## 3 Results and Discussion
### Characterization of the Historic Study Case
#### 3.1.1 Formal Characters of Rural Historic Buildings: Clusters
\begin{table}
\begin{tabular}{c c c c c c} \hline
**ID** & \(\Delta\)**HW\({}_{\bf 11}\)** & \(\Delta\)**HL\({}_{\bf 11}\)** & \(\Delta\)**EV\({}_{\bf 11}\)** & \(\Delta\)**EW\({}_{\bf 11}\)** & \(\Delta\)**BFO\({}_{\bf 11}\)** \\ \hline
3 & 0.057 & 0.145 & 0.019 & 0.048 & 0.013 \\
7 & 0.036 & 0.076 & 0.019 & 0.048 & \(-\)0.032 \\
23 & \(-\)0.014 & \(-\)0.102 & 0.019 & 0.048 & 0.038 \\
24 & \(-\)0.110 & 0.012 & 0.019 & 0.048 & \(-\)0.026 \\
27 & \(-\)0.148 & 0.014 & 0.019 & 0.048 & 0.009 \\
32 & 0.031 & \(-\)0.076 & 0.019 & 0.048 & \(-\)0.079 \\
35 & \(-\)0.104 & \(-\)0.096 & 0.019 & 0.048 & \(-\)0.051 \\
37 & \(-\)0.022 & 0.003 & 0.019 & 0.048 & 0.030 \\
43 & 0.067 & \(-\)0.099 & 0.019 & 0.048 & 0.030 \\
44 & 0.057 & \(-\)0.081 & 0.019 & 0.048 & \(-\)0.045 \\
45 & \(-\)0.098 & \(-\)0.116 & 0.019 & 0.048 & 0.073 \\
52 & \(-\)0.090 & 0.055 & 0.019 & 0.048 & 0.043 \\
53 & 0.116 & 0.078 & 0.019 & 0.048 & 0.080 \\
54 & \(-\)0.058 & \(-\)0.071 & 0.019 & 0.048 & 0.105 \\
46 & 0.090 & \(-\)0.074 & 0.019 & \(-\)0.092 & \(-\)0.037 \\
47 & 0.102 & \(-\)0.090 & 0.019 & 0.048 & 0.029 \\ \hline \end{tabular}
\end{table} 
Table 8: Differences of parameters of \(i\)-th contemporary building consonant with historic building cluster 1 and those expressed by the centroids of that cluster. \begin{table}
\begin{tabular}{c c c c c c} \hline
**ID** & \(\Delta\)**HW\({}_{\bf 11}\)** & \(\Delta\)**HL\({}_{\bf 11}\)** & \(\Delta\)**EV\({}_{\bf 11}\)** & \(\Delta\)**EW\({}_{\bf 11}\)** & \(\Delta\)**BFO\({}_{\bf 11}\)** \\ \hline
1 & 0.031 & 0.184 & 0.019 & 0.048 & \(-\)0.009 \\
2 & 0.001 & 0.103 & \(-\)0.145 & \(-\)0.282 & 0.002 \\
4 & 0.217 & 0.308 & 0.019 & 0.048 & \(-\)0.043 \\
5 & 0.263 & 0.293 & 0.019 & 0.048 & \(-\)0.036 \\
6 & 0.286 & 0.035 & 0.019 & 0.048 & 0.005 \\
8 & \(-\)0.067 & 0.041 & \(-\)0.216 & \(-\)0.305 & 0.000 \\
9 & 0.062 & 0.204 & 0.019 & 0.048 & \(-\)0.014 \\  
016 \\
31 & \(-\)0.154 & \(-\)0.101 & 0.019 & \(-\)0.017 & 0.034 \\
33 & 0.586 & 0.142 & 0.019 & 0.048 & \(-\)0.116 \\
34 & \(-\)0.244 & \(-\)0.166 & 0.019 & 0.048 & 0.072 \\
36 & \(-\)0.220 & \(-\)0.049 & 0.019 & 0.048 & 0.203 \\
38 & \(-\)0.114 & \(-\)0.002 & \(-\)0.268 & \(-\)0.363 & \(-\)0.004 \\
39 & \(-\)0.187 & \(-\)0.107 & 0.019 & 0.048 & 0.091 \\
40 & \(-\)0.214 & \(-\)0.216 & 0.019 & 0.048 & \(-\)0.034 \\
41 & 0.586 & 0.021 & 0.019 & 0.048 & \(-\)0.010 \\
42 & 0.147 & 0.199 & 0.019 & 0.048 & \(-\)0.103 \\
49 & \(-\)0.177 & \(-\)0.145 & \(-\)0.157 & \(-\)0.522 & 0.071 \\
50 & \(-\)0.173 & 0.025 & 0.019 & 0.048 & 0.066 \\
51 & 0.361 & \(-\)0.024 & 0.019 & \(-\)0.187 & \(-\)0.016 \\
48 & 0.166 & 0.029 & 0.019 & 0.048 & 0.079 \\
10 & 0.115 & 0.229 & \(-\)0.067 & \(-\)0.195 & \(-\)0.031 \\ \hline \end{tabular}
\end{table} 
Table 9: Differences of parameters of \(i\)-th contemporary building consonant with historic building cluster 1 and those expressed by the centroids of that cluster. The trend of the single parameters in the three graphs of Figure 9 represents a situation in which, for the clusters 1 and 2 there are cases in which the values of \(\delta\) have a strong deviation from the centroid values. In particular, for the values of \(\delta\)EV1 and \(\delta\)EW1 in cluster 1 and \(\delta\)EV2 and \(\delta\)EW2 in cluster 2, where the values are close to 1 (11% of cases). The diagrams in Figure 9 show \(\delta\) value between each parameter of every building and the corresponding 70 th percentile of every cluster of historical building. The trend of the individual parameters in the three graphs in Figure 9 represents a situation where clusters 1 and 2 have cases where \(\delta\) values have a strong deviation from the centroid values. Specifically, for the values of \(\delta\)EV1 and \(\delta\)EW1 in cluster 1 and \(\delta\)EV2 and \(\delta\)EW2 in cluster 2 where values are close to 1 (11% of cases). Figure 9: \(\delta\) values between each building and the 70 th percentile of the corresponding historic cluster.