## 4 Experimental Results and Analysis
\begin{table}
\begin{tabular}{c l c c c} \hline \hline
**ID** & **Dataset** & **SVM** & **F-SVM** & **WR-SVM** \\ \hline
1 & Iris & 96.67 \(\pm\) 0.41 & 97.33 \(\pm\) 0.64 & 98.12 \(\pm\) 0.37 \\
2 & Waveform3 & 87.56 \(\pm\) 1.20 & 87.64 \(\pm\) 0.67 & 88.81 \(\pm\) 0.91 \\
3 & Glass & 66.36 \(\pm\) 1.97 & 74.55 \(\pm\) 0.96 & 74.94 \(\pm\) 0.96 \\
4 & USPS & 97.92 \(\pm\) 0.45 & 98.85 \(\pm\) 0.38 & 98.96 \(\pm\) 0.42 \\
5 & Synthetic & 85.67 \(\pm\) 1.42 & 92.71 \(\pm\) 0.49 & 93.04 \(\pm\) 0.45 \\
6 & Segment & 97.36 \(\pm\) 0.99 & 98.23 \(\pm\) 0.47 & 98.62 \(\pm\) 0.42 \\
7 & Sonar & 86.19 \(\pm\) 1.35 & 95.71 \(\pm\) 0.82 & 97.85 \(\pm\) 0.93 \\
8 & Musk & 99.73 \(\pm\) 0.21 & 99.86 \(\pm\) 0.14 & 99.86 \(\pm\) 0.16 \\
9 & Zoo & 93.64 \(\pm\) 1.39 & 97.27 \(\pm\) 0.54 & 98.03 \(\pm\) 0.39 \\
10 & Breast Cancer Dataset & 97.82 \(\pm\) 0.71 & 99.18 \(\pm\) 0.24 & 99.57 \(\pm\) 0.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the average classification accuracy (%) of kernel WR-SVM by Kernel-SVM and Kernel-F-SVM. Figure 11: Features distribution of the synthetic dataset. one step higher than F-SVM. The performance of WR-SVM cannot be less than the base model in any case because when the data has some scattered points, the performance of the model will be improved and will remain the same in another case. It is noticed from the experiments that when MEB of both classes overlap each other than some samples of both classes can be in intersected area as shown in Figure 12. The non-linear separating line can classify these points, but it is difficult to draw the non-linear boundary between all classes in the case of a multi-class problem. To evaluate the performance of the proposed WR-SVM in terms of computational cost, time factor is considered. The big O notation is commonly used time and space complexity measure to illustrate the worst time taken by the algorithm. As the time complexity of SVM for \(n\) training samples is \(O(n^{3})\) while the space complexity is \(O(n^{2})\). F-SVM takes one step after the classification of the data, which was the calculation of the radius of MEB. F-SVM takes one step after the classification of the data, which calculates the radius of MEB. The calculation of MEB for \(n\) number of classes can increase the time complexity and take more space. While in the case of WR-SVM, the radius of MEB is, and the classification parameters, i.e., w and b, are calculated simultaneously. While calculating the radius of MEB, weights are assigned to each sample, and the weighted mean is calculated. The weighted mean helps the model to reduce the radius of MEB. F-SVM takes the time to calculate the mean of each class, while the proposed method takes the same time to assign weights to each sample. Consequently, the time complexity of both F-SVM and WR-SVM is the same, which is \(O(n^{4})\). Sometimes, it is impossible to draw the non-linear boundary between two classes in actual feature space, so the kernel tricks can be used to transform the data to another kernelized feature space, as shown in Figure 13. In the case of testing samples, when the data are dekernelized to the original feature space, the testing samples can be located on another side of the hyperplane. So, there is a need for MEB, which encloses the samples within a limited area. Figure 12: Intersected area of two MEBs using mean. We have performed two sets of experiments in our work. The first step is to classify all samples that are given in the training set. Then the second step is to find the radius of MEB by using the weighted mean of class. Classification is performed on a continuous numeric dataset listed in Table 1. The following steps are performed to classify the data. 1. First of all, one class is separated from all others to apply one against all techniques. Here we apply conventional SVM to get the value of \(w\) and \(b\) such as classifier
2. Check whether these two classes are linearly separable or not by applying linear SVM as discussed before. 3.