发表机构
Chongqing University of Posts and Telecommunications; Chongqing Open University（重庆邮电大学; 重庆开放大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对多核k均值易受噪声边界样本影响、粒球与融合核几何不匹配的问题，提出DK-GBMKKM，通过核空间动态粒球交替优化提升聚类性能，在12个公开数据集上表现出色且代码开源。
AI 中文摘要
多核k均值通过学习基核的组合来整合互补的非线性相似性，但其逐点优化对噪声和边界样本敏感，且反复处理样本级核矩阵。粒球表示将局部样本组组织为介观单元，但在输入空间生成的粒球可能与多核学习过程中演化的融合核几何结构不一致。本文提出动态核空间粒球多核k均值（DK-GBMKKM），该方法在当前融合核空间中生成粒球，并交替进行核权重学习与粒球隶属度更新，使表示能适应融合核几何结构的变化。进一步构造样本大小加权的粒球核以保留不同大小粒球的贡献，且证明了其半正定性及相关等价性质。在12个公开数据集上的实验表明，DK-GBMKKM具有出色的整体聚类性能，代码已开源以支持可复现性。
英文摘要
Multiple kernel $k$-means integrates complementary nonlinear similarities by learning a combination of base kernels. Its pointwise optimization, however, is sensitive to noisy and boundary samples and repeatedly operates on sample-scale kernel matrices. Granular-ball representations organize local sample groups into mesoscopic units, but granular balls generated once in the input space may be inconsistent with the fused-kernel geometry that evolves during multiple kernel learning. We propose dynamic kernel-space granular-ball multiple kernel $k$-means (DK-GBMKKM). The method generates granular balls in the current fused kernel space and alternates kernel-weight learning with granular-ball membership updates, allowing the representation to adapt to changes in the fused-kernel geometry. A sample-size-weighted granular-ball kernel is further constructed to preserve the contributions of balls of different sizes, and its positive semidefiniteness and related equivalence properties are established. Experiments on 12 public datasets demonstrate the strong overall clustering performance of DK-GBMKKM. The code has been open-sourced for reproducibility: https://github.com/lianxiaoyu724/DK-GBMKKM.
