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-color 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.

中文翻译：

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双变量卫星时间序列的聚类：分位数方法

聚类在统计学和机器学习中受到了广泛关注，其目的是开发能够从原始数据中获取信息以进行探索性分析的统计模型和自主算法。已经开发了几种技术来仅考虑整个期间的平均值来对采样的单变量向量进行聚类，因此它们无法充分探索数据的潜在分布以及其他特征，尤其是在存在结构化时间序列的情况下。我们提出了一种基于模型的聚类技术，该技术基于分位数回归，允许我们在不同的分位数水平上对双变量时间序列进行聚类。我们使用非对称拉普拉斯分布对簇内密度进行建模，从而允许我们考虑数据分布中的不对称性。我们通过模拟研究评估所提出技术的性能。然后将该方法应用于从与营养状态指数相关的全局彩色卫星数据中观察到的聚类时间序列，目的是评估它们的时间动态，以便在加贝斯湾的营养状态方面识别同质区域。