A Faster k-means++ Algorithm

k-means++ is an important algorithm for choosing initial cluster centers for the k-means clustering algorithm. In this work, we present a new algorithm that can solve the k-means++ problem with nearly optimal running time. Given n data points in ℝ^d, the current state-of-the-art algorithm runs in O(k ) iterations, and each iteration takes O(nd k) time. The overall running time is thus O(n d k^2). We propose a new algorithm FastKmeans++ that only takes in O(nd + nk^2) time, in total.