# Incremental Dilations Using CNN for Brain Tumor Classification
## 3 Results
Comparing the Basic CNN and the Dilated CNN, we can determine that the dilated CNN model has better precision compared to the Basic CNN model. The Table 3 displays a comparative side by side analysis of the various classification metrics, namely the True Positive, False Negative, False Positive, and True Negative rates. The above Table 4 provides an in-depth analysis of the gridding phenomenon and the effects of the various dilation rates. Using high dilation rates, the model cannot learn from the finer features, similarly using a low dilation rate, the model does not pick up on the coarse features. A well-balanced model should be able to learn both the coarse and fine features of the images. Using the \((4,2,1)\) model provides the best-case scenario. The TPR (true positive rate) and FPR (false positive rate) are important AUC/ROC (Area Under The Curve/Receiver Operating Characteristics) [38] metrics that help to determine the amount of information learnt by the model and how well it is able to distinguish between the classes. In the ideal case, \(TPR=1\) and the \(FPR=0\). Table 5a compares the metrics across the various architectures and determines the Dilated CNN architecture with \(TPR=0.96\) and \(FPR=0.03\) is the best. Table 5b \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Model** & **TP** & **FN** & **FP** & **TN** \\ \hline ANN & 0.34920635 & 0.04761905 & 0.07936508 & 0.52380952 \\ Basic CNN & 0.38095238 & 0.01587302 & 0.06349206 & 0.53968254 \\ Dilated CNN (4, 2, 1) & 0.38095238 & 0.01587302 & 0.01587302 & 0.58730159 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: True Positive, False Negative, False Positive and True Negative rates compared across Simple ANN, Basic CNN and Dilated CNN. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Model** & **TP** & **FN** & **FP** & **TN** \\ \hline Dilated CNN (2, 2, 2) & 0.38095238 & 0.01587302 & 0.03174603 & 0.57142857 \\ Dilated CNN (4, 4, 4) & 0.3968254 & 0.0 & 0.06349206 & 0.53968254 \\ Dilated CNN (6, 6, 6) & 0.34920635 & 0.04761905 & 0.03174603 & 0.57142857 \\ Dilated CNN (4, 2, 1) & 0.38095238 & 0.01587302 & 0.01587302 & 0.58730159 \\ Dilated CNN (4, 2, 2) & 0.36507937 & 0.03174603 & 0.01587302 & 0.58730159 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparing True Positive, False Negative, False Positive, True Negative rates across different configuration of dilation rates for the convolution layers. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Model** & **Accuracy** & **Precision** & **Recall** & **F-Measure** \\ \hline ANN & 0.87301587 & 0.81481481 & 0.88 & 0.84615384 \\ Basic CNN & 0.92063492 & 0.85714285 & 0.96 & 0.90566037 \\ Dilated CNN (4, 2, 1) & 0.96825397 & 0.96 & 0.96 & 0.96 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Accuracy, Precision, Recall and F-measure compared across Simple ANN, Basic CNN and Dilated CNN. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Model** & **TP** & **FN** & **FP** & **TN** \\ \hline Dilated CNN (2, 2, 2) & 0.95238095 & 0.92307692 & 0.96 & 0.94117647 \\ Dilated CNN (4, 4, 4) & 0.93650794 & 0.86206897 & 0.96 & 0.92592592 \\ Dilated CNN (6, 6, 6) & 0.92063492 & 0.91666667 & 0.88 & 0.89795918 \\ Dilated CNN (4, 2, 1) & 0.96825397 & 0.96 & 0.96 & 0.96 \\ Dilated CNN (4, 2, 2) & 0.95238095 & 0.95833334 & 0.92 & 0.93877551 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparing Accuracy, Precision, Racall and F-Measure across different configurations of dilation rates for the convolution layers. compares the AUC/ROC metrics for the different dilation rates. Using an incremental dilation rate allows the model to learn the coarse as well as fine features, resulting in the maximum amount of information learnt by the model. To compare the model performance in terms of computational resources required, we have designed the three models with a similar architecture in mind. This allows us to have a reasonably accurate analysis of the compute overhead (additional time required to setup the network architecture and data loaders) and efficiency of each network.