## 2 Methodology
### Suggested U-Net Model
When dealing with limited data, it is important to use a cost function that can help prevent overfitting and improve generalization performance. One such cost function is the Tversky loss, which is an extension of the Dice loss, that includes an additional parameter to control the balance between false positives and false negatives. The Tversky loss has been shown to be effective in medical image segmentation tasks, where the class imbalance between foreground and background pixels can be significant [43; 44; 45]. Thus, in this study, we used the Tversky cost function, as described in Equation (1):  
\[ \begin{split}&\text{loss(y\_true\_y\_pred)}\\ =1-(2\times\text{sum(y\_true}\times\text{y\_pred)}+\text{alpha})/( \text{sum(y\_true}\times\text{y\_pred)}+\text{beta}\times\\ \text{sum(y\_true}\times(1-\text{y\_pred)})+(1-\text{alpha})\times \text{sum((1}-\text{y\_true})\times\text{y\_pred)}+\text{smooth})\end{split}  \tag{1}\]  
where 'y_true' is the ground truth segmentation mask, 'y_pred' is the predicted segmentation mask, 'alpha' and 'beta' are hyperparameters that control the balance between false positives and false negatives, and'smooth' is a smoothing parameter to avoid division by zero. The Tversky loss is a generalization of the Dice loss, where 'alpha = beta = 0.5'. By adjusting the values of 'alpha' and 'beta', one can control the trade-off between false positives and false negatives, and tailor the loss function to one's specific task [43; 44; 45]. To provide a detailed analysis of the impact of various hyperparameters on the performance of the proposed method, more specific information about the methodology, model architecture, and hyperparameters used in our study would be required. However, a general overview of how hyperparameters can influence the performance of deep learning models for image segmentation tasks is provided as follows [4; 10; 46; 47; 48; 49; 50]:  
* Learning Rate: The learning rate determines the step size at which the model adjusts its parameters during training. A higher learning rate may result in faster convergence but could also lead to overshooting and instability. On the other hand, a lower learning rate might result in slower convergence or becoming stuck in local optima. It is essential to find an optimal learning rate that balances convergence speed and stability for the specific model and dataset. We used 0.001 as the value for the Learning Rate;
* Batch Size: The batch size determines the number of samples processed in each training iteration. A larger batch size may lead to faster convergence but requires more memory and computational resources. Conversely, a smaller batch size can result in more noise during training but may help the model generalize better. Finding the right balance between batch size and convergence speed is crucial. Batch Size was 10 in our study;
* Network Architecture: The architecture of the U-Net model itself is an important hyperparameter. The number of layers, layer sizes, skip connections, and other architectural choices can significantly impact the model's capacity to learn and its ability to handle the complexity of breast tumor segmentation. Experimenting with different network architectures, such as varying the number of layers or adjusting the number of filters in each layer, can help optimize performance;
* Regularization Techniques: Regularization techniques such as dropout, batch normalization, or weight decay can help prevent overfitting and improve generalization. The choice of regularization parameters, such as dropout rates or weight decay coefficients, can influence the model's ability to generalize to unseen data. Careful tuning and experimentation with these regularization techniques are essential to achieve optimal performance;
* Data Augmentation: Data augmentation techniques, such as rotation, scaling, or flipping, can help increase the robustness of the model by providing additional training examples.