A Stratified Seed Selection Algorithm for $K$-Means Clustering on Big Data

In <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-means clustering, the selection of initial seeds significantly influences the quality of the resulting clusters. Moreover, clustering large-sized data introduces an additional challenge for seed selection. We propose a novel and scalable seed selection approach by jointly modeling the quality and diversity of the potential seeds through a principled probabilistic stochastic point process. To this end, we also propose a novel seed quality estimation approach on large data. Our approach quantifies the quality of a seed by measuring the divergence between the distribution of similarity between the closest neighbors and that of the randomly chosen neighbors from exhaustive stratified batches of samples. Unlike many existing scalable approaches, we do not rely on a small sample of the original data; instead, we use the entire data, thereby minimizing the chance of leaving out information about a potentially high-quality seed. The extensive evaluation on a set of benchmark data shows that it outperforms a number of strong, well-known, and recent algorithms measured by three standard metrics.