Title: The Price of Explainability for Kernel $k$-means
Primary area: interpretability and explainable AI
Keywords: kernel  $k$-means, explainable clustering, threshold tree

Abstract: The explainability of the machine learning model has received increasing attention recently for security and model reliability reasons. Recently, there has been a surge of interest in interpreting the clustering results of $k$-means and kernel $k$-means algorithms. In this paper, we study explainable kernel clustering and compare the explainable performance of kernel $k$-means algorithms based on different kernels. In particular, we show that kernel $k$-means clustering with the Laplacian kernel has lower price of explainability than that with the Gaussian kernel, which is consistent with the experimental findings of \citet{fleissnerexplaining}. In addition, we propose a new kernel $k$-means interpretability algorithm that directly constructs a dual-threshold tree in the original space to achieve interpretable kernel $k$-means, and experimentally show that it outperforms KIMM, which constructs the threshold tree in the kernel space.