## 4 Discussion  
FS for high-dimensional microarray datasets has always been a challenging task because of the complicated interdependence between features. In high-dimensional microarray datasets, the most critical issues in FS are the effectiveness of the evaluation criterion and the computational complexity of the search strategy. The former ensures that the selected feature subset has high quality, such as high relevance, low redundancy, small size, and good classification performance, while the latter ensures that the feature search can be completed in a short time. Our experimental results on three high-dimensional microarray datasets demonstrate that our algorithm successfully selects the minimum MRNR feature subset, as expected, without using any wrapper methods. Compared to existing IEMs and SEMs, our algorithm achieves better feature quality (as shown in Tables 3, 4 and 6). In contrast, the IEMs perform poorly in FS for high-dimensional datasets due to their neglect of interdependency between features, resulting in the failure to identify and eliminate redundant features in selected subsets (as shown in Figure 3). Additionally, the IEMs struggle to determine the number of features to select, leading to the need for personal experience or wrapper methods, which increases instability and computational complexity. While SEMs can consider feature interdependence, existing SEMs lack effective evaluation criteria to accurately determine maximum relevance with the target class and identify redundant features in the selected subset. Although the SEMs demonstrate more excellence than the IEMs in classification performance and redundancy reduction (as shown in Figures 2-5, and Tables 4 and 6), they still require preset parameters to determine the number of features to select. Determining the optimal feature number is critical for the SEMs, as too few features lead to insufficient relevance, while too many leads to numerous redundant features. Unfortunately, accurately determining the optimal number for high-dimensional datasets is difficult without resorting to more complex wrapper methods. In addition, we analyzed the relationship between feature quality and the classification accuracy of feature subsets using Rel and NFS. We find that the Rel of a feature subset is positively correlated with its classification accuracy, while a small number of redundant features within the feature subset have an uncertain (both positive and negative) impact on its classification accuracy. However, including too many redundant features in a feature subset has a significant negative impact on some machine learning classifiers, such as SVM. The conclusion indirectly highlights the advantages of the minimum MRNR feature subset in terms of feature quality and classification accuracy. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Selected Genes** & **Known Genes** & **Validated Count** & **Effectiveness Rate** \\ \hline BPEx & IGF2, TNNT3, PPAR8, LEP, SIRT1, APOE, TRIM55, FTO & IGF2 [32], TNNT3 [33], PPAR8 [34], LEP [35], SIRT1 [36], APOE [37] & 6 & 75.00\% \\ BPSpnp\_1 & GHR, IGF1, LEP, MC4R, INSL3, PPAR8, SLC10A2, TNAFIP3, RYR1 & CH4R [41], INSL3 [42], PPAR8 [43], SLC10A2 [44], TNFAIP3 [45] & 8 & 89.00\% \\ BPSnp\_2 & IGF2, LEP, FABP3, MC4R, CAST, PLIN1, UCP3, ASIP, ADRB3 & MCF4R [49], CAST [50], PLIN1 [51], UCP3 [52] & 7 & 77.78\% \\ BPSnp\_3 & IGF1, GHR, GH1, LEP, IGFBP3, MTOR, ASIP, NOS3 & IGF1 [53], GHR [54], GH1 [55], LEP & 5 & 62.50\% \\ BPPRRS & CD163, GBP5, MX1, OAS1, MTOR, IGF2 BP1 & CD163 [57], GBP5 [58], MX1 [59], OAS1 [60] & 4 & 66.67\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Gene verification for pig traits. In terms of execution time, the IEMs have obvious advantages because they ignore the relevance between features (as shown in Table 5). In contrast, the SEMs are more time-consuming. Our algorithm, however, achieves relatively short execution times compared to SEMs, though it is more time-consuming than IEMs (as shown in Tables 5 and 7).