PLS Projections to Latent Structures

PLS is a modelling and computational method for establishing quantitative relations between blocks of variables. Such blocks may, for instance, comprise a block of descriptor variables of a set of test systems (X block) and a block of measured responses obtained with these sytems (Y block). A quantitative relation between these blocks will make it possible to enter data, x, for a new systems and make predictions of the expected responses, y, for these systems. 

A PLS model can also be established in the reversed sense, i.e. for finding conditions x which yield a desired response profile y. 

The PLS method was developed by H. Wold [71] and has been further developed and extended to chemical systems by S. Wold [72], A tutorial paper on the method is given in [73]. An important area of application of PLS is in the field of quantitative structure-activity relations [64a, 74]. The applications of PLS for multivariate calibration in analytical chemistry has been thoroughly treated by Martens and Naes [75]. As we shall see, PLS is also a very useful in organic synthesis. 

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PLS has been introduced in the chemometrics literature as an algorithm with the claim that it finds simultaneously important and related components of X and of Y. Hence the alternative explanation of the acronym PLS Projection to Latent Structure. The PLS factors can loosely be seen as modified principal components. The deviation from the PCA factors is needed to improve the correlation at the cost of some decrease in the variance of the factors. The PLS algorithm effectively mixes two PCA computations, one for X and one for Y, using the NIPALS algorithm. It is assumed that X and Y have been column-centred as usual. The basic NIPALS algorithm can best be demonstrated as an easy way to calculate the singular vectors of a matrix, viz. via the simple iterative sequence (see Section 31.4.1) ... 

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

Partial least squares (PLS) projections to latent structures [40] is a multivariate data analysis tool that has gained much attention during past decade, especially after introduction of the 3D-QSAR method CoMFA [41]. PLS is a projection technique that uses latent variables (linear combinations of the original variables) to construct multidimensional projections while focusing on explaining as much as possible of the information in the dependent variable (in this case intestinal absorption) and not among the descriptors used to describe the compounds under investigation (the independent variables). PLS differs from MLR in a number of ways (apart from point 1 in Section 16.5.1) ... 

PLS projection to latent structures or partial least squares... 

E Johansson and M Cocchi 1993. PLS - Partial Least-squares Projections to Latent Structures. In binyi H (Editor) 3D QSAR in Drug Design. Leiden, ESCOM, pp. 523-550. 

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. 

PLS Partial least squares projection to latent structures... 

Wold, S., Johansson, E., Cocchi, M., PLS - Partial least-squares projections to latent structures, in 3D QSAR in Drug Design. Kubinyi, H. (ed.). ESCOM, Leiden, 1993, pp. 523-... 

Principal components analysis (PCA) and project to latent structure (PLS) were suggested to absorb information from continued-process data (Kresta et al., 1991 MacGregor and Kourti, 1995 Kourti and MacGregor, 1994). The key point of these approaches is to utilize PCA or PLS to compress the data and extract the information by projecting them into a low-dimension subspace that summarizes all the important information. Then, further monitoring work can be conducted in the reduced subspace. Two comprehensive reviews of these methods have been published by Kourti and Macgregor (1995) and Martin et al. (1996). 

The inverse calibration method of Projection to Latent Structures (PLS, also known as partial least squares ), is very similar to PCR, and has been a highly utilized tool in PAT [1]. Like the PCR method, PLS uses the... 

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. 

Strom et al., 2001 (73) Principal component analysis (PCA) Projections to latent structures (PLS) 12 Lactoferricin from bovine (LFB) Lactoferricin from murine (LFM) 18 derivatives of LFM that varied at up to 4 positions. LOO 20 Plot of predicted to observed MICs shows good correlation nd... 

Lejon et al., 2004 (72) Projections to latent structures (PLS) 15 LFB derivatives Single training set 11 Prediction of 2 peptides E. coli and S. aureus outside training set was poor 0.957 (E. coli) 0.924 (S. aureus)... 

Additionally, the increased use of model predictive control techniques allows for more degrees of freedom (associated with having more manipulated variables) which in turn tends to improve controllability and therefore decrease process variability. Principal component analysis (PCA) and projection to latent structures (PLS) are tools that can be used to monitor process performance and behavior. 

Several steps are involved in rapid analysis method development. These include gathering appropriate calibration samples, chemical characterization of the calibration samples, developing spectroscopic methods for the rapid technique, projection-to-latent-structures (PLS) regression, validation of the PLS algorithm, and the development of QA/QC procedures.128... 

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]. 

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