Partial multivariate data analysis

Sections 9A.2-9A.6 introduce different multivariate data analysis methods, including Multiple Linear Regression (MLR), Principal Component Analysis (PCA), Principal Component Regression (PCR) and Partial Least Squares regression (PLS). 

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) ... 

The four-volume Handbook of Chemoinformatics—From Data to Knowledge (Gasteiger 2003) contains a number of introductions and reviews that are relevant to chemometrics Partial Least Squares (PLS) in Cheminformatics (Eriksson et al. 2003), Inductive Learning Methods (Rose 1998), Evolutionary Algorithms and their Applications (von Homeyer 2003), Multivariate Data Analysis in Chemistry (Varmuza 2003), and Neural Networks (Zupan 2003). 

Giraud, E., Luttmann, C., Lavelle, F., Riou, J. F., Mailliet, P., and Laoui, A. (2000) Multivariate data analysis using D-optimal designs, partial least squares and... 

SIMCA EMX, P.O.Box 336, S-95125 Lulea, Sweden 2200. Multivariate data analysis by SIMCA (principal component models of classes) and PLS (partial least square) (ref. 20). 

PCA is a statistical technique that has been used ubiquitously in multivariate data analysis." Given a set of input vectors described by partially cross-correlated variables, the PCA will transform them into a set that is described by a smaller number of orthogonal variables, the principle components, without a significant loss in the variance of the data. The principle components correspond to the eigenvectors of the covariance matrix, m, a symmetric matrix that contains the variances of the variables in its diagonal elements and the covariances in its off-diagonal elements (15) ... 

To establish a correlation between the concentrations of different kinds of nucleosides in a complex metabolic system and normal or abnormal states of human bodies, computer-aided pattern recognition methods are required (15, 16). Different kinds of pattern recognition methods based on multivariate data analysis such as principal component analysis (PCA) (8), partial least squares (16), stepwise discriminant analysis, and canonical discriminant analysis (10, 11) have been reported. Linear discriminant analysis (17, 18) and cluster analysis were also investigated (19,20). Artificial neural network (ANN) is a branch of chemometrics that resolves regression or classification problems. The applications of ANN in separation science and chemistry have been reported widely (21-23). For pattern recognition analysis in clinical study, ANN was also proven to be a promising method (8). 

A different approach to mathematical analysis of the solid-state C NMR spectra of celluloses was introduced by the group at the Swedish Forest Products Laboratory (STFI). They took advantage of statistical multivariate data analysis techniques that had been adapted for use with spectroscopic methods. Principal component analyses (PCA) were used to derive a suitable set of subspectra from the CP/MAS spectra of a set of well-characterized cellulosic samples. The relative amounts of the I and I/3 forms and the crystallinity index for these well-characterized samples were defined in terms of the integrals of specific features in the spectra. These were then used to derive the subspectra of the principal components, which in turn were used as the basis for a partial least squares analysis of the experimental spectra. Once the subspectra of the principal components are validated by relating their features to the known measures of variability, they become the basis for analysis of the spectra of other cellulosic samples that were not included in the initial analysis. Here again the interested reader can refer to the original publications or the overview presented earlier. ... 

To take account of interactions between individual components (association, nonlinearities), calibration using multivariate data analysis is often also carried out with mixtures rather than pure substances. Despite this fact, limitations to this method of assessment are encountered quickly. Therefore, the so-called inverse method using the g-matrix is employed, and either principal component regression (PCR) or the partial least squares (PLS) method is used [6, [114], [116]. In both methods, calibration is carried out not with pure substances, but with various mixtures, which must cover the expected concentration range of all components. Within limits, this can allow for non-linearities ... 

Principal component analysis (PCA) is a statistical technique with a long history in multivariate data analysis (see Chemometrics Multivariate View on Chemical Problems) PCA reduces a set of partially cross-correlated data into a smaller set of orthogonal variables (principal components) without a significant loss in the contribution to variation. In effect, the method detects and combines descriptors which behave in a similar way into a new set of variables that are non-correlated, i.e., they are orthogonal. 

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... 

The arrival of computers in every chemical laboratory has made possible the use of multivariate statistical analysis and mathematics in the analysis of measured chemical data. Sometimes, the methods were inadequate or only partially suitable for a particular chemical problem, so handling methods were modified or new ones developed to fit the chemical problem. On the basis of these elements, common to every field of chemistry, in 1974 a new chemical science was identified chemometrics, the science of chemical information. In the same year, Bruce Kowalski and Svante Wold founded the Chemometrics Society, which since then has been spreading information on multivariates in chemistry all over the world. 

Partial Least Squares Regression is a valuable tool in FTIR-spectroscopy, not only for (routine) quantitative analysis of mixtures, but also as a research application. Due to its ability to expose correlations in complex, multivariate data sets, PLS is gaining importance rapidly in spectroscopy-assisted-research. 

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]. 

Chemometrics is the discipline concerned with the application of statistical and mathematical methods to chemical data [2.18], Multiple linear regression, partial least squares regression and the analysis of the main components are the methods that can be used to design or select optimal measurement procedures and experiments, or to provide maximum relevant chemical information from chemical data analysis. Common areas addressed by chemometrics include multivariate calibration, visualisation of data and pattern recognition. Biometrics is concerned with the application of statistical and mathematical methods to biological or biochemical data. 

The methods of data analysis depend on the nature of the final output. If the problem is one of classification, a number of multivariate classifiers are available such as those based on principal components analysis (SIMCA), cluster analysis and discriminant analysis, or non-linear artificial neural networks. If the required output is a continuous variable, such as a concentration, then partial least squares regression or principal component regression are often used [20]. 

An in-depth review of statistical methods for metabonomic data analysis is beyond the scope of this chapter. Briefly, there are a few main approaches to data analysis. Examples of multivariate data analyses include the so-called unsupervised analyses such as PCA, independent component analysis (ICA), and hierarchical clustering analysis (HCA), while partial least square differential analysis (PLS-DA) is... 

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