## 3 Selection of Indicators for the Evaluation  
Evaluation indicators are quantitative indicators for evaluating the performance of the model, and if the selected evaluation indicators are not reasonable, it will affect the orientation of the result analysis. Therefore, different evaluation indicators should be selected for specific data and models.  
In this paper, breast cancer prediction is a binary classification problem, then the classification results can generate a confusion matrix, as shown in Table 1, where \(TP\) indicates that the positive class is predicted as the number of positive classes; \(TN\) indicates that the negative class is predicted as the number of negative classes, which can be referred to as the true counterexample; \(FP\) indicates that the negative class is predicted as the number of positive classes, which is referred to as the first type of error; \(FN\) indicates that the positive class is predicted as the number of negative classes, which is referred to as the second type of error.  
In order to measure the classification effect of the model in this paper, the four perspectives of the model--the overall accuracy of the model, the accuracy of the positive class prediction, the coverage ability of the positive class, and the comprehensive performance--are taken into account. The accuracy, precision, recall, and F1-score are selected as the four main evaluation indicators to evaluate the prediction effect of the model. And these evaluation indicators have values between 0 and 1. The closer the value is to 1, the better the classification effect of the model is. The receiver operating characteristic (ROC) curve is also selected as an assistant indicator to compare the classification effect among the models. The specific meanings are as follows:  
1. Accuracy: represents the total proportion of all predictions that are correct (positive and negative categories) and can be expressed as \(accuracy=\frac{TP+TN}{TP+TN+FP+FN}\). For breast cancer prediction, a high accuracy rate indicates that the model is better at correctly classifying both malignant and benign tumors. Accuracy is justified because it provides an assessment of overall classification accuracy and can help determine the model's ability to discriminate between the two types of tumors.
2. Precision: indicates how many of the samples predicted to be positive are truly positive, which can be expressed as \(precision=\frac{TP}{TP+FP}\), also known as PPV.
3. Recall: indicates how many positive cases in the sample were predicted correctly, which can be expressed as \(precision=\frac{TP}{TP+FN}\), also known as \(TP\).
4. \(F1\)-score: it can be expressed as \(F_{1}=2\frac{PPV\times TPR}{PPV+TP}\). \(F1\)-score is a comprehensive evaluation index of extrinsic methods. For breast cancer prediction, \(F1\)-score is reasonable because it balances the model's ability to correctly classify malignant and benign tumors. It also comprehensively evaluates the precision and recall of the model, which is one of the very important evaluation indicators.
5. The receiver operating characteristic (ROC) curve: in the ROC curve, the horizontal axis is the false positive rate (FPR) and the vertical axis is the true positive rate (\(TP\)). The points closer to (0, 1) correspond to the better classification performance of the model. AUC is the area under the ROC curve, between 0 and 1. As a numerical value it can be visualized to evaluate the classifier, the larger the value the better. When \(AUC=1\), it is a perfect classifier. When \(0.5<AUC<1\), it is better than random guessing. When \(AUC=0.5\), like random guessing, the model has no predictive value. When \(AUC<0.5\), the model is less predictive than random guessing.