## 4 Experimental Results  
All the experiments were tested on a Linux operating system using 11 th Gen Intel Core i9-11900 @2.50 GHz Ram CORSAIR VENGEANCE LPX 32 GB (16 GBx2) DDR4 3200 MHz NVIDIA GeForce 1060 6 GB to process proposed model. We implemented all our experiment uses the FER2013 dataset, which is a benchmark FER dataset consisting of nearly 35,887 48 \(\times\) 48 pixel 8-bit greyscale images of various people's facial expressions, determined by their facial emotions as show in Figure 4.  
The data points were split into 3 datasets: 28,709 training data points, 3589 validation data points, and 3589 test data points, as shown in Table 3. The facial images encompass both male and female subjects and 7 emotion classes (Angry, Disgust, Fear, Happy, Sad, Surprise, Neutral) as Figure 5. Due to various levels of exposure, illumination, and occlusions, manual annotation is approximately 65\(\pm\)% accurate on this dataset, and the imbalanced dataset is challenging, as shown in Figures 5 and 6. Figure 4: Example of benchmark images contained in the FER2013 database (Available online: [[https://www.kaggle.com/datasets/msambare/fer2013](https://www.kaggle.com/datasets/msambare/fer2013)]([https://www.kaggle.com/datasets/msambare/fer2013](https://www.kaggle.com/datasets/msambare/fer2013)) (accessed on 6 December 2023)). Figure 5: The class label distribution of the training data. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Datasets** & **Training Data** & **Validation Data** & **Test Data** \\ \hline Number of samples & 28,709 & 3589 & 3589 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The divided datasets. Figure 6: The class label distribution of the validation data. As the number of datasets increases, the data are imbalanced between the 7 classes. The most common class of the FER dataset is happy, followed by neutral, sad, fear, angry, surprise and disgust. In particular, the disgust class is a more difficult class than the others. The hyperparameters of the CNN are optimized for FER2013 as Table 4. Moreover, the models fine-tune the different hyperparameters of the CNN models. The proposed method was evaluated on FER2013. The accuracies (%) of the models on the FER dataset are compared in Table 4. The accuracy performance of the 7-ensemble CNN is compared with those of other models, referencing in [26; 27; 28] given accuracy 71.20%, 72.40%, 73.39% and 73.40% in the similar environment with FER2013, respectively, who proposed a developed and fine-tuning CNN model as same as environment within 7 multi-class and imbalance datasets. Our proposed model, namely, the HoE-7 ensemble, achieves an accuracy of 75.15% which used combined by Xception, DCNN, VGG16, EffcientNetB2, DenceNet, RestNet50 and InceptionRestnetv2, and the HoE-6 ensemble achieves a slightly lower accuracy than HoE-7 ensemble which used combination of Equation (1) by DCNN, VGG16, EffcientNetB2, DenceNet, RestNet50 and InceptionRestnetv2 to accuracy 73.73%. The original single CNN models as Xception, DCNN, EffcientNetB2, VGG16, DenceNet, RestNet50 and InceptionRestNetV2 achieve 65.19%, 66.75%, 68.09%, 68.20%, 69.10%, 69.70% and 71.60% accuracies, respectively. The experimental results demonstrate the robustness and strong performance of the 7-ensemble CNN Ensemble model. Figure 7 depicts the confusion matrix for the final model on the FER2013 testing set, which classifies multiple classes into 7 emotions. The confusion matrix can be analyzed using true labels and predictions labels with values between 0 and 1, where 1 is the highest true positive value for the true class and prediction class. The analysis of model performance shows that the model most effectively categorizes the \"happy\" and \"surprise\" emotions because the number of training and validation points for these emotions were sufficient for our proposed model, yielding the best classification performance. The \"happy\" and \"surprise\" emotions are challenging to classify; however, the HoE-7 CNN yields robust and useful FER accuracies of 0.91 and 0.85, respectively.