracting much attention from many researchers [24; 25]. In many application scenarios, high-dimensional datasets with missing data pose a common challenge. Not only can the missing data possibly lead to the dysfunction of learning algorithms, but also the high-dimensional characteristic can be a huge obstruct to obtaining a good data analysis result. Considering that data imputation and feature selection both serve to improve data quality, it is possible that combining data imputation and feature selection can improve the efficiency and accuracy of learning algorithms to a greater extent, especially on high-dimensional missing datasets. Some studies have shown that applying feature selection and data imputation simultaneously is conducive to improving the performance of imputation methods [26]. Moreover, the Differential Evolution algorithm involving KNN imputation, Clustering and Feature selection (DEKCF) [27] method combines three techniques to enhance the method's ability, and demonstrated a further improvement in classification accuracy. However, the differential evolution algorithm is only used for feature selection in DEKCF, and the imputation capability of the differential evolution algorithm is neglected. As mentioned above, evolutionary algorithms are successfully employed in both data imputation and feature selection, but there is little research that uses evolutionary algorithms to simultaneously implement the two techniques. The potential of this integrating strategy still needs evaluation and analysis. Particle Swarm Optimization (PSO) is a prominent evolutionary algorithm that mimics the foraging behavior observed in fish and bird flocks. It is well known for its superior search capabilities and good scalability, and has been widely applied in various optimization applications [28]. Based on the fact that PSO has been successfully applied and has obtained good results in both feature selection and missing data imputation fields [29; 30], in this study, we propose Particle-Swarm-Optimization-based Feature selection and Imputation (PSOFI), a sophisticated algorithm for handling classification problems with missing mixed data.