Relationships between PCA and PLS-regressio

Abstract

22This work aims at comparing several features of Principal Component Analysis (PCA) and Partial Least Square s 23Regression (PLSR), as techniques typically utilized for modeling, output prediction, and monitoring of multivar24iate processes. First, geometric properties of the decomposition induced by PLSR are described in re lation to the 25PCA of the separated input and output data ( X-PCA and Y-PCA, respectively). Then, analogies between the 26modelsderivedwithPLSRand YX-PCA(i.e.,PCAofthejointinput–outputvariables)arepresented;andregarding 27toprocessmonitoringapplications,thespeci ficPLSRandYX-PCAfaultdetectionindicesarecompared.Numerical 28examples are used to illustrate the relationships between latent models, output predictive models, and fault 29detection indices. The three alternative approaches (PLSR, YX-PCA and Y-PCA plus X-PCA) are compared with 30regard to their use for statistical modeling. In particular, a case study is simulated and the results are used for 31enhancing the comprehension of the PLSR properties and for evaluating the discriminato ry capacity of the 32fault detection indices based on the PLSR and YX-PCA modeling alternatives. Some recommendations are 33given in order to choose the more appropriate approach for a speci fic application: 1) PLSR and YX-PCA have 34similar capacityfor faultdetection,but PLSRisrecommended for processmonitoring because itpresents a better 35diagnosingcapability;2)PLSRismorereliableforoutputpredictionpurposes(e.g.,forsoftsens ordevelopment); 36and 3) YX-PCA is recommended for the analysis of latent patterns imbedded in datasets.