论文标题
通过单数值分解方法稀疏主组件回归
Sparse principal component regression via singular value decomposition approach
论文作者
论文摘要
主成分回归（PCR）是一个两阶段的过程：第一阶段执行主成分分析（PCA），第二阶段构建了一个回归模型，其解释变量被第一阶段获得的主要成分代替。由于仅使用解释变量执行PCA，因此主组件没有有关响应变量的信息。为了解决该问题，我们就奇异价值分解方法提出了PCR的一个阶段程序。我们的方法基于两个损失函数，一个回归损失和PCA损失，正则化稀疏。所提出的方法使我们能够获得具有有关解释变量和响应变量的信息的主成分加载。通过使用交替的乘数方法来开发估计算法。我们进行数值研究以显示所提出的方法的有效性。
Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage constructs a regression model whose explanatory variables are replaced by principal components obtained by the first stage. Since PCA is performed by using only explanatory variables, the principal components have no information about the response variable. To address the problem, we propose a one-stage procedure for PCR in terms of singular value decomposition approach. Our approach is based upon two loss functions, a regression loss and a PCA loss, with sparse regularization. The proposed method enables us to obtain principal component loadings that possess information about both explanatory variables and a response variable. An estimation algorithm is developed by using alternating direction method of multipliers. We conduct numerical studies to show the effectiveness of the proposed method.
