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.

Mexico is among the five countries with the largest number of reported deaths from COVID-19 disease, and the mortality rates associated to infections are heterogeneous in the country due to structural factors concerning population. This study aims at the analysis of clusters related to mortality rate from COVID-19 at the municipal level in Mexico from the perspective of Data Science. In this sense, a new application is presented that uses a machine learning hybrid algorithm for generating clusters of municipalities with similar values of sociodemographic indicators and mortality rates. To provide a systematic framework, we applied an extension of the International Business Machines Corporation (IBM) methodology called Batch Foundation Methodology for Data Science (FMDS). For the study, 1,086,743 death certificates corresponding to the year 2020 were used, among other official data. As a result of the analysis, two key indicators related to mortality from COVID-19 at the municipal level were identified: one is population density and the other is percentage of population in poverty. Based on these indicators, 16 municipality clusters were determined. Among the main results of this research, it was found that clusters with high values of mortality rate had high values of population density and low poverty levels. In contrast, clusters with low density values and high poverty levels had low mortality rates. Finally, we think that the patterns found, expressed as municipality clusters with similar characteristics, can be useful for decision making by health authorities regarding disease prevention and control for reinforcing public health measures and optimizing resource distribution for reducing hospitalizations and mortality.