## 3 Materials and Methods
### Proposed Framework
#### 3.2.2 Explainable AI  
XAI demonstrated the black-box approach recognized in DL models and revealed the precise reasoning behind their predictions [55]. As the complexity of DL models has increased, XAI has become an important strategy, particularly in domains where critical decisions are needed, such as for medical image analysis [56]. Medical experts have been able to more easily understand the results of these DL models and use them to quickly and accurately diagnose cysts, normal growths, kidney stones, and tumors [57].Therefore, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**S.N.** & **Layer Type** & **(E, K, S)** & **Output Shape** & **Parameters** & **FLOPs** \\ \hline
1 & Input & - & (150, 150, 3) & 0 & - \\
2 & Conv2D + relu & (3, 3, 1) & (148, 148, 63) & 1792 & 25,233,408 \\
3 & MaxPool2D (2) & - & (74, 74, 64) & 0 & 296 \\
4 & Conv2D + relu & (3, 3, 1) & (72, 72, 64) & 36,928 & 5,971,968 \\
5 & MaxPool2D (2) & - & (36, 36, 64) & 0 & 144 \\
6 & Conv2D + relu & (3, 3, 1) & (34, 34, 64) & 36,928 & 1,331,712 \\
7 & MaxPool2D (2) & - & (17, 17, 64) & 0 & 68 \\
8 & Conv2D + relu & (3, 3, 1) & (15, 15, 64) & 36,928 & 259,200 \\
9 & MaxPool2D (2) & - & (7, 7, 64) & 0 & 28 \\
10 & Conv2D + relu & (3, 3, 1) & (5, 5, 64) & 36,928 & 5760 \\
11 & MaxPool2D (2) & - & (2, 2, 64) & 0 & 8 \\
12 & Flatten & - & 256 & 0 & 131,072 \\
13 & dropout (0.2) & - & 256 & 0 & - \\
14 & Dense + relu + l2 & & & & \\  & (0.0001) & - & 128 & 32,896 & 65,536 \\
15 & Dense + Softmax + & & & & \\  & l2 (0.0001) & - & 4 & 512 & 1024 \\ \hline \hline \multicolumn{5}{c}{Total parameters} & \multicolumn{3}{c}{182,916} \\ \hline \hline \multicolumn{5}{c}{Total FLOPs} & \multicolumn{3}{c}{33,000,224} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Total parameters (trainable and non-trainable) of the proposed CNN model. Variables F, K, S, and FLOP denote the filters, kernel size, stride, and floating-point operations, respectively. Figure 3: Visual representation of the proposed CNN model. Shapley additive explanation (SHAP) and local interpretable model-agnostic explanation (LIME), two popular XAI algorithms, were specified in this study. By normalizing the marginal feature values, SHAP assessed the influence of the model features. The scores exemplified the significance of each pixel on a predicted image and were used to substantiate their classification. To obtain the Shapley value, all potential combinations of characteristics of kidney abnormalities were used. Red pixels increased the likelihood of predicting a class once the Shapley values were converted into pixels, while blue pixels reduced the likelihood [58]. The Shapley values were generated by Equation (1). \[\phi_{i}=\sum_{S\subseteq N\setminus\{i\}}\frac{|S|!(M-|S|-1)!}{M!}[f_{x}(S \cup\{i\})-f_{x}(S)] \tag{1}\]  
where \(f_{x}\) is the adjustment of the output by Shapely values for feature \(i\). Feature \(N,S\) is the subset of the features, and \(\frac{|S|!(M-|S|-1)!}{M! }\) is the weighing factor that determined the number of permutations of the subset \(S\) are present. The predicted result, \(f_{x}(S)\), was calculated using Equation (2). \[f_{x}(S)=E[f(x)|x_{S}] \tag{2}\]  
where each original trait replaced \((x_{i})\), using SHAP, and a binary variable \(z^{{}^{\prime}}_{i}\) is replaced that represents whether \(x_{i}\) is absent or present, as shown in Equation (3)  
\[g(z^{{}^{\prime}})=\phi_{0}+\sum_{i=1}^{M}\phi_{i}z^{{}^{\prime}}_{i}=\sum feature Contribution+bias \tag{3}\]  
where the primordial model \(f(x)\), in Equation (3), \(g(z^{{}^{\prime}})\) is the local surrogate model, feature \(i\) is based on the result, and \(\phi_{i}\) assisted in understanding the model. To interpret the representation of an instance being presented in a way that could be explained, \((x\in\mathbb{R}^{d})\) using LIME, a binary vector \((x^{{}^{\prime}}\in\{0,1\}^{d^{{}^{\prime}}})\) represented the \"absence\" or \"presence\", and a continuous patched super-pixel was considered.