Sparse functional principal component analysis in a new regression framework
Sparse functional principal component analysis in a new regression framework
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DOI：
10.1016/j.csda.2020.107016
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发表时间：
2020-12-01
影响因子：
1.8
通讯作者：
Cao, Jiguo
中科院分区：
文献类型：
--
作者：
Nie, Yunlong;Cao, Jiguo
函数主成分分析被广泛用于探索随机曲线样本的主要变异来源。这些变化的主要来源由功能主成分（FPC）表示。传统的FPCA方法得到的模糊概率密度函数在整个域上都是非零的，在实际应用中很难解释。主要的重点是估计功能主成分（FPCs），这是只有在子区域非零，被称为稀疏FPCs。这些稀疏的FPCs不仅代表了主要的变异源，而且可以用来识别存在这些主要变异的子区域。目前的方法通过在传统的特征分解框架中增加一个惩罚项来获得稀疏的FPCs。然而，这些方法成为一个NP难优化问题。为了克服这个问题，提出了一种新的回归框架来估计FPCs，相应的优化不是NP难的。当稀疏性参数为零时，使用所提出的稀疏FPCA方法估计的FPCs与使用传统FPCA方法估计的FPCs是等价的。仿真结果表明，当模糊概率仅在子区域内为非零时，稀疏FPCA方法比其他方法能更准确地估计模糊概率。通过探索107辆柴油卡车的加速度曲线之间的主要变化，证明了所提出的方法，其中估计的稀疏FPC的非零区域被发现很好地分离。(C)2020爱思唯尔B.V.保留所有权利。
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. The main focus is to estimate functional principal components (FPCs), which are only nonzero in subregions and are referred to as sparse FPCs. These sparse FPCs not only represent the major variation sources 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, a novel regression framework is proposed to estimate FPCs and the corresponding optimization is not NP-hard. The FPCs estimated using the proposed sparse FPCA method is shown to be equivalent to the FPCs using the conventional FPCA method when the sparsity parameter is zero. Simulation studies illustrate that the proposed sparse FPCA method can provide more accurate estimates for FPCs than other available methods when those FPCs are only nonzero in subregions. The proposed method is demonstrated by exploring the major variations among the acceleration rate curves of 107 diesel trucks, where the nonzero regions of the estimated sparse FPCs are found well separated. (C) 2020 Elsevier B.V. All rights reserved.