Alphabet size selection for symbolization of dynamic data-driven systems: An information-theoretic approach

Symbolic time series analysis (STSA) is built upon the concept of symbolic dynamics that deals with discretization of dynamical systems in both space and time. The notion of STSA has led to the development of a pattern recognition tool in the paradigm of dynamic data-driven application systems (DDDAS), where a time series of sensor signals is partitioned to obtain a symbol sequence that, in turn, leads to the construction of probabilistic finite state automata (PFSA). Although modeling of PFSA from symbol sequences has been widely reported, similar efforts have not been expended to investigate how to find an appropriate alphabet size for partitioning of time series so that the symbol sequences can be optimally generated. This paper addresses this critical issue and proposes an information-theoretic procedure of data partitioning to extract low-dimensional features from time series. The key idea lies in optimal partitioning of the time series via maximization of the mutual information between the input state probability vector and pattern classes. The proposed procedure has been validated by two examples. The first example elucidates the underlying concept of data partitioning for parameter identification in a Duffing system with a sinusoidal input excitation. The second example is built upon time series of chemiluminescence data to predict lean blow-out (LBO) phenomena in a laboratory-scale combustor. Classification performance of data partitioning is analyzed in each of the two examples.