arXiv:2410.15304cs.LG2024-10被引 1

通过局部回归整合多个核,提升聚类鲁棒性与精度。

Multiple Kernel Clustering via Local Regression Integration

  • 用局部核回归捕捉数据流形结构,预测聚类结果。
  • 仅需1个超参数,变量数大幅减少,抗噪能力更强。
  • 在10个主流方法中表现最优,适合高噪声场景聚类。

多核方法通常忽视多核数据的内在流形结构,并以二次数量级变量估计共识核矩阵,易受候选核中的噪声和异常值影响。本文首先提出基于核化局部回归的聚类方法(CKLR),通过在局部区域进行核回归,捕捉核数据的局部结构并预测聚类结果。进一步扩展为多核局部回归聚类方法(CMKLR):为每个候选核构建核层级的局部回归稀疏系数矩阵,有效刻画核层级流形结构;再通过线性权重聚合所有系数,生成共识稀疏局部回归系数,显著降低候选变量数量,增强对多核数据中噪声和异常值的鲁棒性。所提方法克服了上述两大局限,仅引入一个可调超参数。大量实验表明,该方法在基准数据集上的聚类性能优于10种前沿多核聚类方法。

原文摘要 · Abstract (English)

Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple candidate kernels. This paper first presents the clustering method via kernelized local regression (CKLR). It captures the local structure of kernel data and employs kernel regression on the local region to predict the clustering results. Moreover, this paper further extends it to perform clustering via the multiple kernel local regression (CMKLR). We construct the kernel level local regression sparse coefficient matrix for each candidate kernel, which well characterizes the kernel level manifold structure. We then aggregate all the kernel level local regression coefficients via linear weights and generate the consensus sparse local regression coefficient, which largely reduces the number of candidate variables and becomes more robust against noises and outliers within multiple kernel data. Thus, the proposed method CMKLR avoids the above two limitations. It only contains one additional hyperparameter for tuning. Extensive experimental results show that the clustering performance of the proposed method on benchmark datasets is better than that of 10 state-of-the-art multiple kernel clustering methods.

聚类多核学习局部回归流形学习

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