*2.4. AMG-MHSEG Algorithm*

As described in [32], we presented a AMG-MHSEG classification framework of HSIs. The advantages of this framework are summarized as follows. First, the marker selection is performed using a AMG-derived approach, which is more effective than the classification-derived methods proposed by Tarabalka et al. [31]. The selection of markers in the classification-derived methods depend highly on the performance of the pixel-wise classifiers. Moreover, the selected markers may be greatly different due to randomly selection of training samples. The previously mentioned difficulties always cause uncertainty in the classification maps. However, the markers selected by the AMG-derived approach are only determined by structure features of HSIs. Second, the combination of the multigrid representation approach of HSIs and the MHSEG algorithm can provide the multiscale segmentation maps. The main steps of the AMG-MHSEG algorithm are introduced in Algorithm 1.


#### **3. The Proposed Classification Framework**

In this section, the classical SVM classifier with the spectral-spatial kernel is first described. Then, the integration of the spectral, spatial and hierarchical structure information into a composite kernel framework is presented in our methodology. Figure 2 illustrates the schematic diagram of the SVM-SSHK method.

**Figure 2.** Schematic diagram of the SVM-SSHK method.
