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.

In most big cities, public transports are enclosed and crowded spaces. Therefore, they are considered as one of the most important triggers of COVID-19 spread. Most of the existing research related to the mobility of people and COVID-19 spread is focused on investigating highly frequented paths by analyzing data collected from mobile devices, which mainly refer to geo-positioning records. In contrast, this paper tackles the problem by studying mass mobility. The relations between daily mobility on public transport (subway or metro) in three big cities and mortality due to COVID-19 are investigated. Data collected for these purposes come from official sources, such as the web pages of the cities’ local governments. To provide a systematic framework, we applied the IBM Foundational Methodology for Data Science to the epidemiological domain of this paper. Our analysis consists of moving averages with a moving window equal to seven days so as to avoid bias due to weekly tendencies. Among the main findings of this work are: a) New York City and Madrid show similar distribution on studied variables, which resemble a Gauss bell, in contrast to Mexico City, and b) Non-pharmaceutical interventions don’t bring immediate results, and reductions to the number of deaths due to COVID are observed after a certain number of days. This paper yields partial evidence for assessing the effectiveness of public policies in mitigating the COVID-19 pandemic.

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