Kernel functions are a powerful tool to enhance the $k$-means clustering algorithm via the kernel trick. It is known that the parameters of the chosen kernel function can have a dramatic impact on the result. In supervised settings, these can be tuned via cross-validation, but for clustering this is not straightforward and heuristics are usually employed. In this paper we study the impact of kernel parameters on kernel $k$-means. In particular, we derive a lower bound, tight up to constant factors, below which the parameter of the RBF kernel will render kernel $k$-means meaningless. We argue that grid search can be ineffective for hyperparameter search in this context and propose an alternative algorithm for this purpose. In addition, we offer an efficient implementation based on fast approximate exponentiation with provable quality guarantees. Our experimental results demonstrate the ability of our method to efficiently reveal a rich and useful set of hyperparameter values.

本文研究核参数对核$k$-means聚类算法的影响，给出一下RBF核参数下界，建议使用基于快速近似指数函数的算法进行参数搜索，并提供了一种高效实现方法。实验结果证明了该方法能够有效地揭示一组丰富而有用的超参数值。

离线化: 针对核聚类的快速高效超参数搜索