# Breast Cancer Image Classification Using Phase Features and Deep Ensemble Models
## 3 Proposed Methodology
### Feature Extraction CNN-Based Model  
This work considers four variants of EfficientNetV2 as feature extractors. The MIAS, mini-DDSM, and CSAW-M datasets are combined, and one ROI of size 256 \(\times\) 256 pixels is extracted for each mammogram, as shown in Figure 2. Next, a 3-channel image is created utilizing Equations (7)-(9), with the local phase, local orientation, and phase congruence as the respective channels. Note that the employed phase image features provide information on both broad and fine details of the breast tissue for classification. Afterwards, for the EfficientNetV2S to EfficientNetV2 XL models in Table 5, the last layers are removed, and only the values of a 1280-element vector of the last fully connected (FC) layer are considered as features for all models. However, in many cases, classification models are more efficient, with compact vectors containing only the most significant features [51]. Dimensionality reduction is crucial for processing high-dimensional data, as it removes redundant features and increases classification efficiency [52]. This task also reduces the complexity of classification models and improves accuracy by retaining the most relevant information, thereby decreasing computing time [53]. The proposed model employs simple statistical descriptors for dimensionality reduction instead of more complex techniques. Specifically, the following statistics are used to reduce the dimensionality of the FC layer:  
\[\mu(FC)=\frac{1}{L}\sum_{i=1}^{L}FC(i) \tag{10}\]  
\[\sigma^{2}(FC)=\frac{1}{L-1}\sum_{i=1}^{L}[FC(i)-\mu(FC)]^{2} \tag{11}\]  
\[\sigma(FC)=\sqrt{\sigma^{2}(FC)} \tag{12}\]  
\[max(FC)=\max_{i=1,\ldots L}(FC(i)) \tag{13}\]  
\[min(FC)=\min_{i=1,\ldots L}(FC(i)). \tag{14}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model Variant** & **Input Shape** & **Output Vector Length** \\ \hline V2S & \(384\times 384\) & 1280 \\ V2M & \(480\times 480\) & 1280 \\ V2L & \(480\times 480\) & 1280 \\ V2 XL & \(512\times 512\) & 1280 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Specifications of EfficientNetV2 model variants, including input image shape and the output vector length of the final fully connected layer. Consequently, the final descriptor for each mammogram is  
\[S_{FC}=\Big{[}\mu(FC),\sigma^{2}(FC),\sigma(FC),\text{max}(FC),\text{min}(FC) \Big{]}. \tag{15}\]  
This dimensionality reduction approach aims to simplify classification, reduce computational complexity, and mitigate the risk of overfitting without significantly degrading essential information, particularly when working with small medical imaging datasets. To classify the descriptor \(S_{FC}\), four machine learning-based ensemble classifiers were employed: voting, stacking, bagging, and boosting [54; 55; 56; 57]. These classifiers were selected for their strong predictive performance, improved generalization, and reduced risk of overfitting. Also, these classifiers are robust to moderate class and dataset imbalances, making them well suited for the combined datasets used in this study. In addition, no data augmentation or resampling techniques were applied in order to preserve the original data distribution and evaluate the proposed method under realistic clinical conditions. Algorithm 1 presents the pseudocode of the proposed method for feature extraction and breast cancer detection.