# Segment-Based Clustering of Hyperspectral Images Using Tree-Based Data Partitioning Structures
## 3 Results and Comparisons
### Effect of Number of Clusters  
The comparison with two recent unsupervised clustering methods, segment-based projected clustering using mutual nearest neighbor (PCMNN) [7] and fast spectral clustering (FSC) [6], is performed in order to assess the effectiveness of the CLUS-BPT method. Both of the methods are specifically developed for hyperspectral image classification. PCMNN is a three-stage framework involving segmentation, region merging, and projected clustering. FSC is a spectral clustering method for unsupervised HSI classification with experiments on eight different HSI data sets. Classical spectral clustering is not capable of dealing with large-scale HSI classification. Hence, FSC performs efficient affinity matrix approximation and the effective resolution of eigenvalue decomposition of Laplacian matrix. Figures 6 and 7 show the NMI scores as a function of increasing \(k\) for the data sets. The proposed method scores the highest NMI when \(k\) is the original number of clusters for five out of eight images, as shown in Figure 6. However, for PaviaC, the peak NMI value of 0.5806 is achieved for \(k=17\). In the case of Salinas and Indian Pines images, CLUS-BPT scores the peak NMI values at \(k=26\) and \(k=20\) respectively. Table 2 reports clustering evaluation scores for all of the compared methods on different hyperspectral image data sets. For the proposed method, the shown NMI, purity, and OA scores correspond to \(k\) values, which have achieved the highest NMI value. For PCMNN, NMI, and OA scores are reported on Salinas and PaviaU scenes, whereas purity and NMI scores are available on all data sets except PaviaC for FSC. Overall, CLUS-BPT results in the highest values for almost all accuracy indicators. The ground truth, class color codes, and the classification results of the CLUS-BPT method are presented for comparison in Figures 8 and 9. For Indian Pines and Salinas-A, Table 2 shows that  
Figure 5: Average Normalized Mutual Information (NMI) values (10 runs) versus the number of regions (\(P_{R}\)) for (**a**) PaviaC and PaviaU, (**b**) Salinas and Indian Pines, (**c**) Jasper Ridge and Urban, and (**d**) Salinas-A and Samson. CLUS-BPT results in higher NMI and purity values when compared to the FSC method. CLUS-BPT scores the highest NMI value at \(k=20\) and \(k=6\) for Indian Pines and Salinas-A, respectively. Figure 8a,b show that CLUS-BPT has misclassified corn-type classes as soybeans or hay-windrowed for Indian Pines. On the other hand, it can be observed that the proposed method is able to detect the Salinas-A scene classes with minor error in Figure 8c,d. The proposed method achieves the highest NMI of 0.8882 at \(k=26\) for Salinas scene, outperforming the other compared techniques. The Salinas cluster map that is shown in Figure 9b reveals that the proposed method identifies all of the 16 classes of Salinas image, except \"grapes untrained\", which is assigned to vineyard untrained class, scoring an overall accuracy of 89.37%. In the case of PaviaU, Table 2 shows that CLUS-BPT scores the highest NMI value of 0.5806 for \(k=17\), whereas FSC method scores the lowest, 0.5654 for \(k=13\). In addition, a marked difference in the successful identification of classes is observed between the proposed method (\(OA=82.44\%\)) and PCMNN (\(OA=57.98\%\)). Figure 9c,d illustrate that some difficulty was faced by CLUS-BPT in identifying the shadows and self-blocking bricks classes of PaviaU. Figure 6: NMI values that were obtained at different number of clusters for the proposed method. Figure 7: NMI values obtained at different number of clusters for the proposed method, for Salinas and Indian Pines images. Figure 8: Cluster maps that were obtained from the proposed CLUS-BPT (**left**) and ground reference color codes of classes for Indian Pines, Salinas-A, Samson, and Urban scenes (**right**). Figure 9: Cluster maps obtained from the proposed CLUS-BPT (left) and ground reference color codes of classes for Salinas, PaviaU, PaviaC, and Jasper Ridge scenes (right).