Functional principal components analysis via penalized rank one approximation
Functional principal components analysis via penalized rank one approximation
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DOI：
10.1214/08-ejs218
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发表时间：
2008-01-01
影响因子：
1.1
通讯作者：
Buja, Andreas
中科院分区：
文献类型：
--
作者：
Huang, Jianhua Z.;Shen, Haipeng;Buja, Andreas
函数主成分分析（FPCA）的两种现有方法是由Rice and Silverman（1991）和Silverman（1996）提出的，两者都基于最大化方差，但以不同的方式引入惩罚。在这篇文章中，我们提出了一种替代方法FPCA使用惩罚秩一近似的数据矩阵。我们的贡献是四方面的：（1）通过考虑测量值在尺度变换下的不变性，新公式揭示了FPCA的正则化应该如何进行，并提出了一种有效的计算幂算法：（2）它自然地结合了离散函数数据的样条平滑;（3）与平滑样条的连接还便于构造用于平滑参数选择的交叉验证或广义交叉验证准则，其允许有效计算;（4）对于不同的FPC，允许不同的平滑参数。该方法说明了一个真实的数据的例子和模拟。
Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in different ways. In this article we propose an alternative approach to FPCA using penalized rank one approximation to the data matrix. Our contributions are four-fold: (1) by considering invariance under scale transformation of the measurements, the new formulation sheds light on how regularization should be performed for FPCA and suggests an efficient power algorithm for computation; (2) it naturally incorporates spline smoothing of discretized functional data; (3) the connection with smoothing splines also facilitates construction of cross-validation or generalized cross-validation criteria for smoothing parameter selection that allows efficient computation; (4) different smoothing parameters are permitted for different FPCs. The methodology is illustrated with a real data example and a simulation.