## 6 Experimental Results and Analysis
### Analysis of Experimental Results
#### 6.3.6 Comparative Analysis of BDP-LR Model Results with Other Models  
The prediction effect of the BDP-LR model in this paper is compared with the DP-NB [35], DP-RF [36], DP-DT [36], and GDP-EBM [37] models under the consideration of privacy preservation. The variation of the four main evaluation indicators with \(\varepsilon\) for each model is shown in Figure 6.  
The results show that when increasing the value of privacy budget \(\varepsilon\) from 0.001 to 2 with WDBC data, the four main evaluation indicators of each model gradually increase and fluctuate up and down a certain value range with the increase in privacy budget \(\varepsilon\). According to Formula (2), the smaller \(\varepsilon\) is, the better the privacy protection effect is. So, the critical value of \(\varepsilon\) needs to be selected to provide balance between the model's classification performance and privacy protection effect. According to the trend of the four main evaluation indicators in Figure 6, 0.8 is chosen as the privacy budget value of the BDP-LR model when the model has better classification performance and a stronger privacy protection effect. At a privacy budget \(\varepsilon\) of 0.8, the experimental results of the BDP-LR model are compared with other machine learning models based on differential privacy. The performance of each model is evaluated using the ROC curve with AUC, as shown in Figure 7. In addition, the average values of the four main evaluation indicators obtained by running 100 experiments are shown in Table 9. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Literature** & **Method of Feature Selection** & **Method of Classification** & **Time** & **Accuracy** \\ \hline
[26] & ABC & XGBost & 2019 & 0.928 \\
[21] & GA & SVM & 2020 & 0.988 \\
[20] & GeFeS & KNN & 2020 & 0.985 \\
[18] & \(\chi^{2}\) test + (FT) + (RF) + RF & ET & 2020 & 0.952 \\
[19] & WCHI2 & KNN & 2020 & 0.986 \\
[24] & ALO & BPNN & 2020 & 0.9842 \\
[28] & GWO & KNN & 2020 & 0.948 \\
[23] & BBA & OCCNN & 2020 & 0.935 \\
[22] & Krill herd (KH) + SVM & BPNN & 2021 & 0.978 \\
[27] & Forward selection & LR & 2022 & 0.982 \\
[30] & ESO & RF & 2023 & **0.9896** \\
[12] & - & SV-naive Bayes-3 MetaClassifiers & 2020 & 0.981 \\
[13] & - & IRFR & 2020 & 0.951 \\
[11] & - & (SVM + LR + NB + DT) + ANN & 2022 & 0.983 \\
[9] & - & LR & 2020 & 0.981 \\
[8] & - & RF & 2022 & 0.9624 \\
[10] & EL & 2022 & 0.9814 \\ this paper & Pearson + RF-COB & BCD + LR & **0.9912** \\ \hline \hline \end{tabular}  
* GA = genetic algorithm, GeFeS = generalized wrapper-based feature selection, ET = extra tree, RFE = recursive feature elimination, BPNN = back propagation neural network, IRFRE = improved random forest-based rule extraction, BBA = binary bat algorithm, OCCNN = one-pass generalized classifier neural network, EL = ensemble learning technique, WCHI2 = with chi-square feature selection technique, ALO = ant lion optimization algorithm.  
\end{table} 
Table 8: Comparison of the results of the BGD-LR model with other breast cancer classification models. Figure 6: Comparison of the results of the BDP-LR model with other machine learning models based on differential privacy: (**a**) accuracy; (**b**) precision; (**c**) recall; (**d**) F1-score. Figure 7: ROC curve for each model when \(\varepsilon\) is 0.8: the closer the AUC value is to 1, the higher the prediction accuracy is. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Evaluation Indicators** & **BDP-LR** & **GDP-EBM** & **DP-NB** & **DP-RF** & **DP-DT** \\ \hline Accuracy & 0.9721 & 0.9439 & 0.8927 & 0.9070 & 0.8793 \\ Precision & 0.9975 & 0.9826 & 0.9786 & 0.9276 & 0.9506 \\ Recall & 0.9664 & 0.9443 & 0.8825 & 0.9545 & 0.8931 \\ \(F1\)-score & 0.9816 & 0.9620 & 0.9119 & 0.9402 & 0.9175 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Classification effect of BDP-LR model compared with other models when \(\varepsilon\) is 0.8. As shown in Figure 7, the AUC value of the BDP-LR model is 0.9974. The AUC values for the GDP-EBM and DP-NB models are 0.9694 and 0.9663, respectively.