Title: Sparse principal component regression via singular value decomposition
Authors: Shuichi Kawano - The University of Electro-Communications (Japan) [presenting]
Abstract: Principal component regression (PCR) is a two-stage procedure. The first stage is principal component analysis (PCA). The second stage is regression in which the obtained principal components are regarded as new explanatory variables. Since PCA is based on the explanatory variables, the principal components have no information on the response variable. To address this problem, we propose a one-stage procedure for PCR based on singular value decomposition. The loss function consists of a combination of the regression loss and PCA loss with sparse regularization. The proposed method enables us to obtain principal component loadings that are related to both explanatory variables and a response variable. We conduct numerical studies to examine the effectiveness of the proposed method.