Partial least square regression modeling

FIGURE 5.6 Partial least-squares regression model showing the correlation between alanine (nmol/g cheese) predicted by GC-FID and FTIR. The model shows a high degree of linear correlation (r-value = 0.99) and a low estimated standard error of prediction (12.70 nmol/g cheese). 

Aznar, M., Lopez, R., Cacho, J., Ferreira, V. (2003). Prediction of aged red wine aroma properties from aroma chemical composition. Partial least squares regression models. J. Agric. Food Chem., 51, 2700-2707. 

Figure 23 True vs. predicted tryptophan concentration using a one-factor partial least squares regression model...

The final partial least squares regression model after R components in the nonorthogonal t-vector version reads (by defining again T = [tj,..., tR and W = [w, ..., w ])... 

Depending on what kind of information is needed, different possibilities exist for using a multilinear partial least squares regression model on new data. If only the prediction of y is wanted, it is possible to obtain a set of regression coefficients that relates X directly to y. This has been shown in detail by Smilde and de Jong for the multilinear PLS1 model [de Jong 1998, Smilde 1997] as follows. The first score vector ti is... 

Quality and Geographic Origin Chemical Measurements by Partial Least-Squares Regression Modeling. 

Instead promoter strength was predicted quantitatively based on a PLS-R(Partial Least Squares Regression) model named PSP (Promoter Strength Predictive) using nucleotide sequences of 49 promoters from an E. coli SPL. 42 of the promoters were used as training set in a leave-one-out cross-validated model determining the... 

Zhu,W., De Leer, E.W. B., Keimedy, M., and Kelderman, P. (1997). Study of a partial least-squares regression model for rare earth element determination by inductively coupled plasma mass spectrometry.J./l [Pg.287]

Marhaba, T.F., Bengraine, K., Pu, Y, and Arago, J. (2003). Spectral fluorescence signatures and partial least squares regression Model to predict dissolved organic carbon in water. J. Hazard. Mater., 97, 83-97. 

Partial Least Squares Regression, also called Projection to Latent Structures, can be applied to estabfish a predictive model, even if the features are highly correlated. 

On the other hand, techniques like Principle Component Analysis (PCA) or Partial Least Squares Regression (PLS) (see Section 9.4.6) are used for transforming the descriptor set into smaller sets with higher information density. The disadvantage of such methods is that the transformed descriptors may not be directly related to single physical effects or structural features, and the derived models are thus less interpretable. 

Partial least-squares path modeling with latent variables (PLS), a newer, general method of handling regression problems, is finding wide apphcation in chemometrics. This method allows the relations between many blocks of data ie, data matrices, to be characterized (32—36). Linear and multiple regression techniques can be considered special cases of the PLS method. 

Bennett KP, Embrechts MJ. An optimization perspective on kernel partial least squares regression. In Suykens JAK, Horvath G, Basu S, Micchelli J, Vandewalle J, editors. Advances in learning theory methods, models and applications. Amsterdam lOS Press, 2003. p. 227-50. 

Partial least squares regression (PLS). Partial least squares regression applies to the simultaneous analysis of two sets of variables on the same objects. It allows for the modeling of inter- and intra-block relationships from an X-block and Y-block of variables in terms of a lower-dimensional table of latent variables [4]. The main purpose of regression is to build a predictive model enabling the prediction of wanted characteristics (y) from measured spectra (X). In matrix notation we have the linear model with regression coefficients b ... 

We will see that CLS and ILS calibration modelling have limited applicability, especially when dealing with complex situations, such as highly correlated predictors (spectra), presence of chemical or physical interferents (uncontrolled and undesired covariates that affect the measurements), less samples than variables, etc. More recently, methods such as principal components regression (PCR, Section 17.8) and partial least squares regression (PLS, Section 35.7) have been... 

Dayal, B. S., MacGregor, J. F., Taylor, P. A., Kildaw, R., and Marcikio, S., Application of Feedforward Neural Networks and Partial Least Squares Regression for Modelling Kappa Number in a Continuous Kamyr Digester, Pulp Paper Can., 95(1) 26 (1994)... 

Multivariate calibration has the aim to develop mathematical models (latent variables) for an optimal prediction of a property y from the variables xi,..., jcm. Most used method in chemometrics is partial least squares regression, PLS (Section 4.7). An important application is for instance the development of quantitative structure—property/activity relationships (QSPR/QSAR). 

A relatively recent development in QSAR research is molecular reference (MOLREF). This molecular modelling technique is a method that compares the structures of any number of test molecules with a reference molecule, in a quantitative structure-activity relationship study (27). Partial least squares regression analysis was used in molecular reference to analyse the relation between X- and Y-matrices. In this paper, forty-two disubstituted benzene compounds were tested for toxicity to Daphnia... 

Partial least squares regression (PLS) [WOLD et al., 1984] is a generalized method of least squares regression. This method uses latent variables i, 2,. .., i.e. matrix U, for separately modeling the objects in the matrix of dependent data Y, and t, t2,. .., i.e. matrix T, for separately modeling the objects in the matrix of independent data X. These latent variables U and T are the basis of the regression model. The starting points are the centered matrices X and Y ... 

Partial Least Squares Regression is one of the many available regression techniques. Regression techniques are used to model the relation between 2 blocks of variables, called independent or x variables and dependent or y variables (figure 12.15 a). The general regression equation is (figure 12.15 b) ... 

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