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Activity Number: 305 - New Nonparametric Methods for Functional Data
Type: Contributed
Date/Time: Tuesday, July 31, 2018 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #330619 Presentation
Title: Sparse Functional Principal Component Analysis in a New Regression Framework
Author(s): Yunlong Nie* and Jiguo Cao
Companies: Simon Fraser University and Simon Fraser University
Keywords: functional data; dimension reduction ; locally support; functional principal component
Abstract:

The functional principal component analysis is widely used to explore major sources of variation in a sample of random curves. These major sources of variation are represented by functional principal components (FPCs). The FPCs from the conventional FPCA method are often nonzero in the whole domain and are hard to interpret in practice. In this paper, we consider the problem of estimating functional principal components (FPCs), which are only nonzero in subregions. The resulting sparse FPCs not only represent the major variance resources but also can be used to identify the subregions where those major variations exist. The current methods obtain sparse FPCs by adding a penalty term on the length of nonzero regions of FPCs in the conventional eigendecomposition framework. However, these methods become an NP-hard optimization problem. To overcome this issue, we propose a novel regression framework to estimate FPCs and the corresponding optimization is not NP-hard. We also show that the FPCs estimated with our proposed sparse FPCA method is equivalent to the FPCs using the conventional FPCA method when the sparsity parameter is zero. Simulation studies illustrate that the proposed


Authors who are presenting talks have a * after their name.

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