Multiple kernel clustering (MKC) optimally combines a group of predefined kernel matrices to improve clustering performance. Although demonstrating promising performance in various applications, most of existing approaches adopt the min–min formulation, which could be sensitive to perturbation with adversarial samples. Moreover, existing MKC algorithms often involve several hypermeters preventing them into further real applications. To address these issues, we propose a parameter-free effective sparse simple multiple kernel $k$-means algorithm with max–min optimization formulation in this paper. To be specific, we propose to optimize the widely used unsupervised kernel alignment criterion by minimizing the kernel coefficient and maximizing the clustering partition matrix. Unlike traditional min–min formulation, the max–min kernel alignment is robust to adversarial sample perturbation and free of hyper-parameters. An optimization method based on semi-infinite linear program is designed to solve the complicated optimization problem. Extensive experiments on six multiple kernel benchmark data sets demonstrate the effectiveness of the proposed method.

中文翻译：

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具有半无限线性程序优化的备用简单 MKKM

多核聚类 (MKC) 优化组合一组预定义的核矩阵以提高聚类性能。尽管在各种应用中表现出良好的性能，但大多数现有方法都采用 min-min 公式，该公式可能对对抗样本的扰动敏感。此外，现有的 MKC 算法通常涉及多个 hypermeter，阻止它们进入进一步的实际应用。为了解决这些问题，我们提出了一种无参数的有效稀疏简单多核$克$-means 算法与本文中的最大-最小优化公式。具体而言，我们建议通过最小化内核系数和最大化聚类分区矩阵来优化广泛使用的无监督内核对齐标准。与传统的 min-min 公式不同，max-min 核对齐对对抗样本扰动具有鲁棒性，并且没有超参数。针对复杂的优化问题，设计了一种基于半无限线性规划的优化方法。在六个多核基准数据集上的大量实验证明了所提出方法的有效性。