Abstract

Clustering is a popular problem with many applications. We consider the k-means problem in the situation where the data is too large to be stored in main memory and must be accessed sequentially, such as from a disk, and where we must use as little memory as possible. Our algorithm is based on recent theoretical results, with significant improvements to make it practical. Our approach greatly simplifies a recently developed algorithm, both in design and in analysis, and eliminates large constant factors in the approximation guarantee, the memory requirements, and the running time. We then incorporate approximate nearest neighbor search to compute k-means in (where n is the number of data points; note that computing the cost, given a solution, takes . We show that our algorithm compares favorably to existing algorithms both theoretically and experimentally, thus providing state-of-the-art performance in both theory and practice.