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.

A hybrid variant of the Fuzzy C-Means and K-Means algorithms is proposed to solve large datasets such as those presented in Big Data. The Fuzzy C-Means algorithm is sensitive to the initial values of the membership matrix. Therefore, a special configuration of the matrix can accelerate the convergence of the algorithm. In this sense, a new approach is proposed, which we call Hybrid OK-Means Fuzzy C-Means (HOFCM), and it optimizes the values of the membership matrix parameter. This approach consists of three steps: (a) generate a set of n solutions of an x dataset, applying a variant of the K-Means algorithm; (b) select the best solution as the basis for generating the optimized membership matrix; (c) resolve the x dataset with Fuzzy C-Means. The experimental results with four real datasets and one synthetic dataset show that HOFCM reduces the time by up to 93.94% compared to the average time of the standard Fuzzy C-Means. It is highlighted that the quality of the solution was reduced by 2.51% in the worst case.

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.

Clustering algorithms have proven to be a useful tool to extract knowledge and support decision making by processing large volumes of data. Hard and fuzzy clustering algorithms have been used successfully to identify patterns and trends in many areas, such as finance, healthcare, and marketing. However, these algorithms significantly increase their solution time as the size of the datasets to be solved increase, making their use unfeasible. In this sense, the parallel processing of algorithms has proven to be an efficient alternative to reduce their solution time. It has been established that the parallel implementation of algorithms requires its redesign to optimise the hardware resources of the platform that will be used. In this article, we propose a new parallel implementation of the Hybrid OK-Means Fuzzy C-Means (HOFCM) algorithm, which is an efficient variant of Fuzzy C-Means, in OpenMP. An advantage of using OpenMP is its scalability. The efficiency of the implementation is compared against the HOFCM algorithm. The experimental results of processing large real and synthetic datasets show that our implementation tends to more efficiently solve instances with a large number of clusters and dimensions. Additionally, the implementation shows excellent results concerning speedup and parallel efficiency metrics. Our main contribution is a Fuzzy clustering algorithm for large datasets that is scalable and not limited to a specific domain.

This paper presents a process that is based on sets of parts, where elements are fixed and removed to form different binary branch-and-bound (BB) trees, which in turn are used to build a parallel algorithm called “multi-BB”. These sequential and parallel algorithms calculate the exact solution for the 0–1 knapsack problem. The sequential algorithm solves the instances published by other researchers (and the proposals by Pisinger) to solve the not-so-complex (uncorrelated) class and some problems of the medium-complex (weakly correlated) class. The parallel algorithm solves the problems that cannot be solved with the sequential algorithm of the weakly correlated class in a cluster of multicore processors. The multi-branch-and-bound algorithms obtained parallel efficiencies of approximately 75%, but in some cases, it was possible to obtain a superlinear speedup.

One of the ways of acquiring new knowledge or underlying patterns in data is by means of clustering algorithms or techniques for creating groups of objects or individuals with similar characteristics in each group and at the same time different from the other groups. There is a consensus in the scientific community that the most widely used clustering algorithm is K-means, mainly because its results are easy to interpret and there are different implementations. In this paper we present an exploratory analysis of the behavior of the main variants of the K-means algorithm (HartiganWong, Lloyd, Forgy and MacQueen) when solving some of the difficult sets of instances from the Fundamental Clustering Problems Suite (FCPS) benchmark. These variants are implemented in the R language and allow finding the minimum and maximum intra-cluster distance of the final clustering. The different scenarios are shown with the results obtained.