Variable selection in multivariate methods using global score estimation

Abstract

Principal components, Least squares, Orthogonalization, Cost-saving selection,

Nonlinear Principal Component Analysis and Its Applications

“…Robert and Escoufier (1976) and Bonifas et al (1984) used the RV -coefficient, and Krzanowski (1987a, b) used Procrustes analysis to evaluate the similarity between the configuration of PCs computed based on selected variables and that based on all variables. Fueda et al (2009) estimated PCs based on a subset of variables and selected a reasonable subset of variables using the estimation technique. Since M.PCA includes variable selection procedures in the analysis, its criteria can be used directly to detect a reasonable subset of variables (e.g., Mori et al 2006).…”

Variable Neighborhood Search Heuristics for Selecting a Subset of Variables in Principal Component Analysis

“…We have focused on the problem of variable selection within the context of PCA, and offer two versions of a new variable neighborhood search heuristic as fast and effective methods. Although we experimented with VNS using the RV coefficient because of its well-established importance in previous studies (Cadima et al, 2004;Dray, 2008;Duarte Silva, 2002;Fueda et al, 2009;Tanaka & Mori, 1997), the heuristics can be adapted easily for other prominent criteria in the PCA literature.…”

“…In most cases, the inclusion of all variables in the statistical analysis is, at best, unnecessary and, at worst, a serious impediment to the correct interpretation of the data. Not surprisingly, the general problem of variable selection in multivariate analysis has been acknowledged for more than 40 years (Beale, Kendall, & Mann, 1967) and continues to be of tremendous importance (Duarte Silva, 2001;Fueda, Iizuka, & Mori, 2009). Especially noteworthy is the development of variable selection methods for the following multivariate statistical models: (1) multiple linear regression (Brusco, Steinley, & Cradit, 2009;Furnival & Wilson, 1974;Miller, 2002), (2) principal component analysis (Jolliffe, 1972Krzanowski, 1987;Tanaka & Mori, 1997), (3) factor analysis (Hogarty, Kromrey, Ferron, & Hines, 2004;Kano & Harada, 2000), (4) discriminant analysis (McCabe, 1975;McKay & Campbell, 1982a, 1982b, and (5) cluster analysis (Brusco & Cradit, 2001;Steinley & Brusco, 2008).…”