# Mmp1
## 4 Experimental Results and Comparative Study  
In order to evaluate our proposed architecture, a preprocessing task was required. First, we resized and normalized the image data to \(128\times 128\) RGB size. Then, we prepared the text e-mail data for the PV-DBOW model by removing stop words and tokenizing these e-mails. On one hand, the hyperparameters of the PV-DBOW used in this experiment included the size of the text e-mail vector set to 300, an initial learning rate of 0.002, and a context window equal to 30. On the other hand, the input of the CNN model was a \(128\times 128\) RGB image. The model contained three convolutional layers, each of them followed by a maximum pooling layer. In addition, the numbers of filters used in the first, second, and third convolutional layers were 32, 64, and 64, respectively. The kernel sizes used in the convolutional layers were set to \(5\times 5\), \(3\times 3\), and \(3\times 3\), while \(2\times 2\) was the kernel size used in the three pooling layers. The rectified linear unit (ReLU) and sigmoid were used as the activation functions. The last pooling layer was flattened to feed it into two hidden layers with 64 and 32 neurons. The model was trained using the hyperparameters cited in Table 2, and then we used the first hidden layer with 64 neurons as a feature vector to describe an image e-mail. The two feature vectors, coming from the PV-DBOW model and the last layer of the trained CNN model, were concatenated to form a robust feature vector describing a hybrid e-mail. This vector was fed to the RF classifier to distinguish between spam and ham e-mails. \begin{table}
\begin{tabular}{c c} \hline \hline
**Optimizer** & **Adam** \\ \hline Learning rate & 0.001 \\ \hline Epochs & 100 \\ \hline Batch size & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The hyperparameters used in the experiments. Table 3 shows the experimental results conducted on Dataset 1, Dataset 2, and Dataset 3. The performance of our proposed architecture was verified using the k-fold cross-validation method. In this paper, we used fivefold cross-validation to divide each of these datasets. One set was used for validation, while the remaining sets were used for the training. The average values of _accuracy_, _recall_, _F1-score_, and _precision_ were calculated after using the fivefold cross-validation method as follows:  
\[Accuracy =\frac{\sum_{i=1}^{k}Accuracy_{i}}{k}, \tag{8}\] \[Recall =\frac{\sum_{i=1}^{k}Recall_{i}}{k},\] (9) \[F1-score =\frac{\sum_{i=1}^{k}F1-score_{i}}{k},\] (10) \[Precision =\frac{\sum_{i=1}^{k}Precision_{i}}{k}, \tag{11}\]  
where \(Precision_{i}\), \(Recall_{i}\), \(Accuracy_{i}\), and \(F1-score_{i}\) for the \(i\)-th set are computed as follows:  
\[Precision =\frac{TP}{TP+FP}, \tag{12}\] \[Recall =\frac{TP}{TP+FN},\] (13) \[Accuracy =\frac{TP+TN}{TP+TN+FP+FN},\] (14) \[F1-score =\frac{2.Precision.Recall}{Precision+Recall}. \tag{15}\]  
The number of ham e-mails that were misclassified (FP), the number of ham e-mails that were correctly classified (TN), the number of spam e-mails that were misclassified (FN), and the number of spam e-mails that were correctly classified (TP) were obtained after classification. The performance results of the MMPC-RF architecture in terms of _accuracy_, _F1-score_, _recall_, and _precision_ are shown in Table 3. The proposed model provided high performance on the different datasets (Dataset 1, Dataset 2, and Dataset 3). After applying the fivefold cross-validation to Dataset 1, Table 4 presents a comparative study with the existing state-of-the-art models. The SVM, classical k-NN, and MMA-MF models achieved an accuracy of 98.25%, 97.83%, and 98.42%, whereas our model achieved the best accuracy with 99.16%. In addition, as demonstrated in Table 4, our model had the best _F1-score_ as compared to other models. On the other hand, the experiments conducted on the Dataset 2 are shown in Table 4, showing that the results obtained using our method exceeded those of all existing models in terms of _accuracy_ and _F1-score_.