Two Types of Partial Least Squares Method in Linear Discriminant Analysis
Partial least squares linear discriminant function (PLSD) is a new discriminant function proposed by Kim and Tanaka (1995a). PLSD uses the idea of partial least squares (PLS) method, which was originally developed in multiple regression analysis, in discriminant analysis. In this paper, two types of PLSD are investigated and evaluated in a simulation study. In the first type named PLSDA(all), a common pooled within-group covariance matrix of all groups is used in modeling PLSD to discriminate all pairs of groups. In the second type named PLSDT(two), pooled within-group covariance matrices based on the related two groups are used in modeling PLSD to discriminate pairs of groups. As the results of the simulation study PLSDA has the better performance than PLSDT in all situations when the covariance matrices are equal in all groups, while PLSDT is better than PLSDA in well conditioned situations when the covariance matrices are different among the groups.
KeywordsPartial Little Square Covariance Matrice Partial Little Square Regression Principal Component Regression Covariance Vector
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