Choice of latent explanatory variables: a multiobjective optimization approach

A multiobjective, optimization-based approach for finding latent explanator y variables for linear models is presented. The best choice of a set of lat ent explanatory variables is made by minimizing a user-specified combinatio n of criteria. In this paper, three criteria are used: (i) the data matrix- related residue, (ii) the observation- or measurement-related residue and ( iii) the condition number of the new data matrix of the latent explanatory variables. Successful application of the proposed technique toward identifi cation of a multivariable pilot-scale plans is presented. The proposed algo rithm is compared with the well-known PLS algorithm, and the result shows t hat the proposed algorithm is better than the PLS algorithm. Copyright (C) 2000 John Wiley & Sons, Ltd.