# Decoding Urban Intelligence: Clustering and Feature Importance in Smart Cities
## Experiments
### Hierarchical Clustering  
The dendrogram in Figure 4 provides a hierarchical clustering of the cities based on their smart city indices (the performance metrics are summarized in Table 4). The method used is the Ward linkage method, which is often used when the goal is to minimize the variance within clusters. It tends to produce clusters that are compact and similar in size, making it effective when the dataset is expected to have spherical clusters. In this case, using smart city metrics, Ward linkage ensures that cities grouped into the same cluster are more similar in terms of their smart city characteristics (e.g., mobility, environment, governance) compared to cities in other clusters. Figure 4: Dendrogram of smart city indices. \begin{table}
\begin{tabular}{l l} \hline \hline
**Cluster** & **Smart Cities** \\ \hline Cluster 1 & Los Angeles, New York, Chicago, Taipei, Philadelphia, Sydney, London, \\  & Adelaide, Melbourne, Tokyo, Perth, Auckland, Osaka, Madrid, Daejeon \\ Cluster 2 & Abu Dhabi, Seoul, Dubai, Budapest, Hong Kong, Prague, Shanghai, \\  & Kuala Lumpur, Moscow, Beijing, St Petersburg \\ Cluster 3 & Oslo, Bergen, Amsterdam, Copenhagen, Stockholm, Montreal, Vienna, \\  & Odense, Singapore, Boston, Zurich, Trondheim, Aalborg, Ottawa, Washington DC, \\  & Stavanger, Helsinki, Vancouver, Berlin, Toronto, Lyon, Paris, Calgary \\ Cluster 4 & Vasteras, Dusseldorf, Reykjavik, Helsingborg, Munich, Hamburg, Geneva, \\  & Luxembourg, Aarhus, Turku, Espoo, Hannover, Strasbourg, Joensuu, \\  & Frankfurt am Main, San Francisco, Oulu, Cologne, Bochum, Stuttgart, \\  & Hameenlinna, Tampere, Jyvaskyla, Vantaa, Bordeaux, Nantes, Marseille, \\  & Leeds, Lahti, Verona, Nice, Tallinn, Edmonton \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._Having identified five clusters, the silhouette score of 0.3750 suggests that the clusters are moderately well-defined but there may be some overlap. The Davies-Bouldin index of 0.8920 shows that the clusters are relatively distinct, with a value closer to 0 indicating better-defined clusters. This score indicates fairly good performance. The Calinski-Harabasz index of 65.32 reflects the ratio of between-cluster dispersion to within-cluster dispersion. A higher value indicates better-defined clusters. These metrics together suggest that the hierarchical clustering model performs moderately well. Cluster Analysis  
The height at which two clusters are joined together represents the distance or dissimilarity between them. Cities are divided into two major clusters at the highest level, represented by the two main branches of the dendrogram. The left major cluster includes cities such as Montreal, Oslo, Helsinki, and Amsterdam. These cities tend to have high scores in smart mobility, environment, and government indices. The sub-clusters within this major cluster represent cities with even more similar characteristics. For example, Oslo and Helsinki are joined at a lower level, indicating they are very similar in their smart city indices. The right major cluster includes cities such as Shanghai, Beijing, Dubai, and Moscow. These cities are distinguished by their high scores in smart economy and smart living indices. The sub-clusters show further granularity. For instance, Beijing and Shanghai are closely related, reflecting their similar scores across various smart city dimensions. The height of the branches indicates the level of similarity or dissimilarity. Cities like Montreal and Oslo are joined at a higher level than Beijing and Shanghai, indicating that the former pair is more similar to each other than to the latter pair. This hierarchical structure helps to identify groups of cities with similar smart city characteristics. The hierarchical clustering displayed in the dendrogram provides insight into the relative similarities and differences among cities based on their smart city indices. Cities that are grouped at lower levels of the dendrogram are more similar to each other than to those joined at higher levels. Table 5 recaps the content of each cluster.