## 4 Results  
In this study, all simulations were conducted on a PC equipped with an Intel i7-9750H CPU (Intel Corporation, Santa Clara, CA, USA) operating at 2.6 GHz, with 16 GB of RAM. For GPU-accelerated computations, the algorithms were executed using an NVIDIA GTX 1660 Ti GPU (NVIDIA Corporation, Santa Clara, CA, USA) with 6 GB of dedicated memory, enhancing computational efficiency, particularly for tasks requiring substantial processing power. The dataset, denoted by \(D=\{(X_{n},\ Y_{n})\ |\ \ X_{n}\ \in\mathbb{R}^{\{224\times 224\}},\ Y_{n}\in\{0,\ 1\}\ \}\), consists of individual image samples \(X_{n}\) with corresponding binary labels \(Y_{n}\), where \(n=1,\ \ldots,\ N\). Here, \(N\) represents the total number of samples, which have a \(224\times 224\) standardized resolution. In our simulations, the dataset is divided into batches, and the batch size is selected as 32. On the other hand, the epoch number is chosen as 100. Moreover, the data is divided using the k-fold cross-validation method. Importantly, the test and training splits were created based on patients rather than individual images, ensuring that images from 10% of the patients were exclusively used as the test set in each fold. This approach better reflects real-world scenarios, where models are often required to generalize to entirely new patients rather than new images from patients already seen during training. According to this strategy, the value of \(k\) is set to 10, such that each fold includes 5 schizophrenia and 5 bipolar patients in the test set, while the remaining patients are used for training. This strategy is similar to the approach described in [25]. To improve the generalization of the model and prevent overfitting, a checkpoint was used to save the best-performing model based on validation accuracy. After training, the performance of the model is evaluated on the test set in terms of performance metrics such as accuracy, precision, recall, F1-Score, AUC, and Matthews correlation coefficient (MCC). Accuracy is defined as the proportion of correctly classified samples to all samples. Let TP, TN, FP, and FN represent true positive, true negative, false positive, and false negative samples, respectively. Then, accuracy is given by  
\[\frac{TP+TN}{TP+TN+FP+FN} \tag{6}\]  
Precision is the ratio of TP samples to all samples predicted as positive by the model and is written as \(TP/(TP+FP)\). On the other hand, recall is the ratio of TP samples to actual positive samples and is expressed as \(TP/(TP+FN)\). The F1-Score is the harmonic mean of recall and precision, and it is important when the dataset is imbalanced, and is written as follows:  
\[2\times\frac{Precision\times Recall}{Precision+Recall} \tag{7}\]  
AUC represents the area under the receiver operating characteristic, which is the trade-off between the true positive rate, \(TP/(TP+FN)\), and the false positive rate, \(FP/(FP+TN)\). Finally, MCC is another performance metric, and it is very useful when the dataset is imbalanced. The MCC is written as  
\[\frac{TP\cdot TN-FP\cdot FN}{\sqrt{(TP+FP)(TP+FN)(TN+FP)(TN+FN)}} \tag{8}\]  
**Data Augmentation:** To enhance the generalizability of the model and prevent overfitting, a data augmentation method is employed on the training images using various transformation techniques. Although there are several transformation techniques used in image classification, not all of them are suitable for medical images. Therefore, the data augmentation techniques applied in this study were carefully selected to ensure they were suitable for medical images, avoiding any transformations that might distort the images. The selected augmentations, such as controlled rotation, flips, brightness adjustment, and rescaling, were chosen to enhance the diversity of the training data without damaging the anatomical or diagnostic integrity of the medical images. The first augmentation technique is rotation. In this method, images were randomly rotated by a specific angle. In our study, we set the angle to a range between 0 and 30 degrees.