## 5 Result of Cluster Analysis
### Classification by the Building Types  
The method for classifying buildings involves hierarchical clustering of the results from K-means clustering at the block level, based on their conceptual morphological properties. This approach provides a level of specificity (typological similarity) in the classification.  
The decision on the number of clusters requires several trials until the minimum cluster variances are merged into a single cluster. After several processes, at the block level, four internal arrangement clusters are identified based on their building morphological variables. Five block clusters are classified into four levels of building type classification within different spatial distributions. To compare the distribution of value types between periods, descriptive statistical analysis is conducted to capture typological types that remained or changed.  
Figure 9: Spatial distribution of the K-means clustering results of the block elongation and block area values.  
According to the cluster results presented in (Figure 10), the transition in building types across the different clusters is evident.  
In Cluster 1 ((\(n=207\)) in 1857 and (\(n=176\)) currently), the multi-courtyard type remains consistent and reflects the most dominant type in the current period. However, there is a significant decrease in the detached type (from 128 to 16) and a noticeable increase in the courtyard type (from 2 to 18) over time, proving the shift towards more diverse building types.  
Cluster 2 had (\(n=310\)) buildings in 1857, but currently, the number of buildings has decreased to (\(n=82\)) due to the shrinkage of the blocks over time. This reduction has significantly decreased both the number and diversity of building types (topology) within the cluster. However, two types--detached and multi-courtyard--have maintained their presence.  
Cluster 3 had (\(n=242\)) buildings in 1857 and has increased to (\(n=363\)) buildings currently. The number of detached buildings has increased from 83 to 96, and the number of multi-courtyard buildings has risen from 74 to 176. This growth, along with the appearance of a new building type--semi-detached--has led to greater diversification of building types within the cluster. The multi-courtyard type still characterizes the typology of the cluster region.  
Due to the decrease in size of Cluster 4 and Cluster 5 over time, the number of buildings has decreased from (\(n=250/181\)) in 1857 to (\(n=173/81\)) currently. Despite this reduction, the multi-courtyard buildings have maintained their significance. Throughout this period, the clusters have retained their typological character, dominated by multi-courtyard (95/77 in 1857 and 48/38 currently), and landmark buildings (72/43 in 1857 and 107/67 currently).  
Overall, the analysis reveals that while the multi-courtyard building type has remained a stable and decisive factor in defining block typologies, other building types, such as detached and semi-detached, have evolved, reflecting broader changes in urban morphology, block usage, and social preferences over time.  
Figure 10: Spatial distribution of the hierarchical clustering results of the building types.