# A Study of Breast Cancer Classification Algorithms by Fusing Machine Learning and Deep Learning
## 4 Methodology
### Feature Selection Algorithm  
To obtain the importance of each feature in the sample, this paper adopts the decision tree method to count the importance of each feature node for the breast cancer classification dataset. To prevent the impact from dividing the samples on the experimental results or the inaccurate feature classification [13], because of individual abnormal sample sets, this paper repeats the experiments by sampling the data several times and training the decision tree separately.  
\[C_{j}=\left(n_{0}*c_{0}-\sum n_{i}*c_{i}\right)/T \tag{3}\]  
Shown in Equation (3) is the formula for calculating the degree of importance of each feature (denoted as j) a, where \(n_{0}\) represents the number of statistical samples supporting that feature node, \(c_{0}\) represents the calculated Gini [3] value for that feature node, while \(n_{i}\) and \(c_{i}\) represent the numbers of samples of all sub-nodes of that node and their Gini values, and \(T\) is the combined number of samples of the calculated nodes in this formula. \(T\) is added to prevent the difference in magnitude caused by the number of samples under different nodes.  
Figure 5 shows the histogram of the number of times each sample was collected after sampling 30% of the samples from the training set as training samples for 1000 times. Figure 6 shows the statistical results of the accuracy of the decision tree trained individually using the 30% of samples obtained from each sampling as training samples.  
Figure 4: The different modules used and the information transformation process.  
As shown in Figure 5, the random sampling method in this paper is uniformly distributed sampling and each sample is sampled with approximately equal probability. As shown in Figure 6, 30% of the data are utilized in training, while 70% of the data are used as testing in the training set. The decision tree classification accuracy level proves to be quite high, and its feature weight division value is quite informative (As shown in Figure 7).  
In this paper, the experiments explore the performance effect of auxiliary classification models for breast cancer in the case of small-sample experimental data, suggesting that smaller numbers of features reduce the feature dimensionality, prevent the model from fitting the data in unnecessary dimensions, and therefore, reduce overfitting for particular samples. At the same time, since the tree model forms separate branches for each feature dimension, using low-dimensional key features can reduce the complexity of the overall tree structure.  
Figure 5: The histogram of the number of times each sample was collected after sampling 30% of the samples from the training set.  
Figure 6: The decision tree classification accuracy level.  
After performing the experiments 1000 times, the importance metric C calculated for each feature was summed to obtain the final importance value for each feature. This value, averaged over multiple samplings, eliminates overfitting errors that may be caused by a single sampling experiment, and the results are more representative of the feature importance profile on the overall dataset. As shown in (Figure 5), features such as cave points_worst, perimeter_worst, radius_worst, cave points_mean, and concavity_mean occupy the vast majority of the information in the data, and these parameters will be used as input to the machine learning model for learning in the following.  
Figure 7: Weigh map of importance value of different statistical breast cancer data features.