An adaptive symbolic discretization scheme for the classification of temporal datasets using NSGA-II

In this work, an adaptive algorithm for the symbolic discretization of time series is introduced. This approach, called MODiTS, consists of defining a different alphabet vector for each word segment. The number of alphabets and the word size are optimized automatically using a well-known multi-objective algorithm: Non-dominated Sorting Genetic Algorithm (NSGA-II). NSGA-II was adapted to help find the appropriate symbolic representation scheme for each temporal database based on the minimization of three objective functions (Entropy, Complexity, and Compression). Each scheme was evaluated based on the misclassification error rate calculated by means of the Decision Tree, which also provides relevant information about the regions, relationships or patterns within each database, in addition to its function as a descriptive tool to help understand temporal data. Our proposal was compared with two symbolic discretization algorithms: Symbolic Aggregate approximation (SAX), and Evolutionary Programming (EP). The statistical results suggest that our algorithm is a useful tool in finding competitive symbolic representation schemes with a lower dimensionality reduction rate and an acceptable level of classification error.