Reviews: Statistical and Computational Trade-Offs in Kernel K-Means

Summary The paper investigates the kernel k-means problem, proposing a new approximation of the method based on Nystrom embeddings. In particular, both the statistical accuracy and computational efficiency of the proposed approximation is studied. The main contribution is the derivation of a theoretical bound limiting the error cost; the proposed method can achieve such theoretical guarantee with a computational cost of (O(\sqrt{n})). In practice, this implies that using \sqrt{n} points (with n being the original sample size) is enough to obtain a good enough approximation. The authors also propose an approach to choose the points while ensuring a balance trade off between preserving a good approximation and a small complexity (dictionary size).