Mini-Batch Kernel k-means

We present the first mini-batch kernel k-means algorithm, offering an order of magnitude improvement in running time compared to the full batch algorithm. A single iteration of our algorithm takes widetildeO(kb2) time, significantly faster than the O(n2) time required by the full batch kernel k-means, where n is the dataset size and b is the batch size. Extensive experiments demonstrate that our algorithm consistently achieves a 10-100x speedup with minimal loss in quality, addressing the slow runtime that has limited kernel k-means adoption in practice. We further complement these results with a theoretical analysis under an early stopping condition, proving that with a batch size of widetildeOmega(max γ4, γ2 · ε-2), the algorithm terminates in O(γ2/ε) iterations with high probability, where γ bounds the norm of points in feature space and ε is a termination threshold. Our analysis holds for any reasonable center initialization, and when using k-means++ initialization, the algorithm achieves an approximation ratio of O(log k) in expectation. For normalized kernels, such as Gaussian or Laplacian it holds that γ=1. Taking ε = O(1) and b=Theta(log n), the algorithm terminates in O(1) iterations, with each iteration running in widetildeO(k) time.