标题： 带有多个协变量的大规模函数数据分析的惩罚聚类 显示英文标题

标题： Penalized Clustering of Large Scale Functional Data with Multiple Covariates

摘要： 本文提出了一种通过函数数据分析方法处理具有多个协变量的大规模数据的惩罚聚类方法。在所提出的方法中，响应和协变量通过非参数多元函数（固定效应）联系在一起，这些函数在建模各种函数特征方面具有很大的灵活性，例如跳跃点、分支和周期性。函数ANOVA被用来进一步分解再生核Hilbert空间中的多元函数，并提供主效应和交互作用的相关概念。简洁的随机效应用于捕获各种相关结构。混合效应模型嵌套在一个广义混合模型中，其中函数数据的异质性被刻画出来。我们提出了一个惩罚性的Henderson似然方法来进行模型拟合，并设计了一个拒绝控制的EM算法来进行估计。我们的方法通过广义交叉验证来选择平滑参数。此外，使用贝叶斯置信区间来衡量聚类的不确定性。进行了模拟研究和真实数据实例以调查所提出方法的经验性能。开源代码可以在R包MFDA中获得。 显示英文摘要

摘要： In this article, we propose a penalized clustering method for large scale data with multiple covariates through a functional data approach. In the proposed method, responses and covariates are linked together through nonparametric multivariate functions (fixed effects), which have great flexibility in modeling a variety of function features, such as jump points, branching, and periodicity. Functional ANOVA is employed to further decompose multivariate functions in a reproducing kernel Hilbert space and provide associated notions of main effect and interaction. Parsimonious random effects are used to capture various correlation structures. The mixed-effect models are nested under a general mixture model, in which the heterogeneity of functional data is characterized. We propose a penalized Henderson's likelihood approach for model-fitting and design a rejection-controlled EM algorithm for the estimation. Our method selects smoothing parameters through generalized cross-validation. Furthermore, the Bayesian confidence intervals are used to measure the clustering uncertainty. Simulation studies and real-data examples are presented to investigate the empirical performance of the proposed method. Open-source code is available in the R package MFDA.