A Simple but Powerful Heuristic Method for Accelerating $k$ -Means Clustering of Large-Scale Data in Life Science

K-means clustering has been widely used to gain insight into biological systems from large-scale life science data. To quantify the similarities among biological data sets, Pearson correlation distance and standardized Euclidean distance are used most frequently; however, optimization methods have been largely unexplored. These two distance measurements are equivalent in the sense that they yield the same k-means clustering result for identical sets of k initial centroids. Thus, an efficient algorithm used for one is applicable to the other. Several optimization methods are available for the Euclidean distance and can be used for processing the standardized Euclidean distance; however, they are not customized for this context. We instead approached the problem by studying the properties of the Pearson correlation distance, and we invented a simple but powerful heuristic method for markedly pruning unnecessary computation while retaining the final solution. Tests using real biological data sets with 50-60K vectors of dimensions 10-2001 (~400 MB in size) demonstrated marked reduction in computation time for k = 10-500 in comparison with other state-of-the-art pruning methods such as Elkan's and Hamerly's algorithms. The BoostKCP software is available at http://mlab.cb.k.u-tokyo.ac.jp/~ichikawa/boostKCP/.