# A Classification Method for Incomplete Mixed Data Using Imputation and Feature Selection
## 3 Results  
We conducted exhaustive experiments to evaluate the performance of PSOFI, as described in this section. To ensure fair results, three conventional statistics-based imputation methods and two evolutionary algorithm-based imputation methods are used for comparison. Specifically, MI [11], KNN [12], and Regularized Expectation Maximization (REM) [32] are chosen as statistical-based methods, while MOGI [20] and DEKCF [27] are selected as evolutionary-algorithm-based imputation methods. Additionally, to demonstrate the  
Figure 3: Flow chart of PSOFI. effectiveness of combining the proposed imputation method and feature selection, we included two variants of PSOFI: PSO-based IMputation (PSOIM) without feature selection and PSO-based Feature Selection (PSOFS) without imputation. Twelve different kinds of datasets from the UCI (the datasets are available 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 ) ) machine learning repository are chosen; their characteristics are shown in Table 1, the words in parentheses are abbreviated for the name of the datasets, and \"Type\" denotes the type of features that the dataset contains. BCC, Park, BTSC, and HV only contain quantitative features, while Lymp, Spec, Monk, and DBWS contain only categorical features, and Sta, ILPD, Aus, and GL have mixed features. In addition, HV, DBWS, and GL datasets have more than one hundred features. These datasets can provide an impartial assessment of our method. As the datasets are originally complete, we artificially construct missing datasets with different Missing Rates (MRs). The MR denotes the ratio of missing values to the total number of values in a dataset. We randomly select and replace values with \"NaN\" through non-replicated sampling, and repeat this process until the dataset reaches the desired MR. Therefore, the performance of PSOFI can be evaluated fairly and conveniently. The experiments are conducted on a test platform consisting of Windows 10 operating system, Matlab 2020b, Intel i5-7300 HQ, and 16 GB of RAM. We set \(K\) of KNN to 5 and use the default parameters provided by the open-source code (the source code is available at [[https://github.com/tapios/RegEM](https://github.com/tapios/RegEM)]([https://github.com/tapios/RegEM](https://github.com/tapios/RegEM)) (accessed on 12 April 2024 ) ) for REM. For MOGI, we evaluate it with a population size of 40, 300 iterations, 0.8 crossover percentage, 0.2 mutation percentage, and 0.02 mutation rate. For DEKCF, we set the number of populations to 40, the number of iterations to 300, and other parameter settings to be consistent with the reference [27]. We use a population size of 40 and 300 iterations for PSOFI, with \(w=0.5\), \(\alpha=\beta=1\). The quantitative feature parameter range is set between the maximum and minimum occurrence values. The parameter settings for PSOIM and PSOFS are kept consistent with PSOFI. As MOGI is a multi-objective algorithm, we select a random solution from the results as the final solution. After the aforementioned imputation methods are applied, the K-nearest neighbor classifier is utilized for classification. This classifier computes the Euclidean distance between samples and predicts the label of a sample based on its K-nearest neighbors, which is a popular choice due to its simplicity and ease of use. In this study, the \(K\) value for the classifier is set to the commonly used value of 5, as reported in the literature [33]. We evaluate the methods using MRs of 5%, 10%, 20%, 30%, 40%, and 50% on each dataset. The training partition and the testing partition are 80% and 20% of the original datasets, respectively, and the testing partition is only used for classifier evaluation to avoid data leakage. Each algorithm is independently conducted 20 times. The accuracy of the