Clustering of bivariate satellite time series: a quantile approach

Clustering has received much attention in Statistics and Machine learning with the aim of developing statistical models and autonomous algorithms which are capable of acquiring information from raw data in order to perform exploratory analysis.Several techniques have been developed to cluster sampled univariate vectors only considering the average value over the whole period and as such they have not been able to explore fully the underlying distribution as well as other features of the data, especially in presence of structured time series. We propose a model-based clustering technique that is based on quantile regression permitting us to cluster bivariate time series at different quantile levels. We model the within cluster density using asymmetric Laplace distribution allowing us to take into account asymmetry in the distribution of the data. We evaluate the performance of the proposed technique through a simulation study. The method is then applied to cluster time series observed from Glob-colour satellite data related to trophic status indices with aim of evaluating their temporal dynamics in order to identify homogeneous areas, in terms of trophic status, in the Gulf of Gabes.