## 4 Discussion
### Relationship between _ISV_ and _Lssc_  
An additional analysis was performed to understand the relationship between the effectiveness of LSSC and the degree of _ISV_ in the data. Hence, two indices, namely _Index1_ and _Index2_, were defined for each classification problem. _Index1_ was used to reflect the  
\begin{table}
\begin{tabular}{r r r r r r r} \hline \hline
**Problem** & **KSC** & **KSC2** & **DBTC** & **ESDR** & **XAB** & **GACV** & **LSSC** \\ \hline
1 & 2.21 & 2.22 & 0.20 & 0.21 & 2.12 & 1.31 & 4.91 \\
2 & 181.85 & 181.47 & 12.22 & 15.80 & 141.15 & 89.84 & 738.46 \\
3 & 205.72 & 207.95 & 38.16 & 9.90 & 104.05 & 82.10 & 1309.69 \\
4 & 203.88 & 205.48 & 14.84 & 19.58 & 142.74 & 95.23 & 1467.00 \\
5 & 209.10 & 210.07 & 13.35 & 20.86 & 150.53 & 98.61 & 1529.19 \\
6 & 313.58 & 316.27 & 42.36 & 16.06 & 169.13 & 129.10 & 577.19 \\
7 & 102.80 & 103.30 & 10.85 & 16.87 & 75.34 & 49.74 & 224.57 \\
8 & 90.65 & 90.68 & 8.18 & 9.35 & 69.58 & 44.45 & 199.50 \\
9 & 191.61 & 191.53 & 11.51 & 15.64 & 483.72 & 203.65 & 654.59 \\ \hline Mean & 166.82 & 167.66 & 16.85 & 13.81 & 148.71 & 88.23 & 745.01 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Computational time (s) for each selection criterion.  
\begin{table}
\begin{tabular}{l r r r r r r} \hline \hline  & **KSC** & **KSC2** & **DBTC** & **ESDR** & **XAB** & **GACV** \\ \hline \hline \(p\)**value** & 1.2 \(\times\) 10\({}^{-5}\) & 9.6\(\times\)10\({}^{-6}\) & 6.5\(\times\)10\({}^{-4}\) & 1.9\(\times\)10\({}^{-4}\) & 9.0\(\times\)10\({}^{-5}\) & 2.7\(\times\)10\({}^{-5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 5: \(T\)-test results for classification accuracies obtained by the LSSC and others.  
degree of ISV in each problem; the ISV of the data are disclosed when the data are evaluated by LOSOCV because it is a subject-independent test which separates the data of a tested subject from those of the others. Therefore, all data from each classification problem were evaluated using the LOSOCV and five-fold cross validation as the subject-independent and subject-dependent tests, respectively. The classification accuracy for the best SVM model was found for each test. Let us define the accuracy for the subject-independent test as \(ACC_{SIT}\) and that for the subject-dependent test as \(ACC_{SDT}\); \(Index1\) can then be obtained as  
\[Index1=\frac{ACC_{SDT}-ACC_{SIT}}{ACC_{SDT}} \tag{6}\]  
to represent the relative deterioration of the classification accuracy by ISV in the data. \(Index2\) shows the relative effectiveness of the LSSC compared with the conventional selection criterion, namely KSC. When the classification accuracies by KSC and LSSC (in Table 2) are defined as \(ACC_{KSC}\) and \(ACC_{LSSC}\), \(Index2\) can be calculated as  
\[Index2=\frac{ACC_{LSSC}-ACC_{KSC}}{ACC_{KSC}}. \tag{7}\]  
Table 6 lists \(Index1\) and \(Index2\) values for each of the problems. \(Index1\) was observed to be low in problems 3, 5, and 6 because of the small ISV in the data. \(Index2\) was also low in the cases of problems 3, 5, and 6. However, \(Index1\) was relatively high for problems 2, 7, and 8, and \(Index2\) was also high for the same problems. The relationships between the indices can be observed more obviously in the scatter plot of Figure 1. A problem that had a high \(Index1\) had a higher \(Index2\