## 1 Introduction
In the process of prediction, feature selection can eliminate irrelevant variables and redundant features to achieve effective dimensionality reduction and improve the accuracy of the algorithm [25]. [PERSON], [PERSON] et al. [26] proposed a new feature selection method based on bee colony (ABC) and extreme gradient boosting (XGBoost), which effectively reduced the dimensionality of the dataset, and the accuracy of the XGBoost was 0.928 on the WDBC dataset. Nevertheless, the study is limited to theories related to decision trees. [PERSON] et al. 's [27] study on the WDBC dataset showed that the LR model was the best classifier, and the accuracy of the LR model could be improved from 0.972 to 0.982 by using the forward feature selection method. [PERSON], [PERSON] et al. [28] proposed a new grey wolf optimizer (GWO) algorithm combining two-stage variation to solve the feature selection problem and selected the KNN classifier to classify breast cancer data, of which the accuracy of the final model could reach 0.9482. [PERSON], [PERSON] et al. [29] proposed a breast cancer prediction XGBoost ensemble model based on known feature patterns. In order to deal with the impact of data balance on classification results, SMOTE was used to process the data, and then the naive Bayes classifier (NB), DT, and RF were combined with XGBoost to classify the data. According to experimental analysis, the classification effect of the XGBoost-random forest ensemble classifier was the best. The classification accuracy of the model was 0.982. [PERSON], [PERSON] et al. [30] proposed a unique feature selection method based on eagle strategy optimization (ESO), the gravitational search optimization (GSO) algorithm, and their hybrid algorithm, which could select the fewest features to achieve the highest accuracy. Experimental results showed that the proposed method achieved great results on the WDBC dataset with an accuracy of 0.9896. Machine learning methods have contributed to the early diagnosis of breast cancer. Making improvements to the classification model and processing the data using feature selection methods can improve the classification of breast cancer, but the classification of breast cancer is still not optimal for the existing research. In addition, there is a risk of leaking specific private information in the training data to attackers through the structure of the model [31]. In recent years, the leakage of private information of patients has occurred frequently. With the advancement of cloud technology and big data, it is easier for attackers to collect patients' private information and speculate about patients' sensitive information through correlation and other means [32]. Therefore, while combining machine learning models with cancer diagnosis, it is also necessary to pay attention to the privacy protection of data. Commonly used privacy protection techniques are anonymity-based privacy protection, encryption-based privacy protection, and noise-based privacy protection [33]. Differential privacy technology based on noise was proposed by [PERSON] [34] of Harvard University in 2006 by adding a series of \"noise\" to the original data, making it difficult for attackers to achieve accurate calculation of an individual user's privacy data, so as to improve the efficiency of data sharing and use under the premise of protecting data security. The application of privacy protection technology in data mining has become a research hotspot in the field of artificial intelligence [35; 36; 37], and how to achieve the combination with machine learning with a smaller accuracy loss cost is still an urgent problem to be solved [38]. In summary, there are two main problems in the study of breast cancer prediction: (1) how to improve the prediction effect through feature selection and model improvement; (2) how to improve the classification effect and at the same time make the model have privacy protection function. To solve these two problems, this paper proposes a new hybrid feature selection method to process data.