With the emergence of numerical sensors in many aspects of everyday life, there is an increasing need in analyzing multivariate functional data. This work focuses on the clustering of such functional data, in order to ease their modeling and understanding. To this end, a novel clustering technique for multivariate functional data is presented. This method is based on a functional latent mixture model which fits the data into group-specific functional subspaces through a multivariate functional principal component analysis. A family of parsimonious models is obtained by constraining model parameters within and between groups. An Expectation Maximization algorithm is proposed for model inference and the choice of hyper-parameters is addressed through model selection. Numerical experiments on simulated datasets highlight the good performance of the proposed methodology compared to existing works. This algorithm is then applied to the analysis of the pollution in French cities for 1 year.

中文翻译：

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在特定于组的功能子空间中聚类多元功能数据

随着数字传感器在日常生活的许多方面的出现，对分析多元函数数据的需求日益增长。这项工作着重于此类功能数据的聚类，以简化其建模和理解。为此，提出了一种用于多元功能数据的新颖聚类技术。该方法基于功能性潜在混合模型，该模型通过多元功能主成分分析将数据拟合到特定于组的功能子空间中。通过约束组内和组之间的模型参数，获得了一组简约模型。提出了一种期望最大化算法进行模型推断，并通过模型选择解决了超参数的选择问题。在模拟数据集上进行的数值实验表明，与现有工作相比，该方法具有良好的性能。然后将该算法应用于法国城市一年的污染分析。