A Surrogate-Assisted Symbolic Time-Series Discretization Using Multi-breakpoints and a Multi-objective Evolutionary Algorithm

The enhanced multi-objective symbolic discretization for time series (eMODiTS) method employs a flexible discretization scheme using different value cuts for each non-equal time interval, which requires a computational cost for evaluating each objective function. Therefore, surrogate models were implemented to minimize this disadvantage. Nevertheless, each solution found by eMODiTS is a different-sized vector, so the surrogate model must be able to handle data sets under this characteristic. Consequently, this work's contribution lies in analyzing the surrogate models' implementation on the time series discretization, where each potential scheme is a real-number different-sized vector. For this reason, the surrogate model proposed was k-nearest Neighbors for regression with Dynamic Time Warping as a distance measure. Results suggest our proposal finds a suitable approximation to the final eMODiTS solutions with a functions evaluation reduction rate between 15% and 95%. However, according to Pareto front performance measures, the proposal Pareto front is competitive compared to the eMODiTS Pareto front, reaching an average Generational Distance (GD) between 0.0447 and 0.0536. Moreover, the average Hypervolume Ratio (HVR) ranges between 0.334 and 0.3891. Finally, our proposal compared against SAX-based methods presents a similar behavior regarding classification tasks and statistical tests.