Minimum Description Length based Granular-Ball Tree Regularization for Spectral Clustering

TL;DR

This paper introduces MDL-GBTRSC, a spectral clustering method that leverages a granular-ball tree regularized by minimum description length to improve local connectivity and affinity graph construction.

Contribution

It proposes a novel MDL-based granular-ball tree regularization technique that enhances spectral clustering by better capturing local structures and relationships.

Findings

Achieves the best average ARI and NMI on real and synthetic datasets.

Effectively regularizes the affinity graph using local MDL model selection.

Improves clustering stability by using reciprocal neighborhood continuity.

Abstract

Spectral clustering largely depends on the affinity graph, yet constructing a graph that preserves reliable local connectivity while adapting to heterogeneous data structures remains challenging. Existing granular-ball-based spectral clustering methods usually reduce graph complexity by using coarse-grained representatives. However, the learned local regions are often treated as graph nodes or anchors, and their structural information is not sufficiently used to regularize the original sample-level graph. To address this issue, this paper proposes a Minimum Description Length based Granular-Ball Tree-Regularized Spectral Clustering method, termed MDL-GBTRSC. The proposed method constructs a granular-ball tree through local MDL model selection, with reciprocal neighborhood continuity used to discourage splits that break reliable local connections. The stable leaf balls obtained from the tree provide coding-scale information for regularizing the sample-level affinity graph. In addition, a shared-neighbor bridge code is introduced to adjust weak local bridge relations without requiring an additional user-specified threshold. In this way, MDL-GBTRSC connects interpretable local representation learning with affinity graph construction in a unified spectral clustering framework. Experiments on real and synthetic datasets show that MDL-GBTRSC achieves the best average ARI and NMI under the adopted fixed-configuration protocol compared with classical spectral clustering baselines and representative granular-ball, micro-cluster, and anchor-based methods.