## 3 Fuzzy Kernel Nearest Feature Line Embedding (FKNFLE)
### Classification Results
In contrast, from Figure 10b-f, parameters \(K_{3}\) and \(K_{4}\) resulted in a higher variance of classification rates. In other words, the NFLE parameters \(K_{1}\) and \(K_{2}\) were not sensitive to the classification rates, and the parameters \(K_{3}\) and \(K_{4}\) of fuzzy \(k\) nearest neighbor were sensitive to the classification rates. According to the results of the sensitivity analysis of the four parameters, the parameters selected in the proposed algorithm were \(K_{1}=8\), \(K_{2}=28\), \(K_{3}=14\), and \(K_{4}=28\), which are consistent with the parameters in the cross-validation test. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**FKNFILE**} & \multicolumn{3}{c}{**KNFILE**} & \multicolumn{3}{c}{**FNFILE**} & \multicolumn{3}{c}{**NFLE**} \\ \cline{2-13}  & \multicolumn{3}{c}{**\(k\)-Value**} & \multicolumn{3}{c}{**\(k\)-Value**} & \multicolumn{3}{c}{**\(k\)-Value**} & \multicolumn{3}{c}{**\(k\)-Value**} \\ \cline{2-13}  & **1** & **3** & **4** & **1** & **3** & **4** & **1** & **3** & **4** & **1** & **3** & **4** \\ \hline IPS-10 & 83.34 & 84.19 & 85.11 & 83.07 & 83.55 & 84.19 & 78.37 & 78.98 & 79.10 & 77.59 & 78.89 & 78.93 \\ Pavia City Center & 97.59 & 98.18 & 98.24 & 96.55 & 96.84 & 96.88 & 95.08 & 95.32 & 95.51 & 94.58 & 95.26 & 95.41 \\ Pavia University & 91.31 & 92.13 & 92.36 & 89.50 & 90.04 & 90.19 & 85.10 & 86.05 & 86.57 & 83.80 & 84.63 & 85.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The classification performance using various _k_-NN for data set IPS-10 (in percentage). Figure 10: _Cont._  
Figure 10: Cont. Furthermore, due to the proposed algorithm being based on kernelization and fuzzification, the performance comparison between the proposed algorithms and the well-known kernelization-based algorithm GCK-MLR (Generalized composite kernel-multinomial logistic regression) [17,30] is illustrated in Tables 8 and 9. Basically, algorithm GCK-MLR is a multinomial logistic regression (MLR)-based classifier of composite kernels in which four kernels, spectral, spatial, spectral-spatial cross information, and spatial-spectral cross information kernels, deeply impact the classification results. The training configurations in [17] were quite different from ours. Besides, it is unfair for comparing the results of a single kernel (KNFLE) method with those of multi-kernels (GCK-MLR). In the experiment, we re-trained the classifier using the same configurations of [17]. The training configurations and classification results have directly been referred from [17]. Moreover, only the results using a single spectral kernel \(K^{o}\) were used for the fair comparison. Datasets IPS of 16 classes and Pavia University were evaluated as shown in Tables 8 and 9, respectively. Considering the IPS dataset of 16 classes in Table 8, algorithm GCK-MLR outperforms the proposed method at the overall accuracy index, while the average accuracy rate is lower than those of algorithms FKNFLE and KNFLE. In Table 9, the overall accuracy and average accuracy rates of the proposed method are both higher than those of algorithm GCK-MLR.