Clustering techniques applied to multivariate data are a very useful tool in Statistics and have been fully studied in the literature. Nevertheless, these clustering methodologies are less well known when dealing with functional data. Our proposal consists of introducing a clustering procedure for functional data using the very well known techniques for clustering multivariate data. The idea is to reduce a functional data problem to a multivariate data problem by applying the epigraph and the hypograph indexes to the original data and to its first and second derivatives. All the information given by the functional data is therefore transformed to the multivariate context, being sufficiently informative for the usual multivariate clustering techniques to be efficient. The performance of this new methodology is evaluated through a simulation study and it is also illustrated through real data sets.
翻译:适用于多变量数据的集群技术是统计中非常有用的工具,文献中已对此进行了充分研究,然而,在处理功能数据时,这些集群方法不太广为人知,我们的建议是采用非常熟悉的多变量数据集群技术,对功能数据采用分组程序,采用功能数据,通过模拟研究对原始数据及其第一和第二衍生物应用传记和测算索引,将功能数据问题降低到多变量数据问题。因此,功能数据提供的所有信息都转换为多变量环境,具有足够的信息性,使得通常的多变量组合技术具有效率。通过模拟研究评估这一新方法的绩效,并通过真实数据集加以说明。