文章基本信息

标题：Nonparametric clustering of functional data using pseudo-densities
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作者：Mattia Ciollaro ; Christopher R. Genovese ; Daren Wang 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2016
卷号：10
期号：2
页码：2922-2972
DOI：10.1214/16-EJS1198
语种：English
出版社：Institute of Mathematical Statistics
摘要：We study nonparametric clustering of smooth random curves on the basis of the $L^{2}$ gradient flow associated to a pseudo-density functional and we discuss the conditions under which the clustering is well-defined both at the population and at the sample level. We provide an algorithm to idenify significant local modes of the estimated pseudo-density, which are associated to informative sample clusters, and we prove its consistency and other statistical properties. Our theory is developed under weak assumptions, which essentially reduce to the integrability of the random curves. If the underlying probability distribution is supported on a finite-dimensional subspace, we show that the proposed pseudo-density functional and the expectation of a kernel density estimator induce the same gradient flow, hence the same population clustering. Although our theory is developed for smooth curves that belong to a potentially infinite-dimensional functional space, we provide consistent procedures that can be used with real functional data (discretized and noisy curves). We illustrate these procedures by means of applications both on simulated and real datasets.