## 4 Results and Discussion  
The customized ConvNet image identification and classification system presented in this report demonstrated very accurate results in classifying input images into three main diagnostic categories. The three classification labels corresponding to the brain's state were healthy, low-grade tumor or high-grade tumor. In the evaluation phase, we used four measures to prove the efficiency of the proposed approach including accuracy, precision, recall and F1 score, which are defined in Appendix D[36]. Figure 7 illustrates the confusion matrix along with the labels of the three classes in our dataset. These four measures were calculated using the confusion matrix, which was generated after running our trained ConvNet on the testing subset consisting of 587 image samples. Figure 6: Detailed architecture. Table 6 lists the outcomes from measures of 587 cases using our neural network model with an accuracy of 91.3%. The accuracy metric sometimes does not effectively reflect the performance of models due to the availability of imbalance labels in the dataset or increasing number of labels [37]. Thus, three other measures are used to address such possible constraints. Precision and recall metrics represent the cases that are predicted correctly over all positive predictions and observations respectively. The precision value of 91.79% in this study indicates that our classification model accurately predicts the required label 91.79% of the time. Similarly, the required label is predicted with 92.25% in all the presented image cases. This implies better performance of the proposed architecture in classifying the brain tumor into one of the three grade levels. Moreover, we utilized the F1 score measure, which combines the precision and recall metrics to evaluate the test's accuracy and is defined as the weighted harmonic mean of the precision and recall of the test. The F1 score balanced the two metric values and provided performance with 92.05% of predicted labels. We have selected ConvNets over other deep network architectures including recurrent or recursive neural networks (defined in Appendix E) mainly because ConvNets can classify data in a hierarchical way. This means that lower layers are used to learn low-level features like edges, blobs and corners, while the higher layers combine these basic features to identify high-level shapes. On the other hand, recurrent neural networks are suitable for the sequential data; an image would be a sequence with only one object, which does not make recurrent networks useful for this kind of classification. A recursive neural network can be seen as a generalization of the recurrent neural network, which has a specific type of skewed tree structure and is mostly applied in learning sequence and tree structures in natural language processing. Therefore, choosing ConvNets is the most optimum among all the other neural network architectures. There can be an argument in favor of using an architecture with a lesser number of layers instead of using the modified AlexNet (AlexNet\({}_{m}\)). To be certain, we performed a comparative analysis between the AlexNet\({}_{m}\) and the three convolutional layer neural network (ConvNet-3). The detailed architecture \begin{table}
\begin{tabular}{c c} \hline Accuracy & 0.9116 \\ Precision & 0.9179 \\ Recall & 0.9225 \\ F1 Score & 0.9205 \\ \hline \end{tabular}
\end{table} 
Table 6: Classification results. Figure 7: Confusion matrix with labels. of ConvNet-3 can be seen in the table in Appendix F. With the use of ConvNet-3, we achieved an accuracy, precision, recall and F1 score of 85.71%, 85.26%, 87.68% and 86.45%, respectively. These results demonstrate that the deeper ConvNet (AlexNet\({}_{m}\)) outperforms the less deep ConvNet (ConvNet-3), which confidently justifies our choice of a deeper network. We have used only FLAIR MR images in this study because we wanted our system to be able to solve the classification problem achieving the highest possible performance relying only on one type of MR image.