# Segment-Based Clustering of Hyperspectral Images Using Tree-Based Data Partitioning Structures
## 3 Results and Comparisons
### Computational Time  
Figure 10 lists the computational time on Salinas, PaviaU, Salinas-A, and Indian Pines data sets for the proposed CLUS-BPT method in the presented experimental setup. The computational time is computed as a function of an increasing number of regions \(N_{P_{R}}\) from 50 to 1000, in steps of 50. The number of clusters \(k\) matching the highest NMI value is fixed, as indicated in Table 2 for Salinas, PaviaU, Salinas-A, and Indian Pines, respectively.  
In Figure 10, it can be observed that the computational time increases along with the increase of the number of regions for Salinas and PaviaU images, while the computational time increases at a lower rate for the same number of regions is observed for Indian Pines and Salinas-A images. This difference is due to having images with high spatial dimensions, such as \(512\times 217\) and \(610\times 610\) for Salinas and PaviaU, respectively. On the other hand, Salinas-A has spatial image dimensions that are about \(7\times\) smaller than Salinas and PaviaU. In addition, Figure 10 shows a near-linear execution time for the Salinas image. It can be concluded that large spatial dimension images lead to a large number of regions being processed and, thus, to the increased computational time. A significant improvement in terms of computational time can be achieved by performing the PCA stage in parallel, since there are no data dependencies between the PCA stage and segmentation stage.  
Table 3 shows the average times for producing cluster maps in the presented experiments on eight publicly available data sets that are reported in [6]. The displayed values are the average of ten runs. These values are obtained by setting the parameters, as indicated in Table 2. As it can be observed, the CLUS-BPT framework takes more time than FSC to output the best results in almost all of the data sets. PaviaU image experiment achieves the largest timing difference, while the difference in the clustering accuracy between CLUS-BPT and FSC is not substantial. On the other hand, the clustering accuracy difference is significant for Salinas image and, hence, the large timing difference can be justified. The execution time difference between CLUS-BPT and FSC is smaller for the other data sets, including Indian Pines, Salinas-A, Samson, and Jasper. In addition, Table 3 shows that the execution time for PCMNN is higher than FSC and CLUS-BPT for Salinas image.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & \multicolumn{8}{c}{**Framework**} \\ \cline{2-13}
**Data Set** & \multicolumn{2}{c}{**PCMNN [7]**} & \multicolumn{4}{c}{**FSC [6]**} & \multicolumn{4}{c}{**CLUS-BPT**} \\ \cline{2-13}  & **NMI** & **OA(\%)** & \(k\) & **Purity** & **NMI** & \(k\) & **Purity** & **NMI** & **OA(\%)** & \(k\) & \(N_{P_{R}}\) \\ \hline Salinas & 0.8586 & 82.06 & 24 & 0.62 & 0.72 & 16 & 0.7638 & 0.8882 & 89.37 & 26 & 48 \\ PaviaU & 0.5654 & 57.98 & 13 & 0.61 & 0.57 & 16 & 0.6996 & 0.5806 & 82.44 & 17 & 400 \\ Indian Pines & - & - & - & 0.46 & 0.49 & 16 & 0.5758 & 0.6025 & 57.75 & 20 & 32 \\ Salinas-A & - & - & - & 0.85 & 0.81 & 6 & 0.8753 & 0.8572 & 91.22 & 6 & 6 \\ Samson & - & - & - & 0.91 & 0.75 & 3 & 0.6896 & 0.6698 & 87.93 & 3 & 6 \\ Urban & - & - & - & 0.51 & 0.33 & 4 & 0.90 & 0.3906 & 79.96 & 4 & 128 \\ Jasper Ridge & - & - & - & 0.91 & 0.76 & 4 & 0.7652 & 0.5658 & 76.73 & 4 & 32 \\ PaviaC & - & - & - & - & - & - & 0.8412 & 0.8369 & 83.97 & 9 & 150 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Evaluation of clustering performance for HSI data sets.