title: A new strategy to prevent over-fitting in partial least squares models based on model population analysis.
abstract: Partial least squares (PLS) is one of the most widely used methods for chemical modeling. However, like many other parameter tunable methods, it has strong tendency of over-fitting. Thus, a crucial step in PLS model building is to select the optimal number of latent variables (nLVs). Cross-validation (CV) is the most popular method for PLS model selection because it selects a model from the perspective of prediction ability. However, a clear minimum of prediction errors may not be obtained in CV which makes the model selection difficult. To solve the problem, we proposed a new strategy for PLS model selection which combines the cross-validated coefficient of determination (Qcv(2)) and model stability (S). S is defined as the stability of PLS regression vectors which is obtained using model population analysis (MPA). The results show that, when a clear maximum of Qcv(2) is not obtained, S can provide additional information of over-fitting and it helps in finding the optimal nLVs. Compared with other regression vector based indictors such as the Euclidean 2-norm (B2), the Durbin Watson statistic (DW) and the jaggedness (J), S is more sensitive to over-fitting. The model selected by our method has both good prediction ability and stability.
authors.affiliation: Department of Chemistry, University of Bergen, Bergen N-5007, Norway; School of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China.
authors.forename: Bai-Chuan
authors.initials: BC
authors.lastname: Deng
authors.affiliation: School of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China.
authors.forename: Yong-Huan
authors.initials: YH
authors.lastname: Yun
authors.affiliation: School of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China. Electronic address: yizeng_liang@263.net.
authors.forename: Yi-Zeng
authors.initials: YZ
authors.lastname: Liang
authors.affiliation: School of Pharmaceutical Sciences, Central South University, Changsha 410083, PR China. Electronic address: oriental-cds@163.com.
authors.forename: Dong-Sheng
authors.initials: DS
authors.lastname: Cao
authors.affiliation: School of Mathematics and Statistics, Central South University, Changsha 410083, PR China.
authors.forename: Qing-Song
authors.initials: QS
authors.lastname: Xu
authors.affiliation: Yunnan Food Safety Research Institute, Kunming University of Science and Technology, Kunming 650500, PR China.
authors.forename: Lun-Zhao
authors.initials: LZ
authors.lastname: Yi
authors.affiliation: School of Chemistry and Chemical Engineering, Central South University, Changsha 410083, PR China.
authors.forename: Xin
authors.initials: X
authors.lastname: Huang
mesh_terms: D000465:Algorithms; D016018:Least-Squares Analysis; D008956:Models, Chemical; D012984:Software; D013025:Glycine max / Q000737:chemistry / Q000378:metabolism; D013056:Spectrophotometry, Ultraviolet
keywords: Cross-validation; Model population analysis; Model selection; Model stability; Over-fitting; Partial least squares