## 4 Discussion  
Setting up the grid through the map extension allows for the discrimination of urbanized /non-urbanized cells with a methodology in which the subjectivity of the operator is limited to the choice of cell dimension. Hence, translations can be used to have a standardized shift from which the performances of the clustering methods can be evaluated. This choice improves the ability of single cells to delimit the urban and non-urban environment. Preferring the translation of the cell to random and static positioning ensures that the operator has higher control and efficiency in the analysis of the single tiles [40]. Grid shifting clearly leads to a rearrangement of the frequencies inside the cells, resulting in different performances of the clustering algorithms to recognize them as urbanized/non-urbanized. Furthermore, the use of the UA dataset poses as a more detailed spatial analysis through which the sector discipline is moving [39]. Being already preprocessed according to uniform standards, this dataset allows one to avoid elaborated preprocessing steps for untrained employees/inexpert users and for a more differentiated result [40]. The choice of the cell dimension of 2 square km supports, contrary to other approaches, the possibility of detecting neighboring portions of the urbanized area, highlighting the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**K—MEANS METHOD,** & & & & & & & \\
**FIVE CLASSES OF** & & **S\({}_{0}\) (km\({}^{2}\))** & **S\({}_{1}\) (km\({}^{2}\))** & **S\({}_{2}\) (km\({}^{2}\))** & **S\({}_{3}\) (km\({}^{2}\))** & **Total Mean (km\({}^{2}\))** \\ \hline \multirow{4}{*}{**Artificial areas**} & **Mean** & 0.366799 & 0.373849 & 0.381433 & 0.365336 & 0.36606753 \\  & **Min** & 0 & 0 & 0 & 0.007381 & 0.003690363 \\  & **Max** & 1.900423 & 1.945933 & 1.915146 & 1.769396 & 1.834909834 \\  & **Mean** & 1.024998 & 1.027607 & 1.053506 & 1.064393 & 1.044695669 \\
**Agricultural areas** & **Min** & 0.05609 & 0.026234 & 0.080825 & 0.094188 & 0.075138679 \\  & **Max** & 1.936165 & 1.954988 & 1.974852 & 1.975681 & 1.955923058 \\  & **Mean** & 0.604997 & 0.595129 & 0.561606 & 0.567071 & 0.586034235 \\
**Natural areas** & **Min** & 0 & 0.000774 & 0.003879 & 0 & 0 \\  & **Max** & 1.219838 & 1.230902 & 1.224494 & 1.201435 & 1.210636192 \\  & **Mean** & 0.003124 & 0.003333 & 0.003372 & 0.003115 & 0.003119508 \\
**Water bodies** & **Min** & 0 & 0 & 0 & 0 & 0 \\  & **Max** & 0.042653 & 0.046287 & 0.046287 & 0.038076 & 0.040364711 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum, minimum and mean class values for each grid shift of the best K—Means method (considering only urbanized cells). Figure 10: Area covered by each UA class, resulting from all the dissolved shifts for the five UA classes K—Means method. connection with the natural one and, above all, the ecotone continuity between these two systems [48; 49]. The cluster analyses performed considering the distinction between urban and non-urban areas return high values of the BSS/TSS ratio for the K--Means method. Despite this, the relative graphic elaborations show a classification that does not manage to reflect the real urbanized axis, as compared to the UA dataset. For this reason, the analyses with the dataset considering the main five Urban Atlas classes were performed. In this case, the results show better clusterization values (BSS/TSS ratio). The highest had an improvement from 0.660526 to 0.72593, also showing closer correspondence with the developed urban axis from the Urban Atlas dataset. This means that, in this case of increasing information in the dataset, due to the use of five different classes instead of the distinction between artificial/non-artificial areas does not lead to a misclassification, but it improves the analyses and the relative graphic representations. Nevertheless, despite good separation with a BSS/TSS ratio of 0.72593 for the S\({}_{0}\) grid shift, some areas still escape the classification method.