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Abstract:
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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
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