Partial least squares extraction, component

This chapter ends with a short description of the important methods, Principal Component Regression (PCR) and Partial Least-Squares (PLS). Attention is drawn to the similarity of the two methods. Both methods aim at predicting properties of samples based on spectroscopic information. The required information is extracted from a calibration set of samples with known spectrum and property. 

Chemometric evaluation methods can be applied to the signal from a single sensor by feeding the whole data set into an evaluation program [133,135]. Both principle component analysis (PCA) and partial least square (PLS) models were used to evaluate the data. These are chemometric methods that may be used for extracting information from a multivariate data set (e.g., from sensor arrays) [135]. The PCA analysis shows that the MISiC-FET sensor differentiates very well between different lambda values in both lean gas mixtures (excess air) and rich gas mixtures (excess fuel). The MISiC-FET sensor is seen to behave as a linear lambda sensor [133]. It... 

There is an approach in QSRR in which principal components extracted from analysis of large tables of structural descriptors of analytes are regressed against the retention data in a multiple regression, i.e., principal component regression (PCR). Also, the partial least square (PLS) approach with cross-validation 29 finds application in QSRR. Recommendations for reporting the results of PC A have been published 130). 

Linear discriminant analysis (LDA) is aimed at finding a linear combination of descriptors that best separate two or more classes of objects [100]. The resulting transformation (combination) may be used as a classifier to separate the classes. LDA is closely related to principal component analysis and partial least square discriminant analysis (PLS-DA) in that all three methods are aimed at identifying linear combinations of variables that best explain the data under investigation. However, LDA and PLS-DA, on one hand, explicitly attempt to model the difference between the classes of data whereas PCA, on the other hand, tries to extract common information for the problem at hand. The difference between LDA and PLS-DA is that LDA is a linear regression-like method whereas PLS-DA is a projection technique... 

Near-infrared (NIR) spectroscopy is becoming an important technique for pharmaceutical analysis. This spectroscopy is simple and easy because no sample preparation is required and samples are not destroyed. In the pharmaceutical industry, NIR spectroscopy has been used to determine several pharmaceutical properties, and a growing literature exists in this area. A variety of chemoinfometric and statistical techniques have been used to extract pharmaceutical information from raw spectroscopic data. Calibration models generated by multiple linear regression (MLR) analysis, principal component analysis, and partial least squares regression analysis have been used to evaluate various parameters. 

For overlapping peaks the data matrix contains linear combinations of the pure spectra of the overlapping components in its rows, and combinations of the pure elution profiles in its columns. Multivariate analysis of the data matrix may allow extraction of useful information from either the rows or columns of the matrix, or an edited form of the data matrix [107,116-118]. Factor analysis approaches or partial least-squares analysis can provide information on whether a given spectrum (known compound) or several known compounds are present in a peak. Principal component analysis and factor analysis can be used to estimate the maximum number of probable (unknown) components in a peak cluster. Deconvolution or iterative target factor analysis can then be used to estimate the relative concentration of each component with known spectra in a peak cluster. 

Principal component analysis and partial least squares analysis are chemometric tools for extracting and rationalizing the information from any multivariate description of a biological system. Complexity reduction and data simplification are two of the most important features of such tools. PCA and PLS condense the overall information into two smaller matrices, namely the score plot (which shows the pattern of compounds) and the loading plot (which shows the pattern of descriptors). Because the chemical interpretation of score and loading plots is simple and straightforward, PCA and PLS are usually preferred to other nonlinear methods, especially when the noise is relatively high. ... 

PCA is not only used as a method on its own but also as part of other mathematical techniques such as SIMCA classification (see section on parametric classification methods), principal component regression analysis (PCRA) and partial least-squares modelling with latent variables (PLS). Instead of original descriptor variables (x-variables), PCs extracted from a matrix of x-variables (descriptor matrix X) are used in PCRA and PLS as independent variables in a regression model. These PCs are called latent variables in this context. 

Water is the most important chemical constituent of fruits and vegetables and water highly absorbs NIR radiation, so the NIR spectrum of such materials is dominated by water. Further, the NIR spectrum is essentially composed of a large set of overtones and combination bands. This, in combination with the complex chemical composition of a typical fruit or vegetable causes the NIR spectrum to be highly convoluted. Multivariate statistical techniques are required to extract the information about quality attributes which is buried in the NIR spectrum Developments in multivariate statistical techniques such as partial least squares (PLS) regression and principal component analysis (PCA) are then applied to extract the required information from such convoluted spectra (Cozzolino et al., 2006b McClure, 2003 Naes et al., 2004 Nicolai et al., 2007 ). 

Partial least squares (PLS) analysis allows the simultaneous investigation of the relationships between a multitude of activity data (F matrix) and a set of chemical descriptors (X matrix) through latent variables (Wold et aL, 1984 Geladi and Kowalski, 1986 Hellberg, 1986 Geladi and Tosato, 1990). The latent variables correspond to the component scores in PCA and the respective coefficients to the PCA loading vectors. The PLS model can also be applied when the number of (collinear) descriptors exceeds the number of compounds in the data set. The main difference between PCA and PLS concerns the criteria for extracting the principal components and the latent variables, respectively PCA is based on the maximum variance criterion, whereas PLS uses covariance with another set of variables (X matrix). 

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