## 3 Materials and Methods  
This study utilized the WDBC dataset retrieved from the UCI Machine Learning Repository [29; 30]. The dataset contains 569 observations with 30 numerical features derived from digitized images of Fine-Needle Aspiration biopsies. These features include the standard error, mean, and worst values of attributes such as texture, radius, and perimeter. This dataset was chosen for its widespread use in evaluating AI-based diagnostic systems, balanced representation of benign and malignant cases, and relevance to healthcare applications. Feature selection was performed using the Scikit-learn library in Python. Initially, 15 key features were identified using the univariate selection method. Further refinement was performed, where we evaluated all the features and retained only those selected by at least two methods from Logistic Regression, Best-First Search, and Random Forest. This resulted in the final 14 most relevant features, as shown in Table 1.  
We performed data preprocessing by scaling all the features to a range of 0 to 1, using a StandardScaler to ensure consistency. The dataset was divided into training (80%) and testing (20%) subsets to preserve the class distribution. We carried out the experiments using Python 3.12.3 alongside several libraries to handle data preprocessing, model building, and evaluation. We used TensorFlow.keras from TensorFlow 2.17.0 and Scikit-learn 1.5.0 to develop and train the DL models for tasks like data splitting, scaling, and implementing the MLP classifier. Data manipulation was performed using NumPy 1.26.4 and Pandas 2.2.2, and visualisations were created with Matplotlib 3.9.1 and Seaborn 0.13.2. The WDBC dataset was obtained using the ucimlrepo library.  
All our experiments were executed on a system powered by an Intel(R) Core(TM) i7-10850H CPU running at 2.70 GHz, with 32 GB of RAM and an NVIDIA GeForce RTX 2070 GPU featuring 8 GB of dedicated memory. The system operated on Windows 11 Education (64-bit). This hardware setup ensured sufficient computational resources for training the models and efficiently running adversarial attack simulations. For a better understanding of our research, we have provided a list of the important symbols used in this research with their descriptions, in Table 2:  
\begin{table}
\begin{tabular}{c l l} \hline \hline
**No.** & **Univariate Selection** & **Multi-Method Selection** \\ \hline
1 & radius mean & concave points worst \\
2 & compactness worst & texture mean \\
3 & radius worst & perimeter mean \\
4 & texture mean & concavity worst \\
5 & perimeter mean & concavity mean \\
6 & area se & perimeter worst \\
7 & area worst & area se \\
8 & perimeter se & texture worst \\
9 & texture worst & radius worst \\
10 & perimeter worst & concave points mean \\
11 & concavity worst & area worst \\
12 & concave points worst & smoothness worst \\
13 & concavity mean & area mean \\
14 & area mean & radius mean \\
15 & radius se & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Selected features using univariate and multi-method selection techniques.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Symbol** & **Meaning** \\ \hline \(Z^{(l)}\) & Weighted input to the \(l\)-th layer of the neural network. \\ \hline \(a^{(l)}\) & Activation output of the \(l\)-th layer of the neural network. \\ \hline \(W^{(l)}\) & Weight matrix for the \(l\)-th layer of the neural network. \\ \hline \(b^{(l)}\) & Bias vector for the \(l\)-th layer of the neural network. \\ \hline \hline \end{tabular}
\end{table}
Table 2: List of symbols used in the manuscript.