## 4 Experimental Results
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Method** & **Dataset** & **Penalty Factor C** & **RBF Kernel \(\gamma\)** & **Dataset** & **Penalty Factor C** & **RBF Kernel r** \\ \hline SVM & & 10 & 0.001 & Waveform-2 & 0.1 & \(1/p\) \\ CVS & & 100 & 0.001 & & 10 & 0.01 \\ FLD & Iris-Setosa & 100 & 0.001 & & 100 & 0.001 \\ TRSD & & 100 & 0.001 & & 1 & \(1/p\) \\ \hline SVM & & 10 & 0.1 & Banana & 1 & 1 \\ CVS & & 100 & 0.1 & & 100 & \(1/p\) \\ FLD & Iris-Versicolor & 0.1 & 0.01 & & 10 & \(1/p\) \\ TRSD & & 10 & 1 & & 1 & 1 \\ \hline SVM & & 100 & 0.01 & Mushroom & 100 & 0.001 \\ CVS & Iris-Virginia & 100 & 0.01 & & 10 & 0.001 \\ FLD & & 100 & 0.001 & & 0.01 \\ TRSD & & 100 & 0.1 & & 100 & 0.001 \\ \hline SVM & & 1 & 0.01 & Phishing & 10 & \(1/p\) \\ CVS & & 10 & 0.001 & & 1 & 0.01 \\ FLD & Breast Cancer & 100 & 0.001 & & 100 & 0.001 \\ TRSD & & 1 & 0.1 & & 100 & 0.001 \\ \hline SVM & & 10 & 1 & w8a & 10 & 0.001 \\ CVS & & 100 & 1 & & 10 & 0.001 \\ FLD & Four-class & 100 & 1 & & 10 & 0.001 \\ TRSD & & 100 & 1 & & 1 & 0.001 \\ \hline SVM & & 100 & 1 & a9a & 10 & 0.001 \\ CVS & Checkerboard & 100 & 1 & & 10 & 0.001 \\ FLD & & 100 & 1 & & 100 & 0.001 \\ TRSD & & 100 & 1 & & 10 & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hyper-parameters setting for the experiments. We compare the performance of SVM, CVS, FLD, and TRSD in terms of classification accuracy and the training time (in seconds), summarized in Table 4. We also depicted the performance comparison of the proposed TRSD with CVS and FLD on the five largest datasets when \(\beta=0.1\) in Figure 5. We used log-2 scale for \(y\)-axis in Figure 5. In Table 4, Acc is the accuracy on test data; \(\sigma\) is the standard deviation; and Time is the training time in seconds. Even though the accuracy of the proposed algorithm is slightly degraded in a few cases, it is higher than that of CVS and FLD in most cases. In addition, as \(\beta\) is greater, the accuracy of the proposed algorithm enhanced substantially. For small datasets, there is no significant improvement on computation time compared to the standard SVM since those datasets are already small enough. However, we notice that the training time of TRSD improved quite much when using the large-scale datasets. For statistical analysis, we also performed Friedman test to see that there exists significant difference between the multiple comparing methods in terms of accuracy. If the null hypothesis of the Friedman test is rejected, we performed [PERSON]'s test. Table 5 shows the summary of the [PERSON]'s test results at the significant level \(\alpha=0.05\). In Table 5, the entries (1) TRSD \(>\) CVS (FLD); (2) TRSD \(\approx\) CVS (FLD); (3) TRSD \(<\) CVS (FLD), respectively, denote that: (1) the performance of TRSD is significantly better than CVS (FLD); (2) there in no significant difference between the performances of TRSD and CVS (FLD); and (3) the performance of TRSD is significantly worse than CVS (FLD). Each number in Table 5 means the number of datasets. At \(\beta=0.1\), our proposed method is significantly better than CVS and FLD in 10 and 9 cases among 18 datasets. These numbers increase to 11 and 10 at \(\beta=0.3\). On the other hand, our proposed method is significantly worse than CVS only in 2, 3 and 3 cases; than FLD in 0, 1 and 0 cases at \(\beta=0.1,\ 0.2,\ 0.3\) respectively. Based on the observations in the experiments, we can conclude that our proposed method generates an effective reduction of the training datasets while producing better performance than the existing data reduction approaches. Figure 5: Comparison of the proposed tree-based relative support distance (TRSD) with candidate vectors (CVS) and Fisher linear discriminant analysis (FLD) on the five largest datasets.