Elimination of Uninformative Variables for Multivariate Calibration

Abstract

A new method for the elimination of uninformative variables in multivariate data sets is proposed. To achieve this, artificial (noise) variables are added and a closed form of the PLS or PCR model is obtained for the data set containing the experimental and the artificial variables. The experimental variables that do not have more importance than the artificial variables, as judged from a criterion based on the b coefficients, are eliminated. The performance of the method is evaluated on simulated data. Practical aspects are discussed on experimentally obtained near-IR data sets. It is concluded that the elimination of uninformative variables can improve predictive ability.

Application of a hybrid variable selection method for the classification of rapeseed oils based on 1H NMR spectral analysis

“…The UVE method was put forward in reference [16]. In the conventional uninformative variable elimination method, PLS regression is performed on instrumental response data X and property values (y) of calibration, the optimal latent variable number is calculated firstly, and then, a noise matrix N(n 9 p) with very small amplitude (e.g.…”

“…10 -10 ) is generated and append to the X matrix, forming an extended matrix Z(n 9 2p) (with twice as many variables as the X matrix). Finally,the PLS model is computed on the matrix Z, and the regression coefficient matrix b = [b 1 , …, b p ] of model is calculated through a leave-one-out validation [16]; the reliability of each variable is quantitatively measured according to its stability. The stability of variable j can be calculated as:…”

“…Uninformative variable elimination (UVE) is another novelty variable selection method based on the stability analysis of partial least-square (PLS) regression coefficient [16]. UVE can eliminate the variables which have no more informative variables for modeling than noise.…”

“…In UVE process, wavelength variable whose absolute number of stability value is larger than a cutoff threshold is retained. The cutoff threshold is evaluated by the maximum of absolute stability value of an artificial random variable matrix with very small amplitude [15][16][17]. However, there is a stochastic way for evaluating the cutoff threshold, which is not easy to find the optimal cutoff threshold and results in a defect in the UVE algorithm.…”

Bayesian variable selection for Gaussian process regression: Application to chemometric calibration of spectrometers

“…For example, iterative PLS [19] starts with the random selection of a small number of variables, with variables being added or removed based on the cross validation error. An alternative approach is uninformative variable elimination based on an analysis of the PLS regression coefficients [20]. A third method widely reported in the literature is that of genetic algorithms (GAs) that were originally proposed as a family of stochastic optimization approaches that mimic the principles of genetics and natural selection [21].…”