Beyond Numerical Features: Mixed-Type Clustering of Urban Building Archetypes Using Hierarchical and K-prototypes Methods

Future-proofing the building stock against severe weather events requires a multidisciplinary research approach and the integration of multi-source data. Conducting studies that scale beyond individual buildings to the neighborhood and city levels demands the use of representative archetypes. Building archetypes are standardized representations of similar buildings, commonly used in urban analysis when detailed data for each individual building is unavailable. Archetype-based methods are widely used in urban microclimate studies, urban energy modeling, material stock estimation, and urban decarbonization scenarios. Various grouping techniques (e.g., rule-based and unsupervised) are employed to identify representative archetypes across the building stock. Most previous work has focused primarily on numerical and continuous building features, even though many important features are categorical attributes. Recently, k-prototypes clustering has been proposed in the building-archetype literature to handle mixed numerical-categorical data. This study extends that line of work by applying hierarchical clustering and then systematically comparing hierarchical and k-prototypes in terms of how each method handles mixed-type building features, with particular attention to categorical variables. Specifically, we apply hierarchical clustering with Gower distance to construct a tree-based structure that organizes buildings according to shared physical and functional characteristics. The framework is demonstrated for the residential building stock of San Antonio, Texas. We evaluate the proposed hierarchical approach against k-prototypes clustering using Silhouette and Within-Cluster Sum of Squares (WCSS) scores. The results show that hierarchical clustering with Gower distance yields better-separated and more categorically coherent clusters, whereas k-prototypes with the mixed distance produces more compact, prototype-centered clusters driven by numerical similarity. These contrasting behaviors reveal a trade-off between categorical coherence and numerical compactness in archetype generation and highlight that the choice of clustering method and distance metric should be aligned with the specific goals of urban building archetype analysis.