Improvement to the K-Means algorithm through a heuristics based on a bee honeycomb structure

Abstract

The object clustering problem, according to their similarity measures, can be formulated as a combinatorial optimization problem. The K-Means algorithm has been widely used for solving such problem; however, its computational cost is very high. In this work a new heuristics is proposed for reducing the computational complexity in the classification step of the algorithm based on a honeycomb structure, which the algorithm builds when clusters are visualized in a two-dimensional space. In particular it has been observed that an object can only change membership to neighboring clusters. The heuristics consists of performing distance calculations only with respect to centroids of neighboring clusters, which reduces the number of calculations. For assessing the performance of this heuristics, a set of experiments was carried out that involved 2500, 10000 and 40000 objects uniformly distributed in a two-dimensional space, as well as real-world instances of 3100 and 245 057 objects with 2 and 3 dimensions. The results were encouraging, since the calculation time was reduced 65% on average, with respect to the standard K-Means algorithm for the synthetic instance, and up to 62% on average for the real-world instances, while the quality was reduced on average by 0.05% and 2.5%, respectively.