In this paper we propose a criterion to balance the processing time and the solution quality of k-means cluster algorithms when applied to instances where the number n of objects is big. The majority of the known strategies aimed to improve the performance of k-means algorithms are related to the initialization or classification steps. In contrast, our criterion applies in the convergence step, namely, the process stops whenever the number of objects that change their assigned cluster at any iteration is lower than a given threshold. Through computer experimentation with synthetic and real instances, we found that a threshold close to 0.03n involves a decrease in computing time of about a factor 4/100, yielding solutions whose quality reduces by less than two percent. These findings naturally suggest the usefulness of our criterion in Big Data realms.

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Clustering is one of the main methods for getting insight on the underlying nature and structure of data. The purpose of clustering is organizing a set of data into clusters, such that the elements in each cluster are similar and different from those in other clusters. One of the most used clustering algorithms presently is K-means, because of its easiness for interpreting its results and implementation. The solution to the K-means clustering problem is NP-hard, which justifies the use of heuristic methods for its solution. To date, a large number of improvements to the algorithm have been proposed, of which the most relevant were selected using systematic review methodology. As a result, 1125 documents on improvements were retrieved, and 79 were left after applying inclusion and exclusion criteria. The improvements selected were classified and summarized according to the algorithm steps: initialization, classification, centroid calculation, and convergence. It is remarkable that some of the most successful algorithm variants were found. Some articles on trends in recent years were included, concerning K-means improvements and its use in other areas. Finally, it is considered that the main improvements may inspire the development of new heuristics for K-means or other clustering algorithms.