Ball k-Means: Fast Adaptive Clustering With No Bounds.

This paper presents a novel accelerated exact k-means called as "Ball k-means" by using the ball to describe each cluster, which focus on reducing the point-centroid distance computation. The "Ball k-means" can exactly find its neighbor clusters for each cluster, resulting distance computations only between a point and its neighbor clusters' centroids instead of all centroids. What's more, each cluster can be divided into "stable area" and "active area", and the latter one is further divided into some exact "annular area". The assignment of the points in the "stable area" is not changed while the points in each "annular area" will be adjusted within a few neighbor clusters. There are no upper or lower bounds in the whole process. Moreover, ball k-means uses ball clusters and neighbor searching along with multiple novel stratagems for reducing centroid distance computations. In comparison with the current state-of-the art accelerated exact bounded methods, the Yinyang algorithm and the Exponion algorithm, as well as other top-of-the-line tree-based and bounded methods, the ball k-means attains both higher performance and performs fewer distance calculations, especially for large-k problems. The faster speed, no extra parameters and simpler design of "Ball k-means" make it an all-around replacement of the naive k-means.