# Breast Cancer Image Classification Using Phase Features and Deep Ensemble Models
## 4 Experimental Results
### Performance Comparisons with Existing Methods  
One of the biggest challenges in artificial intelligence and image processing is the accurate diagnosis of breast cancer in digital mammograms. Different strategies based on machine learning, CNNs, and hybrid methods have been developed for this purpose. Despite the importance of making fair performance comparisons among the different existing state-of-the-art methods, it should be taken into account that making a direct comparison between these methods is not always feasible. This is due to several factors, such as the number of classes, training datasets, and evaluation criteria, among others. In addition, implementation details and validation specifications are not always available. Developing a machine learning model for medical diagnosis without using data augmentation is desirable, as it ensures that the model is trained on unaltered training images, thereby preserving clinical relevance. This approach allows for more accurate validation by medical experts. Moreover, avoiding data augmentation helps reduce the risk of overfitting, improving robustness, computational efficiency, and design simplicity. Table 9 presents a performance comparison between the proposed method and six different existing methods, all of which consider the same number of classes and do not use data augmentation. The main similarities and differences between the proposed methodology and these state-of-the-art methods are briefly discussed below. In Muduli [10], 2236 images were used from MIAS, DDSM, and INbreast datasets. A manually extracted ROI was employed for each mammogram, and feature extraction was performed using the fast discrete curvelet transform with wrapping. Dimensionality reduction was carried out using PCA and linear discriminant analysis (LDA). Additionally, the classification was performed using the ELM with parameters optimized with PSO. In our approach, the ROI is given by the central region of the image, and similar to [10], the extracted features are reduced, but using a simplified approach with minimal computational cost. Without specifying the training/testing ratio, the best reported result in Muduli [10] is an accuracy of 98.94%. However, compared with our approach, this model is less complex, as it used only about 14% of the images considered in our methodology. Bacha [11] uses 991 images, which represents only 7% of the total number of images utilized in the development of the proposed model. Feature extraction is performed by the discrete Chebyshev transform from an extracted ROI of size \(127\times 127\) pixels. Without specifying the training/testing ratio, the reported accuracy is nearly 100%, and the AUC is close to unity. In Thawkar [12], 651 images are considered for constructing the model. For ROI extraction, this approach utilizes watershed segmentation in conjunction with morphological filtering. For dimensionality reduction, this method employs an evolutionary algorithm called the crow search algorithm and Harris Hawks optimization (CSHHO). For classification, the ANN and SVM methods are used. Without specifying the training/testing ratio, the best reported results are 97.85% accuracy, 97.45% specificity, and 98.22% sensitivity. It \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Reference** & **Images** & **RepVal** & _Acc (\%)_ & _Pre (\%)_ & _Rec (\%)_ & **F1 (\%)** & **AUC** \\ \hline [PERSON] [10] & 2236 & No & 98.94 & – & – & – & – \\ [PERSON] \& [PERSON] [11] & 991 & No & 100.00 & – & – & – & 1.000 \\ [PERSON] [12] & 651 & No & 97.85 & – & 98.22 & – & – \\ [PERSON] [14] & 1923 & No & 98.62 & – & 98.60 & – & 0.9817 \\ [PERSON] [13] & 633 & No & 96.87 & – & 97.23 & – & 0.980 \\ [PERSON] [27] & 797 & No & 97.90 & 97.36 & – & – & – \\
**Proposed (CSAW-M)** & **10,020** & **Yes** & **93.47** & **87.61** & **93.19** & **90.32** & – \\
**Proposed (mini-DDSM, MIAS, CSAW-M)** & **15,506** & **Yes** & **86.28** & **78.75** & **86.14** & **80.09** & – \\ \hline \hline \end{tabular}
\end{table}