NONLINEAR MANIFOLD REPRESENTATIONS FOR FUNCTIONAL DATA
NONLINEAR MANIFOLD REPRESENTATIONS FOR FUNCTIONAL DATA
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DOI：
10.1214/11-aos936
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发表时间：
2012-02-01
影响因子：
4.5
通讯作者：
Mueller, Hans-Georg
中科院分区：
文献类型：
--
作者：
Chen, Dong;Mueller, Hans-Georg
对于未知的非线性低维空间上的函数数据，我们研究了流形学习，并引入了流形均值、流形函数变分模式和流形函数分量的概念。这些构成了功能数据的非线性表示，补充了经典的线性表示，如特征函数和功能主成分。我们的流形学习程序借用了现有的非线性降维方法的思想，我们修改，以解决功能数据设置。在模拟和应用中，我们研究了位于流形上的函数数据的例子，并验证了流形平均和函数流形分量比传统的横截面平均和函数主分量的上级行为。我们还包括我们的估计在某些假设下的一致性证明。
For functional data lying on an unknown nonlinear low-dimensional space, we study manifold learning and introduce the notions of manifold mean, manifold modes of functional variation and of functional manifold components. These constitute nonlinear representations of functional data that complement classical linear representations such as eigenfunctions and functional principal components. Our manifold learning procedures borrow ideas from existing nonlinear dimension reduction methods, which we modify to address functional data settings. In simulations and applications, we study examples of functional data which lie on a manifold and validate the superior behavior of manifold mean and functional manifold components over traditional cross-sectional mean and functional principal components. We also include consistency proofs for our estimators under certain assumptions.