Multivariate statistical methods are commonly used in the analysis of quantitative structure-activity/property relationships (QSAR and QSPR, respectively). The partial least squares (PLS) method is of particular interest because it can analyze data containing numerous X variables with strongly collinear and noisy characteristics and can simultaneously model several response variables Y. Furthermore, it can provide us with several prediction regions and diagnostic plots as statistical measures. PLS has evolved or changed for coping with the severe demands associated with the complex data structures of X and Y variables. In this review article, we selected five advanced PLS techniques and outlined their algorithms with representative examples. In particular, we made efforts to describe how to disclose the inner relations embedded in data and how to use this information for molecular design.
Keywords: QSAR, QSPR, PLS, GAPLS, OPLS, QPLS, KPLS, multi-way PLS, multi-block PLS, HPLS, SOMPLS
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