Formalization of a Property Penalizing Clustering

Construct a satisfactory formalizable property for quality functions of concrete scenario collections that penalizes clustering, thereby extending the existing desired properties for trajectory-set diversity.

Background

The paper proposes desired properties for quality functions that assess the diversity of trajectory sets generated from scenario classes. One desired behavior is to prefer candidate scenarios located in less-sampled regions. The authors explain that formalizing this behavior requires an appropriate notion of a cluster and a suitable radius, but they do not provide a satisfactory general formalization. The unresolved issue is revisited in the conclusion as a need for a property that penalizes clustering.

References

However, a satisfactory formalization of this property could not be achieved as defining a suitable notion of a cluster proved to be challenging.

— Assessing the Quality of Concrete Scenarios Generated from Scenario Classes for Automated Driving  (2610.18169 - Putze et al., 13 Oct 2026) in Section 4, subsection “Discussion of Additional Properties” (AP1: Preference of less sampled regions)