A multi-way analysis of similarity patterns in longevity improvements

With the increasing availability of temporal data, a researcher often analyzes information saved into matrices, in which entries are replicated in different occasions. Such multidimensional data can be stored in arrays or tensors in a way that relevant patterns among variables can be teased apart by retaining the time-varying nature of the data. In this work, we show how the nonnegative three-way DEcomposition into DIrectional COMponents (DEDICOM) model is able to extract meaningful relational patterns from multi-population mortality data. The dataset considered is provided by the human mortality database (HMD) and refers to three dimensions: countries, age groups and years. The three-dimensional decomposition technique identifies persistent groups of countries with homogeneous mortality behaviours related to the evolutionary process of longevity improvements. Moreover, we exploit both country group information and recurrent neural networks to forecast future trajectories of similarities among countries' mortality. Our work, by specifically describing the mesoscale interactions between countries and their evolution in time, could help to design appropriate actions against longevity risk that may impact the stability conditions of life assurance and pensions.