## 3 Experimental Results and Discussion  
### UL-BTD Framework for Fastest Detection Time/Image Analysis  
We compared competitive machine learning classifiers, viz. SVM, \(k\)-NN, and RF, using the HFS-based training, A-CE-MRI dataset, and OvA coding scheme in order to evaluate the performance of UL-BTD. The robustness and confidence of the system performance were verified by using 10-fold cross-validation for model selection on potential algorithms of choice. The results have been illustrated in Table 4, with the best results emphasized for different ML algorithms. The F-measure was computed, with other metrics, to estimate the individual and average quantitative performance, including a quantitative graphical comparison of SVM, k-NN, and RF algorithms, as shown in Figure 6. The best results have been found to be for SVM (with a polynomial of order 3: P\({}_{3}\)), with the next best found to be \(k\)-NN (with \(k=1\)).  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  
The well-known parameters tuned for the \(k\)-NN algorithm include \(k\in\) (1, 3, 5, 7, 9). Reducing \(k\) gets closer to the training data (low bias), and the model becomes dependent on the particular training samples (high variance). When \(k=1\) the model is being fit to the one-nearest point with the model really close to the training data. The predictability of the model with one-nearest point means the highest possibility of training on noise. The inherent intra-class variance in the dataset and random reshuffling of mini-batch data results in an excellent performance. Similarly, in the case of the RF algorithm, the number of trees (\(N_{t}\)) variation was thoroughly investigated, and results are shown for \(N_{t}\in\) (500, 550, 600, 650). The best tumor prediction result is achieved using (\(N_{t}=600\)) trees. The RF is based on using high variance and low bias trees, resulting in a low bias and low variance forest. We need a number of trees that will improve the model's robustness against overfitting. The excessive number of trees, accompanied by additional computational cost, leads to negligible improvement in results if any.  
We experimented with SVM using kernel type (\(O_{k}\)) as Linear (L), Radial Basis Function (RBF), and Polynomial kernels (P\({}_{\text{o}}\)) of order (o) \(\in\) (2, 3, 4). Higher-order polynomials (o > 3) were not found competitive. The SVM (polynomial kernel with order 3) achieved outclass performance among the three competing algorithms. Accuracy of 99.18% was obtained to categorize glioma, 98.86% for meningioma, and 99.67% for pituitary tumors with an average accuracy of 99.24% accompanied by a minimum number (seven) of false negatives. Meningioma tumors are accompanied by a relatively low-performance index, which is attributed to the fact that it is hardest to discriminate between the two on the basis of their origin and characteristic features [25].  
The visualization of three types of brain tumors using HFS, high-dimensional data, by a variant of Stochastic Neighborhood Embedding known as \"t-SNE\" is shown in Figure 7 for the test case as a scatterplot by assigning each feature vector a location in a non-linear manner to a lower-dimensional (two-dimension) map. It improves visualization by minimizing the central crowding tendency of the points. It may be noted that the discrimination is affected because of false events, high in Glioma and Meningioma overlapping region and our system improves discrimination for complex decision hyperplane existing between three types of tumors. From this point onward, for the rest of the experimentations, except mentioned otherwise, we integrated SVM into the UL-BTD system.  
Figure 6: Quantitative performance comparison of k-NN with \(k\in\) (1, 3, 5, 7), RF with \(N_{t}\in\) [500, 550, 600, 650] and SVM with \(O_{k}\in\) [L, RBF, P\({}_{2}\), P\({}_{3}\)] algorithms.