Variable-chromosome-length genetic algorithm for time series discretization

The symbolic aggregate approximation method (SAX) of time series is a widely-known dimensionality reduction technique of time series data. SAX assumes that normalized time series have a high-Gaussian distribution. Based on this assumption SAX uses statistical lookup tables to determine the locations of the breakpoints on which SAX is based. In a previous work, we showed how this assumption oversimplifies the problem, which may result in high classification errors. We proposed an alternative approach, based on the genetic algorithms, to determine the locations of the breakpoints. We also showed how this alternative approach boosts the performance of the original SAX. However, the method we presented has the same drawback that existed in the original SAX; it was only able to determine the locations of the breakpoints but not the corresponding alphabet size, which had to be input by the user in the original SAX. In the method we previously presented we had to run the optimization process as many times as the range of the alphabet size. Besides, performing the optimization process in two steps can cause overfitting. The novelty of the present work is twofold; first, we extend a version of the genetic algorithms that uses chromosomes of different lengths. Second, we apply this new version of variable-chromosome-length genetic algorithm to the problem at hand to simultaneously determine the number of the breakpoints, together with their locations, so that the optimization process is run only once. This speeds up the training stage and also avoids overfitting. The experiments we conducted on a variety of datasets give promising results.