title: Using variable combination population analysis for variable selection in multivariate calibration.
abstract: Variable (wavelength or feature) selection techniques have become a critical step for the analysis of datasets with high number of variables and relatively few samples. In this study, a novel variable selection strategy, variable combination population analysis (VCPA), was proposed. This strategy consists of two crucial procedures. First, the exponentially decreasing function (EDF), which is the simple and effective principle of 'survival of the fittest' from Darwin's natural evolution theory, is employed to determine the number of variables to keep and continuously shrink the variable space. Second, in each EDF run, binary matrix sampling (BMS) strategy that gives each variable the same chance to be selected and generates different variable combinations, is used to produce a population of subsets to construct a population of sub-models. Then, model population analysis (MPA) is employed to find the variable subsets with the lower root mean squares error of cross validation (RMSECV). The frequency of each variable appearing in the best 10% sub-models is computed. The higher the frequency is, the more important the variable is. The performance of the proposed procedure was investigated using three real NIR datasets. The results indicate that VCPA is a good variable selection strategy when compared with four high performing variable selection methods: genetic algorithm-partial least squares (GA-PLS), Monte Carlo uninformative variable elimination by PLS (MC-UVE-PLS), competitive adaptive reweighted sampling (CARS) and iteratively retains informative variables (IRIV). The MATLAB source code of VCPA is available for academic research on the website: http://www.mathworks.com/matlabcentral/fileexchange/authors/498750.
authors: College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China.
authors: Yong-Huan
authors: YH
authors: Yun
authors: College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China.
authors: Wei-Ting
authors: WT
authors: Wang
authors: College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China; Department of Chemistry, University of Bergen, Bergen N-5007, Norway.
authors: Bai-Chuan
authors: BC
authors: Deng
authors: Heilongjiang University of Chinese Medicine, Heilongjiang, Ha'erbin 150040, PR China.
authors: Guang-Bi
authors: GB
authors: Lai
authors: College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China.
authors: Xin-bo
authors: XB
authors: Liu
authors: College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China.
authors: Da-Bing
authors: DB
authors: Ren
authors: College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China. Electronic address: yizeng_liang@263.net.
authors: Yi-Zeng
authors: YZ
authors: Liang
authors: Joint Lab for Biological Quality and Safety, College of Bioscience and Biotechnology, Hunan Agriculture University, Changsha 410128, PR China. Electronic address: wei_fan@foxmail.com.
authors: Wei
authors: W
authors: Fan
authors: School of Mathematics and Statistics, Central South University, Changsha 410083, PR China.
authors: Qing-Song
authors: QS
authors: Xu
mesh_terms: D000465:Algorithms; D002138:Calibration; D016018:Least-Squares Analysis; D015233:Models, Statistical; D009010:Monte Carlo Method; D015999:Multivariate Analysis
keywords: Exponentially decreasing function; Model population analysis; Multivariate calibration; Partial least squares; Variable combination; Variable selection