Complex systems have been the object of studies across diverse fields, comprising both hard and soft sciences. The data revolution and the enormous amount of data available in recent years allowed for their quantitative analysis. According to the problem under investigation, one can focus on their stationary properties, thus adopting a static description, or analyze their dynamics and their out-of-equilibrium properties. The goal of this thesis is to investigate the dynamical behavior of a complex system using dimensional reduction, a technique aiming to reduce the number of degrees of freedom of the system by constructing a synthetic, more effective representation. Here we focus on a fully unsupervised approach to dimensional reduction by coupling clustering techniques with recent ideas of maximally informative representations.