A composite discretization scheme for symbolic identification of complex systems

Abstract

Phase-space discretization is a necessary step for study of continuous dynamical systems using a symbolic dynamics and language-theoretic approach. It is also critical for many machine learning techniques, e.g., probabilistic graphical models (Bayesian Networks, Markov models). This paper proposes a novel composite discretization method – a univariate discretization, namely Statistical Similarity-based Discretization (SSD) followed by a multi-variate discretization called Maximally Bijective Discretization (MBD). While SSD first quantizes input variables for a complex system identifying different operating conditions, MBD finds a discretization on the output variables given the discretization on the input variables such that the correspondence between input and output variables in the continuous domain is preserved in discrete domain for the underlying dynamical system. The proposed method is applied on both simulated and experimental data and results are compared with classical uniform width, maximum entropy, clustering and self-organizing map based discretization techniques.