Gaussian distributions have been commonly assumed when clustering functional data. When the normality condition fails, biased results will follow. Additional challenges occur as the number of the clusters is often unknown a priori. This paper focuses on clustering non-Gaussian functional data without the prior information of the number of clusters. We introduce a semiparametric mixed normal transformation model to accommodate non-Gaussian functional data, and propose a penalized approach to simultaneously estimate the parameters, transformation function, and the number of clusters. The estimators are shown to be consistent and asymptotically normal. The practical utility of the methods is confirmed via simulations as well as an application of the analysis of Alzheimer's disease study. The proposed method yields much less classification error than the existing methods. Data used in preparation of this paper were obtained from the Alzheimer's Disease Neuroimaging Initiative database.

中文翻译：

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聚类非高斯函数数据

在对功能数据进行聚类时，通常假设高斯分布。当正态性条件失败时，会有偏差的结果随之而来。由于集群的数量通常是先验未知的，因此会出现额外的挑战. 本文侧重于对非高斯函数数据进行聚类，而无需聚类数量的先验信息。我们引入了半参数混合正态变换模型来适应非高斯函数数据，并提出了一种惩罚方法来同时估计参数、变换函数和簇数。估计量显示为一致且渐近正态。这些方法的实际效用通过模拟以及阿尔茨海默病研究分析的应用得到证实。与现有方法相比，所提出的方法产生的分类错误要少得多。用于准备本文的数据来自阿尔茨海默病神经影像学倡议数据库。