MDL-GBG: A Non-parametric and Interpretable Granular-Ball Generation Method for Clustering

Existing granular-ball generation methods are still mainly driven by handcrafted quality measures and heuristic splitting or stopping criteria, which may weaken the transparency of local generation decisions in clustering. To address this issue, this paper proposes Minimum Description Length based Granular-Ball Generation (MDL-GBG), a non-parametric and interpretable granular-ball generation method for clustering. MDL-GBG reformulates granular-ball generation as a local model selection problem under the Minimum Description Length principle. For each granular ball, three candidate explanations are compared, namely a single-ball model, a two-ball model, and a core-ball-residual model, and the model with the shortest description length is selected. In this way, ball retention, splitting, and residual peeling are unified within a common coding-theoretic framework. A residual reassignment mechanism is further introduced to re-evaluate peeled-off boundary samples after stable granular balls are formed. Experiments on 20 UCI datasets show that the stable granular balls generated by MDL-GBG provide an effective upstream representation for clustering. In particular, MDL-GBG+AC achieves the highest average ARI, ACC, and NMI values among the compared methods, while the Friedman-Nemenyi analysis further supports its favorable average ranking. These results indicate that MDL-GBG offers a principled and interpretable alternative to heuristic granular-ball generation strategies.