One of the most used algorithms to solve the fuzzy clustering problem is Fuzzy C-Means; however, one of its main limitations is its high computational complexity. It is known that the efficiency of an algorithm depends, among other factors, on the strategies for its initialization and convergence. In this research, a new convergence strategy is proposed, which is based on the difference of the objective function values, in two consecutive iterations, expressed as a percentage of its value in the next to the last one. Additionally, a new method is proposed to optimize the selection of values of the convergence or stop threshold of the algorithm, which is based on the Pareto principle. To validate our approach, a collection of real datasets was solved, and a significant reduction in the number of iterations was observed, without affecting significantly the solution quality. Based on the proposed method and the experiments carried out, we found it is convenient to use threshold values equal to 0.73 and 0.35 if a decrease in the number of iterations of approximately 75.2% and 64.56%, respectively, is wanted, at the expense of a reduction in solution quality of 2% and 1%, respectively. It is worth mentioning that, as the size of the datasets is increased, the proposed approach tends to obtain better results, and therefore, its use is suggested for datasets found in Big Data and Data Science.

Fuzzy C-Means is a clustering algorithm widely used in many applications. However, its computational complexity is very large, which prevents its use for large problem instances. Therefore, a hybrid improvement is proposed for the algorithm, which considerably reduces the number of iterations and, in many cases, improves the solution quality, expressed as the value of the objective function. This improvement integrates two heuristics, one in the initialization phase and the other in the convergence phase or the convergence criterion. This improvement was called HPFCM. A set of experiments was designed to validate this proposal; to this end, four sets of real data were solved from a prestigious repository. The solutions obtained by HPFCM were compared against those of the Fuzzy C-Means algorithm. In the best case, reductions of an average of 97.65% in the number of required iterations and an improvement in quality solution of 82.42% were observed when solving the SPAM dataset. Finally, we consider that the proposed heuristics may inspire improvements in other specific purpose variants of Fuzzy C-Means.

In recent years, the mortality due to diabetes has increased around the world. In particular, diabetes is the second leading cause of mortality in Mexico, with a heterogeneous distribution of mortality rates at the municipality level. The objective of this study is the analysis of clusters of municipalities with similar values for sociodemographic indices and diabetes mortality. In this sense, an application is presented that was developed using a data science methodology and a machine learning algorithm called fuzzy c-means. For this research, 4,604,360 death certificates from 2019 to 2023 were assessed, among other official data. As a result of the analysis, two key indicators related to diabetes mortality were found, i.e., one is the percentage of population in poverty and the other is population density. The main results of this research are as follows: a direct correlation was found between population density and mortality, and an inverse correlation was found between population in poverty and mortality. In the study interval, it was observed that the cluster with less mortality showed an increase in mortality rate year after year. Finally, we consider that the tendencies found can be useful to public health authorities for optimizing the distribution of resources for treating diabetes and reducing diabetes-related mortality.