*4.3. Experimental results*

#### 4.3.1. The IP Image

In the first experiment, we reported the classification results in the case of *M* = 40 in Table 2 to show the contribution of each kernel in the proposed method with *μSPE* = 0.3, *μSPA* = 0.1 and *μHIE* = 0.6 in *<sup>K</sup>SPE*−*SPA*−*HIE*, *τ* = 1, *σ* = 0.1, *υ* = 0.3, *β* = 0.01 and *S* = 11 were used by the AMG-MHSEG algorithm, and the PC 1-3 and *n* = 8 were used for the constructions of the EMP. For the IP image, the most relevant 30 spectral bands were selected by the FMS algorithm. Table 1 shows that the hierarchical structure information can further increase discriminative capability of the SVM classifier. Specifically, SVM with *KSPE*−*HIE* can increases the OA, AA, and *κ* by 10.31%~15.77%, 6.21%~9.81%, and 11.7%~17.82%, respectively, when compared to SVM with *KSPE*. Furthermore, SVM with *KSPE*−*SPA*−*HIE* can improve the OA, AA, and *κ* over the others in this table by 0.61%~13.65%, 0.25%~8.26%, and 0.69%~15.45% in average, respectively. The improvement of *KSPE*−*SPA*−*HIE* over the other kernels in Table 1 demonstrates that the combination of the spectral, spatial, and hierarchical kernels can generate better classification results than using a single or double kernels in terms of OA, AA, and *κ*. Finally, the SVM classifier with *KSPE*−*SPA*−*HIE* can achieve the highest CAs for 12 of 16 classes above 90%.


**Table 2.** Classification Results [Mean Accuracy (%) ± Standard Deviation] by the SVM Classifier with the Spectral, Spatial and Hierarchical Kernels for the IP Image. The best accuracies are indicated in bold in each raw.

In the second experiment, we applied each classification method to the IP image under different training sets. Table 3 lists the classification results and the last row of this table records the average rank for each method. All of the accuracies of the same row in this table are ranked in descending order and average rank is defined as the mean of the rankings for the same column. We can observe from Table 3 that using composite or multiple kernels in the SVM classifier can well combine the spectral and spatial information and provide higher results in all of the cases than the single feature-stacked kernel methods, including SVM and EMP, except for EPF, which can obtain a lower average rank of 4.94 than that of SVM-CK. The average rank values of SVM-CK and MLR-GCK are 5.72 and 4, respectively, and the superpixel-based methods of SC-SSK and SC-MK are better than these two methods and achieve similar performances with 2.5 and 2.67, respectively, in terms of the average rank. SVM-SSHK can outperform the other methods in terms of OA, AA, and *κ* in the case of different training samples and its average rank reaches 1.33.



Figure 4 illustrates some classification maps by the different methods with 40 training samples per class, corresponding to Table 3 with *M* = 40. The noise in the SVM classification maps in Figure 4a was obviously visible and can be greatly removed by the other kernel methods, which validated that the spatial information is significant for improving the classification results. However, the noise effect was still observed in two classes of *Soybeans-no till* and *Soybeans-min till* in the EMP and MLR-GCK results. The classification maps can be improved by removing the noise in the two previously mentioned classes by SVM-CK and SC-SSK. Nevertheless, the edges of the image were corrupted with the noise by EPF and SVM-CK due to using a fixed-size window for feature extraction. The adaptive neighborhood system of SC-SSK can solve the problem of SVM-CK, but cannot completely remove the noise effect. The SC-MK and SVM-SSHK classification maps were comparable and much better than the others and less noise and classification errors were seen in the SVM-SSHK result by comparison.

**Figure 4.** Classification results of the IP image. (**a**) SVM; (**b**) EMP; (**c**) EPF; (**d**) SVM-CK; (**e**) MLR-GCK; (**f**) SC-SSK; (**g**) SC-MK; and, (**h**) SVM-SSHK.

#### 4.3.2. The UP Image

Similarly, the classification results in the case of *M* = 40 are recorded in Table 4 to evaluate the contribution of each kernel in the SVM-SSHK method, *μSPE* = 0.2, *μSPA* = 0.6, and *μHIE* = 0.2 in *<sup>K</sup>SPE*−*SPA*−*HIE*, *τ* = 1, *σ* = 0.1, *υ* = 0.2, *β* = 0.01, and *S* = 13 were used by the AMG-MHSEG algorithm, and the PC 1-3 and *n* = 8 were used for the constructions of the EMP. For the UP image, the most relevant 30 spectral bands were selected by the FMS algorithm. It can be observed from Table 4 that SVM with *KSPE*−*HIE* can increases the OA, AA and *κ* by 6.51%~13.33%, 5.73%~9.13%, and 8.42%~16.66%, respectively, when compared to SVM with *KSPE*. Furthermore, SVM with *KSPE*−*SPA*−*HIE* can improve the OA, AA, and *κ* over the others in this table by 3.16%~16.56%, 1.47%~11.52%, and 4.12%~21.08% in average, respectively. In addition, SVM with *KSPE*−*SPA*−*HIE* is capable of obtaining the highest CAs for all of the classes above 96% for the UP image, except for the class of *Self-Blocking Bricks*.


**Table 4.** Classification Results [Mean Accuracy (%) ± Standard Deviation] by the SVM Classifier with the Spectral, Spatial and Hierarchical Kernels for the UP Image. The best accuracies are indicated in bold in each raw.

Next, we applied each classification method to the UP image under different training sets and the classification result of each method is listed in Table 5. In this table, the average rank of SVM is lowest with 8, which is the same as in Table 3. EMP, EPF and SVM-CK performed HSI classification with similar average rank values of 5.38, 5.94, and 5.56, achieving the fifth, sixth, and seventh positions in this table, respectively. The remaining methods using composite or multiple kernels can obtain higher average rank values than the previously mentioned methods. For instance, the average rank values of SC-SSK, MLR-GCK, and SC-MK are 4.72, 3.28, and 2.11, respectively. The proposed SVM-SSHK method can achieve the best classification accuracies in all cases of training samples in terms of OA, AA, and *κ*. The improvement of the SSHK over the other composite or multiple kernels indicates that the introduction of the hierarchical structure information for classification can further improve discriminative capability of the kernel methods.



Figure 5 shows the classification results corresponding to Table 5 with *M* = 40. From this figure, we can see that the SVM classification map was corrupted with much noise. Some pixels that belonging to Meadows are incorrectly assigned with a Bare Soil label in the EMP classification map. This problem can be partially resolved by SVM-CK and MLR-GCK to generate better classification results in Figure 5d,e, respectively. The EPF and SC-SSK classification maps became smoother, but several misclassified areas were produced in the middle and bottom of the image. SC-MK improved the SC-SSK classification map by greatly correcting such areas and caused classification errors in other parts of the image as well. For instance, two large areas of two classes of *Asphalt* and *Meadows* in the GTD were labelled to *Bare Soil* and *Self-Blocking Bricks* in the upper-left and right of the image, respectively. SVM-SSHK can better discriminate all of the objects, though very few pixels had false class labels.

**Figure 5.** Classification results of the UP image. (**a**) SVM; (**b**) EMP; (**c**) EPF; (**d**) SVM-CK; (**e**) MLR-GCK; (**f**) SC-SSK; (**g**) SC-MK; and, (**h**) SVM-SSHK.
