Building stock modelling using k-prototype: A framework for representative archetype development

Building stock modelling often employs clustering techniques on the segmented stock data to identify representative archetypes, enabling cost-effective analyses while retaining the diversity and characteristics of the overall stock. However, the effectiveness of these archetypes in representing the original stock attributes remains under-explored, a factor essential for meaningful interpretations of the model outputs. This study investigated the influence of segmentation level, clustering evaluation metric and variable count on archetype representativeness by applying the k-prototype algorithm to the English Housing Survey data. Pre-clustering segmentation significantly influenced the outcomes, leading to the introduction of "minimum segmentation frequency" (MSF) to retain feature diversity in the segmented data. Sensitivity analysis revealed that lower MSF values improve building stock representation, while the choice of clustering evaluation metrics influences optimal number of archetypes for a given MSF. The Davies-Bouldin index consistently identified more archetypes and achieved higher representativeness than the Calinski-Harabasz and Silhouette indices. A comprehensive archetype development framework was devised considering the influencing factors such as geographical and temporal scales, computational cost and research focus. This framework serves as a flexible guide for developing representative archetypes in future building stock modelling studies.