## 3 Results
### BSS/TSS Metric Results  
The analyses of two classes show better BSS/TSS ratios for the K--Means method, with the best values of 0.660526 for the first shift (S\({}_{1}\)) and of 0.659399 for the second one (S\({}_{2}\)) (Table 3). The variability obtained by shifting the grid with the K--Means method is basically low but increases considering different methods, indicating that the K--Means algorithm performs better in separating the dataset into two clusters. Indeed, the second-best value belonging to the Ward's Linkage method reports a ratio of 0.63072, indicating a worse separation.  
The cluster analyses of five UA classes return the best ratios for K--Means, respectively, of 0.72593 for the first grid position (S\({}_{0}\)) and 0.720882 for the third shift (S\({}_{3}\)) (Table 3). Regarding the analyses made considering only artificial and non-artificial areas, the variability of the values calculated for the same K--Means method is low but shows substantial differences with the first approach.  
The analysis performed using five UA classes shows better values for almost all the methods, but the best ones are still those belonging to the K--Means method. The second  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**METHOD** & \multicolumn{4}{c}{**RATIO OF BETWEEN TOTAL SUM OF SQUARES (BSS/TSS)**} \\ \hline \hline  & \multicolumn{4}{c}{**TWO UA CLASSES**} \\ \hline \hline  & \(\mathbf{S_{0}}\) & \(\mathbf{S_{1}}\) & \(\mathbf{S_{2}}\) & \(\mathbf{S_{3}}\) \\ \hline K—Means & 0.655676 & 0.660526 & 0.659399 & 0.625655 \\ K—Medians & 0.457219 & 0.466214 & 0.507931 & 0.51609 \\ K—Medoids (PAM and & 0.450213 (CLARA) & 0.450298 (CLARA) & 0.503916 (CLARA) & 0.530062 (CLARA) \\ CLARA algorithms) & 0.450213 (PAM) & 0.450298 (PAM) & 0.503916 (PAM) & 0.531839 (PAM) \\ Spectral KNN7 & 0.0431401 & 0.301221 & 0.285217 & 0.369646 \\ Spectral mutual—KNN7 & 0.0172236 & 0.0654304 & 0.025808 & 0.00357514 \\ Spectral with Gaussian Kernel & 0.00069968 & 0.000470756 & 0.103149 & 0.0215007 \\ Hierarchical Single & 0.242457 & 0.170793 & 0.0865453 & 0.37389 \\ Hierarchical Ward & 0.654512 & 0.63072 & 0.656826 & 0.623812 \\ Hierarchical Complete & 0.414637 & 0.564536 & 0.606873 & 0.37389 \\ Hierarchical Average & 0.414637 & 0.564536 & 0.499687 & 0.37389 \\ \hline \hline  & \multicolumn{4}{c}{**FIVE UA CLASSES**} \\ \hline  & \(\mathbf{S_{0}}\) & \(\mathbf{S_{1}}\) & \(\mathbf{S_{2}}\) & \(\mathbf{S_{3}}\) \\ \hline K—Means & 0.72593 & 0.71977 & 0.7165 & 0.720882 \\ K—Medians & 0.678369 & 0.66402 & 0.670743 & 0.689813 \\ K—Medoids (PAM and & 0.667808 (CLARA) & 0.670126 (CLARA) & 0.697807 (PLAM) & 0.683157 (PAM) \\ CLARA algorithms) & 0.670513 (PAM) & 0.670126 (PAM) & 0.697807 (PAM) & 0.683157 (PAM) \\ Spectral KNN7 & 0.319202 & 0.349396 & 0.17429 & 0.334059 \\ Spectral mutual—KNN7 & 0.0142809 & 0.164442 & 0.116453 & 0.0970793 \\ Spectral with Gaussian Kernel & 0.0175808 & 0.0339564 & 0.0249459 & 0.0296962 \\ Hierarchical Single & 0.0389586 & 0.0268354 & 0.00450728 & 0.0825486 \\ Hierarchical Ward & 0.662854 & 0.646998 & 0.7101 & 0.715121 \\ Hierarchical Complete & 0.542857 & 0.533737 & 0.707919 & 0.622929 \\ Hierarchical Average & 0.0563574 & 0.719427 & 0.700252 & 0.617819 \\ \hline \hline \end{tabular}
\end{table}
Table 3: BSS/TSS metric results of the cluster analysis considering, respectively, two and five Urban Atlas classes. K = 2. The better values for each method are underscored.  
ones, instead of belonging to only one method (such as [PERSON]'s linkage for the clustering process performed with two UA classes), belongs to different methods. Referring to the S0 shift, K--Medians has the second-best value, and the S1 shift has this value corresponding to the K--Medoids (PAM and CLARA algorithms) method. The S2 and S3 shifts return [PERSON]'s linkage as the second-best clustering method.