Earthquake exposure describes the assets that are exposed to seismic activity and are susceptible to be damaged. In seismic risk applications, it mostly refers to the residential and commercial building portfolios, although in general may also include transport infrastructure and lifelines. Providing an efficient description of a complex urban environment in terms of the structural characteristics of buildings related to their seismic vulnerability is challenging, considering the variety of building practices, materials and configurations. A common approach entails the use of pre-defined building typologies, but this may introduce a bias in the resulting models. Faceted taxonomies have been recently introduced to provide a standardized description of buildings using a rich set of basic attributes, but cannot be used directly for risk-related applications. We argue that a bottom-up approach to exposure modeling might prove instrumental in increasing the quality and reliability of risk assessment, and propose hereby a novel score-based methodology to define and assign building classes to unclassified buildings in a sound and transparent way. The approach can be adopted for standard building classifications as well as for original typologies that may be more efficient in capturing the specific features of the building stock. The proposed methodology efficiently decouples the collection of buildings observations, typical of surveying activities, from the assignment of risk-aimed building classes, and provides a useful tool to practitioners and engineers involved in large-scale earthquake risk assessment. The proposed methodology has been exemplified with a building portfolio collected in France near the geothermal plant of Soultz-sous-Fôrets, and is used to rapidly characterize the seismic exposure of a built environment for induced seismicity applications.