Kernel k-means extends the k-means algorithm to identify non-linearly separable clusters but is inherently sensitive to cluster initialization. To address this challenge, we first formulate the kernel k-means ++ method, which conveys the efficient center initialization strategy of k-means++ from Euclidean to kernel space. Building on this, we propose global kernel k-means ++ ( \(\text {GK}k\text {M}\) ++), a novel clustering algorithm designed to balance clustering error minimization with reduced computational cost. \(\text {GK}k\text {M}\) ++ extends the well-established global kernel k-means algorithm by incorporating the stochastic initialization strategy of kernel k-means++. This approach significantly reduces computational complexity while preserving superior clustering error minimization capabilities akin to traditional global kernel k-means. The experimental results on synthetic, real, and graph datasets indicate that \(\text {GK}k\text {M}\) ++ consistently outperforms both kernel k-means with random initialization and kernel k-means++, while achieving solutions comparable to those provided by the exhaustive and computational intensive global kernel k-means method.
