In order to improve the classification effect of the logistic regression (LR) model for breast cancer prediction, a new hybrid feature selection method is proposed to process the data, using the Pearson correlation test and the iterative random forest algorithm based on out-of-bag estimation (RF-OOB) to screen the optimal 17 features as inputs to the model. Secondly, the LR is optimized using the batch gradient descent (BGD-LR) algorithm to train the loss function of the model to minimize the loss. In order to protect the privacy of breast cancer patients, a differential privacy protection technology is added to the BGD-LR model, and an LR optimization model based on differential privacy with batch gradient descent (BDP-LR) is constructed. Finally, experiments are carried out on the Wisconsin Diagnostic Breast Cancer (WDBC) dataset. Meanwhile, accuracy, precision, recall, and F1-score are selected as the four main evaluation indicators. Moreover, the hyperparameters of each model are determined by the grid search method and the cross-validation method. The experimental results show that after hybrid feature selection, the optimal results of the four main evaluation indicators of the BGD-LR model are 0.9912, 1, 0.9886, and 0.9943, in which the accuracy, recall, and F1-scores are increased by 2.63%, 3.41%, and 1.76%, respectively. For the BDP-LR model, when the privacy budget ε is taken as 0.8, the classification performance and privacy protection effect of the model reach an effective balance. At the same time, the four main evaluation indicators of the model are 0.9721, 0.9975, 0.9664, and 0.9816, which are improved by 1.58%, 0.26%, 1.81%, and 1.07%, respectively. Comparative analysis shows that the models of BGD-LR and BDP-LR constructed in this paper perform better than other classification models.

This study aims to improve the quality of the clustering results of the density peak clustering (DPC) algorithm and address the privacy protection problem in the clustering analysis process. To achieve this, a DPC algorithm based on Chebyshev inequality and differential privacy (DP-CDPC) is proposed. Firstly, the distance matrix is calculated using cosine distance instead of Euclidean distance when dealing with high-dimensional datasets, and the truncation distance is automatically calculated using the dichotomy method. Secondly, to solve the difficulty in selecting suitable clustering centers in the DPC algorithm, statistical constraints are constructed from the perspective of the decision graph using Chebyshev inequality, and the selection of clustering centers is achieved by adjusting the constraint parameters. Finally, to address the privacy leakage problem in the cluster analysis, the Laplace mechanism is applied to introduce noise to the local density in the process of cluster analysis, enabling the privacy protection of the algorithm. The experimental results demonstrate that the DP-CDPC algorithm can effectively select the clustering centers, improve the quality of clustering results, and provide good privacy protection performance.

Cervical cancer remains a significant global public health challenge, particularly in low- and middle-income countries where invasive diagnostic methods are underutilized due to limited medical resources. Machine learning has provided a new pathway to address this challenge, but existing machine learning prediction methods face three major challenges: feature redundancy, class imbalance, and sample scarcity. To address these issues, this study proposes a hybrid data processing strategy with Conditional Tabular Generative Adversarial Networks (CTGAN) and machine learning to construct a more accurate and efficient auxiliary diagnostic model for cervical cancer. The hybrid strategy first employs the Minimal Redundancy Maximal Relevance (mRMR) algorithm and XGBoost-based Recursive Feature Elimination (RFE) for secondary feature screening. Subsequently, the SMOTE-ENN combination sampling method is applied to handle extreme class imbalance, and CTGAN is utilized to augment the dataset, thereby mitigating data scarcity. Experimental validation on the Risk Factors of Cervical Cancer (RFCC) dataset from a Venezuelan hospital demonstrates that, after processing with the proposed hybrid strategy, the Logistic Regression (LR) model achieves the best overall prediction results, with accuracy, precision, recall, and F1-score reaching 99.00%, 99.28%, 98.77%, and 99.02%, respectively, outperforming existing methods.