# Classification Performance of Thresholding Methods in the Mahalanobis-Taguchi System
## 5 Results and Discussion
### Classification Accuracy Results  
Table 9 shows the classification accuracy (in %) for each dataset based on the threshold values obtained via Type I-Type-II, ROC Curve, Chebyshev's Theorem and Box-Cox transformation methods accordingly. The classification process is conducted using the testing sets which consist of normal and abnormal samples. These classification results will indicate how good the MDT to which the normal samples and abnormal samples in the testing sets are differentiated. In general, the classification process is conducted firstly by computing the MD values of all samples (both normals and abnorms) in the testing set. Thus, a decision is made when the MD value of the testing sample having less than or equal to the MDT to be denoted as normal, otherwise it will be considered abnormal. These results are then compared against the true class of the samples (normal and abnormal) to which the accuracy of the classification performance is measured. In Table 9, the classification results correspond to each dataset are shown of which bold fonts indicate superior classification performances against the others. Interestingly, it was clearly shown that none of the four thresholding methods outperformed one of the others in (if it is not for all) most of the datasets. This finding confirms the no free lunch theorem [40] in that there is no single algorithm that suits all datasets. However, an equivalent classification performance (74.21%) by all thresholding methods could be seen in the Titanic dataset. It could also be seen that Type-I-Type-II, ROC curve and the Box \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Training Dataset**} & \multicolumn{6}{c}{**Suggested MDT**} \\ \cline{3-10}  & \multirow{2}{*}{**Dataset**} & **Optimum** & \multirow{2}{*}{**Normal**} & \multirow{2}{*}{**Samples**} & \multirow{2}{*}{**Number**} & \multirow{2}{*}{**TypeII**} & **ROC** & **Chebyshev’s** & **Box-Cox** & **Box-Cox** & **Box-Cox** & **Box-Cox** \\  & & & & & & & & & (\(\Delta\) Value) & (MD Trams- & (MD Trams) \\  & & & & & & & & & & & (MD Trams) \\  & & & & & & & & & & & (MD Trams) \\ \hline
1 & Appendicitis & 4 & 42 & 10 & 2.27 & 2.27 & 1.98 & 0.30 & 0.90 & 2.22 \\  
sconsin & 6 & 222 & 119 & 2.80 & 3.19 & 6.08 & 0.30 & 1.20 & 2.79 \\  & Medical & & & & & & & & & \\
19 & Diagnosis of & 8 & 200 & 17 & 11.52 & 11.52 & 3.63 & 0.20 & 3.10 & 11.16 \\  & Liver Disease & & & & & & & & & & \\  & Taguchi & & & & & & & & & & \\
20 & Character & 14 & 16 & 9 & 11.44 & 11.44 & 1.53 & 211.00 & 211.00 & 1.05 \\  & Recognition & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Optimum Threshold (MDT) obtained. Cox Transformation methods gave equivalent classification accuracies in the Appendicitis, Ionosphere and Spambase datasets as well as in the Medical Diagnosis of Liver Disease dataset of which a perfect classification performance (100%) is achieved from the three threshold methods. Despite the complexities in computing the optimum threshold using Box-Cox transformation method, it produced nearly a perfect classification performance (98.14%) against the other three methods in the ring dataset as well as obtained equal performances with 68.49% and 96.20% accuracies in Banana and Wisconsin datasets respectively against Type-I-Type-II error. On the other hand, Type-I-Type-II error method produced a higher number of successful attempts with 11 successful frequencies over the other three methods for all datasets. Figure 11 illustrates this finding based on the results extracted from Table 8. Furthermore, the Type-I-Type-II error method seems favourable in this case since it is computationally less complex in computing the optimum threshold value as compared to the other three methods. From Table 9, it was interesting to see that each of the thresholding methods outperformed one over the others on different datasets. For example, Chebyshev's Theorem method outperformed the others in Bupa, Coil2000, Haberman-2, Heart, Magic, Phenome, Pima and Wdbc datasets.