Complexity measures aim to characterize the underlying complexity of supervised data. These measures tackle factors hindering the performance of Machine Learning (ML) classifiers like overlap, density, linearity, etc. The state-of-the-art has mainly focused on the dataset perspective of complexity, i.e., offering an estimation of the complexity of the whole dataset. Recently, the instance perspective has also been addressed. In this paper, the hostility measure, a complexity measure offering a multi-level (instance, class, and dataset) perspective of data complexity is proposed. The proposal is built by estimating the novel notion of hostility: the difficulty of correctly classifying a point, a class, or a whole dataset given their corresponding neighborhoods. The proposed measure is estimated at the instance level by applying the k-means algorithm in a recursive and hierarchical way, which allows to analyze how points from different classes are naturally grouped together across partitions. The instance information is aggregated to provide complexity knowledge at the class and the dataset levels. The validity of the proposal is evaluated through a variety of experiments dealing with the three perspectives and the corresponding comparative with the state-of-the-art measures. Throughout the experiments, the hostility measure has shown promising results and to be competitive, stable, and robust.

The outbreak of the COVID-19 disease, spreading all around the world and causing a worldwide pandemic, has lead to the collapse of the health systems of the most affected countries. Due to the ease of transmission, early prevention measures are proved to be fundamental to control the pandemic and, hence, the saturation of the health systems. Given the difficulty of obtaining characteristics of these systems of different countries and regions, it is necessary to define indicators based on basic information that enable the assessment of the evolution of the impact of a disease in a health system along with fair comparisons among different ones. This present paper introduces the Health Sufficiency Indicator ($HSI$), in its accumulated and daily versions. This indicator measures the additional pressure that a health care system has to deal with due to a pandemic. Hence, it allows to evaluate the capacity of a health system to give response to the corresponding needs arising from a pandemic and to compare the evolution of the disease among different regions. In addition, the Potential Occupancy Ratio ($POR$) in both its hospital ward bed and ICU bed versions is here introduced to asses the impact of the pandemic in the capacity of hospitals. These indicators and other well-known ones are applied to track the evolution of the impact of the disease on the Spanish health system during the first wave of the pandemic, both on national and regional levels. An international comparison among the most affected countries is also performed.

La COVID 19 es una enfermedad infecciosa, altamente contagiosa, que se propaga por contacto o cercanía cuando una persona infectada tose o estornuda. Según los estudios actuales la letalidad no es alta, pero a causa de la facilidad de contagio, esta enfermedad ha provocado un estado mundial de pandemia. Debido a ello, se ha originado el colapso de los sistemas sanitarios de todos los países afectados. Dada la dificultad de obtener las características de los sistemas sanitarios de los distintos países, urge obtener indicadores capaces de comparar el estado de estos sistemas y evaluar su evolución, en función de la incidencia y morbilidad de la enfermedad. En este trabajo, se presenta el Indicador de Suficiencia Sanitaria (ISS) que permite evaluar la capacidad que tiene un sistema de salud para responder a las necesidades derivadas de una pandemia. Este indicador es útil para comparar el desarrollo de la enfermedad entre los distintos países con los datos disponibles. Además, se analizan otros indicadores habituales relativos al número de casos, número de fallecidos y número de altas en el sistema de salud. Finalmente, se construyen modelos de aprendizaje máquina para la predicción del ISS y estimar el desarrollo de la enfermedad y su impacto en el sistema sanitario en España, tanto a nivel nacional como a nivel regional.