arXiv:2605.22410cs.LG2026-05

用最小描述长度构建颗粒球树,提升谱聚类的局部结构建模能力。

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

  • 基于最小描述长度选择局部模型,构建具有连续邻域的颗粒球树。
  • 通过叶子球的编码尺度正则化样本级相似图,提升聚类精度。
  • 无需人工设定阈值,自动修复弱连接,适合复杂数据聚类任务。

谱聚类依赖于亲和图,但如何在保持可靠局部连接的同时适应异构数据结构仍具挑战。现有基于颗粒球的方法通常通过粗粒度代表降低图复杂度,但学习到的局部区域常被当作节点或锚点使用,其结构信息未能充分用于正则化原始样本级图。为此,本文提出基于最小描述长度的颗粒球树正则化谱聚类方法(MDL-GBTRSC)。该方法通过局部最小描述长度模型选择构建颗粒球树,利用互邻域连续性抑制破坏可靠局部连接的分裂。树中稳定的叶球提供编码尺度信息,用于正则化样本级亲和图。此外,引入共享邻居桥码,在不需额外用户设定阈值的情况下调整弱局部桥接关系。实验表明,在真实与合成数据集上,MDL-GBTRSC 在固定配置协议下相比经典谱聚类基线及代表性颗粒球、微聚类、锚点方法,实现了最优平均ARI与NMI。

原文摘要 · Abstract (English)

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.

谱聚类颗粒球图正则化无监督学习

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