## 2 Materials and Methods
### Feature Extraction  
Local Binary Pattern--LBP  
The LBP operator is a method used to describe the texture of an image by evaluating the relationships between a pixel and its neighbors [34]. The process involves the following steps:  
* Window selection: For each pixel, a specific neighborhood (usually a 3 \(\times\) 3 window) is selected around it.
* Comparison: The intensity of the central pixel is compared to the intensities of the neighboring pixels. If a neighboring pixel has an intensity greater than or equal to the central pixel, it is marked as 1; if it is smaller, it is marked as 0.
* Binary encoding: The obtained 0s and 1s are arranged in a specific order to form a binary number.
* Pattern assignment: The binary number is assigned as the value of the central pixel, thus generating the LBP codes.
* Histogram creation: After extracting the LBP codes for all pixels, a histogram of these codes is created to obtain texture features.  
In general, LBP\({}_{\text{PR}}\) can be defined with three different circular neighborhoods where P represents the number of neighbors and R represents the sampling radius. The LBP operators we used are shown in Figure 2[34; 35].  
\[LBP_{P,R}(x_{c})=\sum_{p=0}^{p-1}u\left(x_{p}-x_{c}\right)2^{p} \tag{1}\]  
\[u(y)=\{1,\ y\ \geq 0\ \ \ 0,y<0\}\]Here, \(Xc\) represents the generated center pixel, \(Xp\) represents the neighbors of \(Xc\), \(R\) is the distance from the center pixel to the neighbors, and \(P\) is the number of neighbors involved in the processing.  
In this analysis, 3 \(\times\) 3 windows were chosen as they effectively capture local texture information while being computationally efficient. This window size allows each central pixel to be compared with its eight neighboring pixels (LBP\({}_{8,1}\)), making it possible to capture the fine details of the local texture. In this study, for all images, a total of 177 features were obtained from the RGB (Red, Green, Blue) channels, with 59 LBP features extracted from each channel. When selecting the most important features from these, Lasso (Least Absolute Shrinkage and Selection Operator) regression [36] was used. Lasso regression is a popular regression method used to identify important features and eliminate unnecessary ones in high-dimensional datasets. In cases where there are many features, it improves the model's performance and reduces overfitting by shrinking some regression coefficients to zero, ensuring that only the most important features remain in the model. Figure 3 shows how LBP operates on a sample image.  
**Mathematical interpretation of Lasso regression:** Lasso regression is a method used to select important features from a dataset and eliminate unnecessary ones. This method prevents overfitting by shrinking some regression coefficients to zero, thus retaining only the most important features. The Lasso regression problem is explained by the formula given in Equation (2).  
\[\sum_{i=1}^{n}\left(y_{i}-\sum_{j=1}^{p}\beta_{j}x_{ij}\right)^{2}+\lambda\sum _{j=1}^{p}|\beta_{j}| \tag{2}\]  
Figure 3: LBP operates on a sample image.  
Figure 2: Used circular LBP\({}_{\text{PR}}\) operators.  
\(y_{i}\): target variable;
* \(x_{ij}\): input features;
* \(\beta_{j}\): regression coefficients;
* \(\lambda\): the lambda parameter.  
In this study, the lambda parameter was experimentally set to 0.0005 for the Cis, Exo, ExoCis, CisExo, and Control groups. As the lambda value increases, more coefficients converge to zero, and thus fewer features remain in the model.