Persistence-Based Discretization for Learning Discrete Event Systems from Time Series

To get a good understanding of a dynamical system, it is convenient to have an interpretable and versatile model of it. Timed discrete event systems are a kind of model that respond to these requirements. However, such models can be inferred from timestamped event sequences but not directly from numerical data. To solve this problem, a discretization step must be done to identify events or symbols in the time series. Persist is a discretization method that intends to create persisting symbols by using a score called persistence score. This allows to mitigate the risk of undesirable symbol changes that would lead to a too complex model. After the study of the persistence score, we point out that it tends to favor excessive cases making it miss interesting persisting symbols. To correct this behavior, we replace the metric used in the persistence score, the Kullback-Leibler divergence, with the Wasserstein distance. Experiments show that the improved persistence score enhances Persist's ability to capture the information of the original time series and that it makes it better suited for discrete event systems learning.