Partial least-squares regression method

Univariate and multivariate spectroscopy was applied to the analysis of spironolactone in presence of chlorthalidone [17]. Satisfactory results were obtained by partial least squares regression, with the calibration curve being linear over the range 2.92 -14.6 pg/mL. A kinetic-spectrophotometric method was described for the determination of spironolactone and canrenone in urine that also used a partial least-squares regression method [18]. After the compounds were extracted from urine, the spectra were recorded at 400 - 520 nm for 10 minutes at 30 second intervals. The relative error was less than 5%. 

After an alignment of a set of molecules known to bind to the same receptor a comparative molecular field analysis CoMFA) makes it possible to determine and visuahze molecular interaction regions involved in hgand-receptor binding [51]. Further on, statistical methods such as partial least squares regression PLS) are applied to search for a correlation between CoMFA descriptors and biological activity. The CoMFA descriptors have been one of the most widely used set of descriptors. However, their apex has been reached. 

To gain insight into chemometric methods such as correlation analysis, Multiple Linear Regression Analysis, Principal Component Analysis, Principal Component Regression, and Partial Least Squares regression/Projection to Latent Structures... 

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. 

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. 

Section 35.4), reduced rank regression (Section 35.5), principal components regression (Section 35.6), partial least squares regression (Section 35.7) and continuum regression methods (Section 35.8). 

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... 

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). 

Regression can be performed directly with the values of the variables (ordinary least-squares regression, OLS) but in the most powerful methods, such as principal component regression (PCR) and partial least-squares regression (PLS), it is done via a small set of intermediate linear latent variables (the components). This approach has important advantages ... 

Broadhurst, D., Goodacre, R., Jones, A., Rowland, J. J., Kell, D. B. Anal. Chim. Acta 348, 1997, 71-86. Genetic algorithms as a method for variable selection in multiple Unear regression and partial least squares regression, with applications to pyrolysis mass spectrometry. 

Hubert, M., Vanden Branden, K. J. Chemom. 17, 2003, 537-549. Robust methods for partial least squares regression. 

Martens, H., Jensen, S. A. Partial least squares regression A new two-stage NIR calibration method in Proceedings of the 7-th World Cereal and Bread Congress, Prague, 1982, Elsevier, Amsterdam, in press... 

The diffusion of correlation methods and related software packages, such as partial-least-squares regression (PLS), canonical correlation on principal components, target factor analysis and non-linear PLS, will open up new horizons to food research. 

Human perception of flavor occurs from the combined sensory responses elicited by the proteins, lipids, carbohydrates, and Maillard reaction products in the food. Proteins Chapters 6, 10, 11, 12) and their constituents and sugars Chapter 12) are the primary effects of taste, whereas the lipids Chapters 5, 9) and Maillard products Chapter 4) effect primarily the sense of smell (olfaction). Therefore, when studying a particular food or when designing a new food, it is important to understand the structure-activity relationship of all the variables in the food. To this end, several powerful multivariate statistical techniques have been developed such as factor analysis Chapter 6) and partial least squares regression analysis Chapter 7), to relate a set of independent or "causative" variables to a set of dependent or "effect" variables. Statistical results obtained via these methods are valuable, since they will permit the food... 

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... 

It may be possible to use an array of electrodes containing various enzymes in combination with multivariate statistical analyses (principal component analysis, discriminant analysis, partial least-squares regression) to determine which pesticide(s) the SPCE has been exposed to and possibly even how much, provided sufficient training sets of standards have been measured. The construction methods for such arrays would be the same as described in this protocol, with variations in the amounts of enzyme depending on the inhibition constants of other cholinesterases for the various pesticides of interest. 

The calibration methods most frequently used to relate the property to be measured to the analytical signals acquired in NIR spectroscopy are MLR,59 60 principal component regression (PCR)61 and partial least-squares regression (PLSR).61 Most of the earliest quantitative applications of NIR spectroscopy were based on MLR because spectra were then recorded on filter instruments, which afforded measurements at a relatively small number of discrete wavelengths only. However, applications involving PCR and PLSR... 

This method makes use of a test battery to derive a toxicity index that can be employed to classify effluents as a function of their overall toxicity. A formula is given as an example and a procedure to calculate the index using expert judgements and a PLS (Partial Least Square) regression procedure is described using data on 30 effluents. 

Partial least square regression a regression method that maximizes the co-inertia of a table of independent and a table of dependent variables. Volume 2(2). 

Dependencies are mainly investigated by multiple or multivariate regression (one dependent and several independent variables), by multidimensional multivariate regression or partial least squares regression (several dependent and several independent variables), and by the method of simultaneous equations (explicitly allowing for corre-... 

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 ... 

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