Accelerated K-Means Algorithms for Low-Dimensional Data on Parallel Shared-Memory Systems

This paper considers the problem of exact accelerated algorithms for the K-means clustering of low-dimensional data on modern multi-core systems. A version of the filtering algorithm parallelized using the OpenMP (Open Multi-Processing) standard is proposed. The algorithm employs a kd-tree structure to skip some unnecessary calculations between cluster centroids and feature vectors. In our approach, both the kd-tree construction and the iterations of the K-means are parallelized using the OpenMP tasking mechanism. A new task is created for a recursive call performed during kd-tree construction and traversal. The tasks are executed in parallel by the cores of a shared-memory system. In computational experiments, we evaluated the parallel efficiency of our approach and compared its performance to the parallel Lloyd's method, a GPU (Graphics Processing Unit) formulation of the K-means algorithm, and two parallel triangle inequality-based algorithms intended for low-dimensional data. The evaluation was performed on six synthetic datasets from two distributions and seven real-life datasets. The experiments, executed on a 24-core system, indicated that our version of the filtering algorithm had satisfactory or high parallel efficiency. Its runtime was much shorter than those of competing algorithms. However, the advantage of the parallel filtering algorithm decreased rapidly as the dimension of data increased.