A brief note on a new faster covariate's selection (fCovSel) algorithm

Covariate's selection (CovSel) is a variable selection technique in the domain of chemometrics and is commonly used for extracting variables carrying high covariance with response variables. CovSel is a special case of partial least square analysis, where at each weight estimation step, the weight vector is of the binary form to select the variables. In the earlier algorithm of the CovSel which is identical to the nonlinear iterative partial least square (NIPALS), there is a key step of predictor matrix deflation which makes it a time-consuming approach leading to longer time consumption during tasks such as cross-validation or in multiblock multiway CovSel scenarios where a wide number of variables combinations are usually explored for model optimization. We present a new CovSel algorithm called faster CovSel (fCovSel) which drops the need for predictor matrix deflation. By dropping the predictor matrix deflation step, the method naturally becomes faster than the CovSel based on NIPALS. Mathematical and analytical comparisons of the CovSel and the fCovSel in terms of achieving the same solution and time requirements are presented.