## 3 Results and Discussion
### Characterization of the Historic Study Case
#### 3.1.1 Formal Characters of Rural Historic Buildings: Clusters
1.2 Formal Characteristics of the Clusters and Typologies of the Sample of Historical Rural Buildings  
An analytical study of the identity physiognomy characteristics of buildings in the study area was carried out by means of the parametric characterization of the clusters related to typological characters, i.e., the stratification of the sample based on the original functions the buildings were built for (strata A, B, C defined in Section 2.1). First the average parameters of clusters were compared with the respective median values of the strata. The medians were adopted (Table 5) as stable synthetic measures of parameters within the strata, where their distribution is widespread in comparison with clusters. The root-mean-square deviation of the parameters expressing each stratum and cluster were computed and the results are reported in Table 6.  
This quantitative comparison of clusters centroids and strata medians shows that there is no neat correspondence between cluster and stratum, but certain prevalent distribution can be highlighted: cluster 1 is mostly represented by stratum C (83%), while cluster 3 shows closeness only to stratum B as it is entirely made of 44% of its buildings. Therefore cluster 3 is the only result of the clustering procedure which identifies a class of building with a common original function, i.e., hayloft or storage. Cluster 2 contains the characters of all three strata, with a predominance of stratum A and all those buildings characterized by a slender perception with respect to the ground. The analyses highlight that the traditional building typologies of the study area show a complex system of characters concerning form, plan shape, volumetry, summarized as follows (Figures 6 and 7). * stratum A has formal characters belonging to clusters 1 and 2, characterized by closed volumes, full perimeter surfaces and a perception of slender buildings in landscape (the width and length values of the building are similar to each other, and the height is equal to or more than half the value of L and W); \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **STR. A** & **STR. B** & **STR. C** \\ \hline CLUSTER 1 & 0.270 & 0.384 & 0.053 \\ CLUSTER 2 & 0.174 & 0.333 & 0.364 \\ CLUSTER 3 & 0.830 & 0.443 & 0.837 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Root-mean-square deviation. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**STRATUM** & **HW** & **HL** & **EV** & **EW** & **BFO** \\ \hline A & 0.673 & 0.527 & 1.000 & 1.000 & 0.097 \\ B & 0.662 & 0.372 & 0.720 & 0.724 & 0.070 \\ C & 0.508 & 0.310 & 1.000 & 1.000 & 0.123 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Median values of the strata of the historic building sample. * stratum B has very variable formal characteristics, since the sample is distributed in all three clusters, with greater and exclusive representation in cluster 3). It is characterized by rectangular plan shapes that can be either flattened to the ground (cluster 1) or slender (cluster 2) in relation to the height, but always with a permeability-though partial-towards the landscape for EV \(\
eq\) 1 and EW \(\
eq\) 1. The following cases can be identified: buildings with ground floor walls along the entire perimeter and open loggias on the first floor (Figure 6. cluster 1-stratum B), a little portions of build whit a full-height porticos, which can be completely or partially closed, or cases where EV \(\
eq\) 1 and EW \(\
eq\) 1 are greater than 0.7 so that the buildings have a perimeter portion open at least on two (Figure 6. cluster 2-stratum B), or even fully open volumes or small portions of closed volumes, with two or more infilled perimeter sides (Figure 6. cluster 3-stratum B). Cluster 3, in particular, includes historic buildings with original function of barns: initially characterized by empty volumes and just one or two infilled perimeter walls, over time have partially closed the volumes in order to be able to serve as sheltering tools as well. * stratum C represents mainly characters of cluster 1 and in small part of cluster 2.