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.

The number of older adult has increased significantly in most current societies. One problem that is accentuated in the stage of old age is loneliness which is a serious health risk. Therefore, new methods for early detection of this condition that make use of new non-intrusive technologies are required. Loneliness includes four main factors (family, spousal, social and existential crisis). In this paper, four predictive models to determine the level of loneliness of each factor are proposed, focusing on the activities that can be monitored using a Smartphone. Predictive models have been evaluated on basis of their accuracy, sensitivity, specificity, predictive values, type I and type II error rates. This paper also presents the results of the experimentation of the proposed approach in practice and with real users through a mobile application called “!‘Vive!” that implements the predictive models.

The precise allocation of weights to criteria plays a fundamental role in multicriteria decision-making, exerting a significant influence on the obtained results. Ensuring an appropriate weighting of criteria is crucial for conducting a fair and accurate evaluation of various alternatives. In this context, we present an innovative solution that addresses the allocation of weights to attributes in datasets, aiming to overcome limitations and challenges associated with expert consultation in multicriteria problems. The proposed method is grounded in an objective approach and adopts a hybrid perspective by integrating the mathematical principles of Principal Component Analysis with the application of the Entropy Method. This method was implemented along with the exponential weighted sum model in a case study related to the classification of neighborhoods in Mexico City based on the level of marginalization. Results were compared with the marginalization index reported in official sources, using evaluation metrics MAE and MAPE with values of 0.24 and 11.3%, respectively. This research demonstrates the efficiency of the proposed method, which integrates techniques used for attribute weighting, providing a robust and reliable tool for decision-making.