K-means-G*: Accelerating k-means clustering algorithm utilizing primitive geometric concepts

Abstract

The k-means is the most popular clustering algorithm, but, as it needs too many distance computations, its speed is dramatically fall down against high-dimensional data. Although, there are some quite fast variants proposed in literature, but, there is still much room for improvement against high-dimensional large-scale datasets.What proposed here, k-means-g*, is based on a simple geometric concept. For four distinct points, if distance between all pairs except one pair are known, then, a lower bound can be determined for the unknown distance. Utilizing this technique in the assignment step of the k-means, many high-dimensional distance computations can be easily ignored, where small amount of memory is used.Both theoretical and experimental results approves speed of the k-means-g* against recently published fast variants. For over than 50 cases, out of 70 cases of performed experiments, it is faster than other algorithms. The C++ source code for k-means-g* is publicly available.