Mixture of urban form archetypes in Seoul: A signal processing approach

Seoul’s urban morphology reflects successive phases, from colonial rule through rapid urbanization to regeneration, yet most analyses reduce this complexity to static clusters. This study models urban form as mixtures of latent archetypes, casting the task as blind source separation. SimplexNMF, a simplex-constrained non-negative matrix factorization (NMF) algorithm, is applied to 2019 GIS indicators for 1418 500 × 500-m grid cells (buildings, streets, green/water, topography). This study recovers nine interpretable archetypes: organic low-rise residential, low-rise mixed-use, low-density foothill or interchange-edge, linear mid-rise, riverside, high-rise apartment, institutional/public-facility, hilly-terrain, and park-edge patterns. Hybrid clustering of their compositional weights further identifies nine archetype-dominant and six mixed clusters. Comparison with knowledge-based typologies and analysis of two cases (Yeongdong 2 District-a, Jamsil) help interpret these mixtures and demonstrate the complementary roles of data-driven and expert-based approaches, highlighting how plan ideals, local adaptations, and path dependence shaped the evolution of their urban forms. By translating overlapping forms into compositional signals, the framework offers a scalable, theory-informed basis for diagnosing neighborhood character and guiding context-sensitive regeneration in Seoul and similarly layered cities.