Optimized Centroid-Based Clustering of Dense Nearly-square Point Clouds by the Hexagonal Pattern

An approach to optimize centroid-based clustering of flat objects is suggested, which is practically important for efficiently solving metric facility location problems. In such problems, the task is to find the best warehouse locations to optimally service a given set of consumers. An example is assigning mobiles to base stations of a wireless communication network. We suggest a hexagonal-pattern-based approach to partition flat nodes into clusters quicker than the k-means algorithm and its modifications do. First, a hexagonal cell lattice is applied to nodes to approximately determine centroids of the clusters. Then the centroids are used as initial centroids to start the k-means algorithm. The suggested method is efficient for centroid-based clustering of dense nearly-square point clouds of 0.1 million points and greater by using no fewer than 6 lattice cells along an axis. Compared to k-means, our method is at least 10 % faster and it is about 0.01 to 0.07 % more accurate in regular Euclidean distances. In squared Euclidean distances, the accuracy gain is 0.14 to 0.21 %. Applying a hexagonal cell lattice determines an upper bound of the clustering quality gap.