Overview
This research introduces Minimum Description Length based Granular-Ball Tree-Regularized Spectral Clustering (MDL-GBTRSC), a method designed to improve spectral clustering performance. The approach addresses challenges in affinity graph construction, particularly in preserving local connectivity and adapting to heterogeneous data structures. MDL-GBTRSC integrates local representation learning with affinity graph construction within a unified spectral clustering framework by using a granular-ball tree for regularization.
Research Context
Spectral clustering performance is largely dependent on the quality of its affinity graph. A key challenge in constructing such graphs is maintaining reliable local connectivity while simultaneously accommodating diverse data structures. Existing granular-ball-based spectral clustering methods frequently reduce graph complexity using coarse-grained representatives. However, these methods often treat localized regions as graph nodes or anchors, which does not fully exploit their structural information for regularizing the original sample-level graph.
Approach
MDL-GBTRSC constructs a granular-ball tree using local Minimum Description Length (MDL) model selection. This construction process incorporates reciprocal neighborhood continuity to prevent splits that could disrupt reliable local connections. The stable leaf balls generated by this tree provide coding-scale information, which is then used to regularize the sample-level affinity graph. The method also introduces a shared-neighbor bridge code. This code is designed to adjust weak local bridge relations without requiring an additional user-specified threshold. This mechanism aims to connect local representation learning, which is interpretable, with the process of affinity graph construction.
Findings
- MDL-GBTRSC constructs a granular-ball tree through local MDL model selection, integrating reciprocal neighborhood continuity to preserve reliable local connections.
- The stable leaf balls derived from the granular-ball tree contribute coding-scale information for regularizing the sample-level affinity graph.
- A shared-neighbor bridge code is introduced to adjust weak local bridge relations, eliminating the need for an additional user-specified threshold.
- Experiments conducted on both real and synthetic datasets indicated that MDL-GBTRSC achieved the best average Adjusted Rand Index (ARI) and Normalized Mutual Information (NMI). This performance was observed under a fixed-configuration protocol when compared against classical spectral clustering baselines, as well as representative granular-ball, micro-cluster, and anchor-based methods.
Why This Matters
The described approach integrates interpretable local representation learning with affinity graph construction within a unified spectral clustering framework. This integration aims to produce more reliable affinity graphs, which are crucial for the performance of spectral clustering across varied and complex datasets.