## 2 Basic Theory
### Experimental Analyses  
In order to verify the validity of the method in this paper, the feature approximation of the selected four UCI datasets is performed using the rough set (RS) and neighborhood rough set (NRS) with equal-width discretization, and the details of the data descriptions are shown in Table 1; the popular K-Nearest Neighbors (KNN), Classification and Regression Tree (CART), Support Vector Machine (SVM), and Dingo Optimization Algorithm Support Vector Machine (DOA-SVM) are used for the feature reduction in the UCI datasets. and CART, SVM, and DOA-SVM classification algorithms to evaluate the classification ability of the selected features through 5-fold cross-validation. Evaluate the classification ability of the selected features. When calculating the sample neighborhood, the data are first normalized to reduce the impact of the results because of the different attribute scales. Then, the outliers are \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Data Set** & **Sample Size** & **Number of Attributes** & **Number of Categories** \\ \hline Wine & 178 & 14 & 3 \\ Iono & 351 & 34 & 2 \\ Sonar & 208 & 60 & 2 \\ Glass & 214 & 9 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: UCI Dataset Information Table. Figure 3: DOA-SVM flowchart. removed to reduce the interference of the anomalous data; at the same time, the data are normalized concerning the literature [11] for attribute reduction concluded that the neighborhood threshold takes a value size between [0.2, 0.4] is more effective. In this paper, after a 5-fold cross-validation comparison, the best result is obtained when \(\delta=0.2\), the combined results are the best. Table 2 records the number of attributes corresponding to the attribute reduction of the dataset by classical rough set and neighborhood rough set. Table 3 records the classification performance ability of the selected features in each classification algorithm; RS represents the features after reduction based on equal-width discretization and rough sets, NRS represents the features after approximation based on neighborhood rough sets, and Raw represents the original features without approximation. From Table 2, it can be observed that both the equal-width discretization combined with the rough set and the neighborhood rough set-based simplification method can effectively reduce the data dimensionality. It is worth noting that compared with the rough set approach, the neighborhood rough set on the \"Sonar\" dataset has a reduction rate as high as 90%, which clearly indicates that the neighborhood rough set is a more effective means of data dimensionality reduction and redundancy data elimination. Table 3 demonstrates the classification accuracies of each dataset feature under four different classification algorithms. A comparison of the accuracy of rough sets and neighborhood rough sets shows that the latter is usually better than the former. The underlying reason for this difference is that the choice of discretization method has a non-negligible impact on the data, which may lead to a reduction in the relevance of the original data and loss of some information. However, neighborhood rough sets successfully overcome this drawback. By comparing the classification accuracy of Neighborhood Rough Set (NRS) with that of the original data (Raw), it can be found that the accuracy of NRS is equal to or higher than that of the original features, which indicates that NRS can effectively pick out the representative data features, and thus eliminate the redundant features. Finally, in terms of the average value of classification accuracy, DOA-SVM reaches 82.99%, which is