## 3 Results
### Classification Results of SP\({}_{3}\) DOT Images  
For each data set of the DOT images obtained with DE, SP\({}_{3}\), or ERT, we report the sensitivity and the specificity obtained when the data mining results were used to classify the testing data. We report the sensitivity and the specificity at the 95% confidence intervals (CI), which indicates the lower and upper bounds of the sensitivity and the specificity within which we are confident that the true performance of the classifier is located (with up to 95% confidence). The CI was computed to account for the effective sample size of our data, which removes bias that may be introduced into our statistical parameters through correlation between joints of the same subject [36; 44]. Table 2 shows the classification results. The sensitivity and specificity and their respective confidence intervals in the parenthesis achieved when using the reconstruction images generated with the DE, SP\({}_{3}\), and ERT models are summarized in Table 2. The number of true positives (TP), false negatives (FN), true negatives (TN), and false positives (FP) is also presented in Table 2.  
The names of the optimal features selected during the training phase and used in the testing phase are presented in Table 3. The mean and standard error of the optimal features corresponding to the DE, SP\({}_{3}\), and ERT models are plotted in Figure 6. The three optimal features chosen using the SP\({}_{3}\) model were F01:SV:a, F02:ST:a, and F13:VT:a. The first two features are the maximum and minimum values of the three-dimensional data and the sum of transverse slices, respectively (refer to Appendix A for details on the naming convention). The third feature corresponds to the largest coefficient of the FFT transform of the variance between transverse slices. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**TP**} & \multicolumn{1}{c}{**FN**} & \multicolumn{1}{c}{**TN**} & \multicolumn{1}{c}{**FP**} & \multicolumn{1}{c}{**Se**} & \multicolumn{1}{c}{**Sp**} & \multicolumn{1}{c}{**Youden Index**} & \multicolumn{1}{c}{**Number of Features**} \\ \hline DE & 22 & 11 & 34 & 8 & 67 (47, 100) & 81 (65, 100) & 0.48 & 8 \\ SP\({}_{3}\) & 29 & 4 & 39 & 3 & 88 (78, 100) & 93 (85, 100) & 0.81 & 3 \\ ERT & 30 & 3 & 41 & 1 & 91 (83, 100) & 98 (85, 100) & 0.88 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Classification results for SP\({}_{3}\), DE, ERT based reconstructions with the \(k\)-fold method. Figure 6: Mean value and standard error of the optimal features selected from analysis of the (**a**) ERT and (**b**) SP\({}_{3}\)-based reconstruction images. A two-sample Student’s \(t\)-test shows that the differences between the features from subjects with RA and without RA are statistically significant at the \(\alpha=0.01\) level. (**a**) Features denoted by \(\dagger\) are scaled by a factor of 10. (**b**) Features denoted by \(\dagger\) and \(\ddagger\) are scaled by a factor of 50 and 500, respectively. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Model**} & \multicolumn{1}{c}{**Name of Optimal Features**} \\ \hline DE & F01:STa, F04:JT:a, F34:SV:a, F16:VS:a, F03:SV:s, F04:VSs, F05:VSs, F04:VTs \\ SP\({}_{3}\) & & F01:SV:a, F02:ST:a, F26:VT:a \\ ERT & F01:UV:a, F02:SV:a, F05:SV:a, F02:ST:a, F08:JTs \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Names of the optimal features selected during the training phase of the \(k\)-fold method using the SP\({}_{3}\) the DE-, and the ERT-based reconstructions. The five optimal features chosen using ERT-based reconstruction images were F01:UV:a, F02:SV:a, F05:SV:a, F02:ST:a, and F08:JT:s. The first three features are the maximum, minimum, and ratio values of the three dimensional data, respectively. The fourth feature is the minimum of the sum of transverse slices. The fifth feature is the second eigenvalue of the dominant positive Gaussian from a Gaussian mixture model (GMM).