Principal Components Regression by Using Generalized Principal Components Analysis

Autor:	Isamu Nagai, Tomohiro Minamidani, Masakazu Fujiwara, Hirofumi Wakaki
Rok vydání:	2013
Předmět:	Dimension (vector space) Principal component analysis Linear regression Statistics Design matrix Principal component regression Feature selection Cross-validation Mathematics
Zdroj:	JOURNAL OF THE JAPAN STATISTICAL SOCIETY. 43:57-78
ISSN:	1348-6365 1882-2754
Popis:	Principal components analysis (PCA) is one method for reducing the dimension of the explanatory variables, although the principal components are derived by using all the explanatory variables. Several authors have proposed a modified PCA (MPCA), which is based on using only selected explanatory variables in order to obtain the principal components (see e.g., Jolliffie, 1972, 1986; Robert and Escoufier, 1976; Tanaka and Mori, 1997). However, MPCA uses all of the selected explanatory variables to obtain the principal components. There may, therefore, be extra variables for some of the principal components. Hence, in the present paper, we propose a generalized PCA (GPCA) by extending the partitioning of the explanatory variables. In this paper, we estimate the unknown vector in the linear regression model based on the result of a GPCA. We also propose some improvements in the method to reduce the computational cost.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::f93b2d742d1e0eeffe79ce3591efadfa https://doi.org/10.14490/jjss.43.57 Zobrazit plný text záznamu Plný text ve formátu PDF