# Brain Tumor Analysis Using Deep Learning and VGG-16 Ensembling Learning Approaches
## 4 Proposed Research Methodology
### Implementation Details  
Convolutional Neural Network (CNN) and VGG-16 Network Framework  
* CNN  
As a result of the hidden possibilities of using the geometry of the images, CNN's primary applications are in photo editing. In graph analysis, CNN outperforms numerous techniques. Various architectural concepts are combined: receptive fields, batch normalization, and spatial or temporal sub-sampling. Figure 7 depicts the structure of the suggested CNN model.  
For tumor identification, a multi-layer convolutional neural network was constructed and implemented. An input shape of 64 \(\times\) 64 \(\pm\) 3 was built for the MRI scans using a convolutional layer as the start layer, converting all of the pictures into a homogeneous dimension. After collecting all of the images in the same aspect, we developed a convolution kernel entangled with the input layer. We managed 32 convolutional filters of size 3 \(\times\) 3, each with the assistance of 3 channel tensors. The cumulative model, which consisted of seven steps, including the hidden layers, produced the most precise result for malignant concerns. ReLU did not relate to the output since it was used as an activation function. ReLU could be stated mathematically as,  
\[\text{F(x)}=\text{max}\left(0,\text{x}\right) \tag{1}\]  
Processing the MRI image of the brain could lead to overfitting contaminants. We used MaxPooling2D to generate spatial database models based on the input data. This convolutional layer had size 31 \(\times\) 31 \(\times\) 32. The pool size was reduced due to splitting the input photos in both spatial directions (2, 2).  
\[(z)_{x}=\frac{ae^{zi}}{\sum_{i}^{l}ae^{zi}} \tag{2}\]  
The metrics used to analyze the study's outputs included specificity, sensitivity, f-score, and accuracy. These metric values were computed using the confusion matrix. As a  
Figure 7: Flow Diagram of CNN Model.  
consequence, the CNN model parameters were true positive (TP), true negative (TN), false positive (FP), and false-negative (FN).  
\[\text{Accuracy (\%)}=\text{(TP+TN)}/\text{(TP FP TN FN)} \tag{3}\]  
However, as previously stated, accuracy, sensitivity, or recall, as well as the F1-score values, were also considered when examining the CNN performance of the model. These metrics' equations are:  
\[\text{Precision (PPV)}=\text{TP}/\text{(TP FP)} \tag{4}\]  
\[\text{Sensitivity}=\text{TP}/\text{(TP+FN)} \tag{5}\]  
\[\text{F-score}=\frac{2\text{(Precision*Recall)}}{\text{Percion + Recall}} \tag{6}\]  
\[P_{0}=\frac{\text{TP + TN}}{\text{TP FN FP TN}} \tag{7}\]  
\[P_{\text{Yes}}=\frac{\text{TP + TN}}{\text{TP + FN + FP + TN}}\cdot\frac{\text{TP + FN}}{\text{TP + FN + FP + TN}} \tag{8}\]  
\[P_{No}=\frac{\text{FP}+\text{TN}}{\text{TP + FN + FP + TN}}\cdot\frac{\text{FN + TN}}{\text{TP + FN + FP + TN}} \tag{9}\]  
\[P_{e=P_{Yes}+P_{No}} \tag{10}\]  
\(\bullet\) Ensemble Classification  
The Ensemble is a machine-learning method that provides numerous basic models to generate an optimized predictive model. Many ensemble approaches have been identified in the literature; however, the method with the highest number of votes was chosen for this work. In most categorization situations, the majority technique was used. To produce recommendations for each data point, this strategy employed numerous models. Predictions for each model were taken into account. Most models' forecasts were used as final predictions. The suggested technique employed a Convolutional Neural Network (CNN) and a VGG 16 ensemble model. The characteristics were obtained from the VGG 16's final fully-connected layer.