Partial Least Squares Projection of Latent Structures

Wold, S., Johansson, E. and Cocchi, M. (1993). PLS - Partial Least Squares Projection of Latent Structures. In 3D QSAR in Drug Design. Theory, Methods and Applications. (Kubinyi, H., ed.), ESCOM, Leiden (The Netherlands), pp. 523-550. 

Partial least squares projection of latent structures (PLS)... 

Partial least squares projection of latent structures (PLS) is a method for relating the variahons in one or several response variables (Y variables or dependent variables) to the variations of several predictors (X variables), with explanatory or predictive purposes [12-14]. PLS performs particularly well when the various X variables express common information, i.e., when there is a large amount of correlation or even collinearity among them. PLS is a bilinear method where information in the original X data is projected onto a small number of underlying ( latent ) variables to ensure that the first components are those that are most relevant for predicting the Y variables. Interpretahon of the relationship between X data and Y data is then simplified, as this relahonship is concentrated on the smallest possible number of components [15]. 

Partial least squares projection of latent structures (PLS) is a method for relating the variations in one or several response variables (Y variables or dependent variables) to the variations of several predictors (X variables), with explanatory or predictive purposes. 

Norinder, U., Osterberg, T. Theoretical calculation and prediction of drug transport processes using simple parameters and partial least squares projections to latent structures (PLS) statistics. The use of electrotopological state indices./. Pharm. Sci. 2001, 90, 1075-1085. 

There are apparently many multivariate statistical methods partly overlapping in scope [11]. For most problems occurring in practice, we have found the use of two methods sufficient, as discussed below. The first method is called principal component analysis (PCA) and the second is the partial least-squares projection to latent structures (PLS). A detailed description of the methods is given in Appendix A. In the following, a brief description is presented. 

When compounds are selected according to SMD, this necessitates the adequate description of their structures by means of quantitative variables, "structure descriptors". This description can then be used after the compound selection, synthesis, and biological testing to formulate quantitative models between structural variation and activity variation, so called Quantitative Structure Activity Relationships (QSARs). For extensive reviews, see references 3 and 4. With multiple structure descriptors and multiple biological activity variables (responses), these models are necessarily multivariate (M-QSAR) in their nature, making the Partial Least Squares Projections to Latent Structures (PLS) approach suitable for the data analysis. PLS is a statistical method, which relates a multivariate descriptor data set (X) to a multivariate response data set Y. PLS is well described elsewhere and will not be described any further here [42, 43]. 

PCM modeling aims to find an empirical relation (a PCM equation or model) that describes the interaction activities of the biopolymer-molecule pairs as accurate as possible. To this end, various linear and nonlinear correlation methods can be used. Nonlinear methods have hitherto been used to only a limited extent. The method of prime choice has been partial least-squares projection to latent structures (PLS), which has been found to work very satisfactorily in PCM. PCA is also an important data-preprocessing tool in PCM modeling. Modeling includes statistical model-validation techniques such as cross validation, external prediction, and variable-selection and signal-correction methods to obtain statistically valid models. (For general overviews of modeling methods see [10]). 

Wold S, Sjostrom M, Eriksson L. Partial Least Squares Projections to Latent Structures (PLS). In Schleyer PvR, Allinger NL, Clark T, Gasteiger J, Kollman PA, Schaefer HF III, Schreiner PR, eds. Encyclopedia of Computational Chemistry. Vol. 4. Chichester, UK John Wiley and Sons Ltd., 1998 2006-2021. 

Partial least squares regression (PLS) is more important in chemometrics than in other fields of applied statistics (see Partial Least Squares Projections to Latent Structures (PLS) in Chemistry). PLS can be considered as an alternative method to PCR and LDA. The aim of data interpretation is to build a linear model for the prediction of a response y from the independent variables (regressors, features)x],X2- - Xp as given in equation (27) ... 

Chemometrics Multivariate View on Chemical Problems Chromatography Processing of Information Neural Networks in Chemistry Partial Least Squares Projections to Latent Structures (PLS) in Chemistry. 

Algorithms Infrared Data Correlations with Chemical Structure Infrared Spectra Interpretation by the Characteristic Frequency Approach Machine Learning Techniques in Chemistry Molecular Models Visualization Neural Networks in Chemistry NMR Data Correlation with Chemical Structure Partial Least Squares Projections to Latent Structures (PLS) in Chemistry Shape Analysis Spectroscopic Databases Spectroscopy Computational Methods Structure Determination by Computer-based Spectrum Interpretation Zeolites Applications of Computational Methods. 

Linear or nonlinear multiple regression analysis is used as a statistical tool to derive quantitative models, to check the significance of these models and of each individual term in the regression equation. Other statistical methods, such as discriminant analysis, principal component analysis (PCA), or partial least squares (PLS) analysis (see Partial Least Squares Projections to Latent Structures (PLS) in Chemistry) are alternatives to regression analysis (see Che mo me tries Multivariate View on Chemical Problems)Newer approaches compare the similarity of molecules with respect to different physicochemical or other properties with their biological activities. 

Another problem is to determine the optimal number of descriptors for the objects (patterns), such as for the structure of the molecule. A widespread observation is that one has to keep the number of descriptors as low as 20 % of the number of the objects in the dataset. However, this is correct only in case of ordinary Multilinear Regression Analysis. Some more advanced methods, such as Projection of Latent Structures (or. Partial Least Squares, PLS), use so-called latent variables to achieve both modeling and predictions. 

PLS is a method by which blocks of multivariate data sets (tables) can be quantitatively related to each other. PLS is an acronym Partial Least Squares correlation in latent variables, or Projections to Latent Structures. The PLS method is described in detail in Chapter 17. 

Data handling, statistical modeling (projection of latent structures, principal components analysis), and plotting for QSAR. SIMCA-IPI for integrated process intelligence. VAX and PCs. MODDE for experimental design with multiple regression analysis and partial least squares. PCs (Windows). 

PLS Projection to latent structures by means of a partial least squares analysis... 

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