Genetic Algorithms and Cross-correlation Clustering of Time Series

It may turn of interest the problem of finding a proper partition of a set of time series into clusters, where all time series that belong to the same cluster are significantly correlated each other. An obvious difficulty arises because the cross-correlation between each pair of time series is a function of the time lag. Several dissimilarity indexes which take into account the cross-correlation function are considered and compared in order to point out their relative merits and effectiveness in recovering the true cluster structure. A suitable internal criterion for evaluating the computed partition is presented, and its maximisation by means of a genetic algorithm is proposed. A simulation experiment is performed that may suggest what dissimilarity measure is best and what parameters had better selected for implementing the genetic algorithm. Comparison with the well-known and widely used single linkage method, and with the artificial neural network procedure which introduced into practice the clustering criterion that, with some modifications, is adopted here, is carried out as well.