Discriminant analysis factor

The multivariate methods of data analysis, like discriminant analysis, factor analysis and principal component analysis, are often employed in chemometrics if the multiple regression method fails. Most popular in QSRR studies is the technique of principal component analysis (PCA). By PCA one reduces the number of variables in a data set by finding linear combinations of these variables which explain most of the variability [28]. Normally, 2-3 calculated abstract variables (principal components) condense most (but not all) of the information dispersed within the original multivariable data set. 

We will explore the two major families of chemometric quantitative calibration techniques that are most commonly employed the Multiple Linear Regression (MLR) techniques, and the Factor-Based Techniques. Within each family, we will review the various methods commonly employed, learn how to develop and test calibrations, and how to use the calibrations to estimate, or predict, the properties of unknown samples. We will consider the advantages and limitations of each method as well as some of the tricks and pitfalls associated with their use. While our emphasis will be on quantitative analysis, we will also touch on how these techniques are used for qualitative analysis, classification, and discriminative analysis. 

Solberg and co-workers have applied discriminate analysis of clinical laboratory tests combined with careful clinical and anatomic diagnoses of liver disease in order to determine which combinations of the many dozen liver diagnostic tests available are the bes t ( ). These authors found that the measurement of GPT, GMT, GOT, ALP and ceruloplasmin were the most useful enzymatic tests, when combined with other non-enzymatic tests such as the measurement of bilirubin, cholesterol, hepatitis-B associated Australian antigen, etc. Another group of highly useful enzymes, not discussed in this review, are those clotting factors and the enzyme cholinesterase which are synthesized by the liver cells. 

Multivariate chemometric techniques have subsequently broadened the arsenal of tools that can be applied in QSAR. These include, among others. Multivariate ANOVA [9], Simplex optimization (Section 26.2.2), cluster analysis (Chapter 30) and various factor analytic methods such as principal components analysis (Chapter 31), discriminant analysis (Section 33.2.2) and canonical correlation analysis (Section 35.3). An advantage of multivariate methods is that they can be applied in... 

One of the major uses of multivariate techniques has been the discrimination of samples based on sensory scores, which also has been found to provide information concerning the relative importance of sensory attributes. Techniques used for sensory discrimination include factor analysis, discriminant analysis, regression analysis, and multidimensional scaling (8, 10-15). 

It is interesting to note that various QSAR/QSPR models from an array of methods can be very different in both complexity and predictivity. For example, a simple QSPR equation with three parameters can predict logP within one unit of measured values (43) while a complex hybrid mixture discriminant analysis-random forest model with 31 computed descriptors can only predict the volume of distribution of drugs in humans within about twofolds of experimental values (44). The volume of distribution is a more complex property than partition coefficient. The former is a physiological property and has a much higher uncertainty in its experimental measurements while logP is a much simpler physicochemical property and can be measured more accurately. These and other factors can dictate whether a good predictive model can be built. 

Discriminant analysis (DA) performs samples classification with an a priori hypothesis. This hypothesis is based on a previously determined TCA or other CA protocols. DA is also called "discriminant function analysis" and its natural extension is called MDA (multiple discriminant analysis), which sometimes is named "discriminant factor analysis" or CD A (canonical discriminant analysis). Among these type of analyses, linear discriminant analysis (LDA) has been largely used to enforce differences among samples classes. Another classification method is known as QDA (quadratic discriminant analysis) (Frank and Friedman, 1989) an extension of LDA and RDA (regularized discriminant analysis), which works better with various class distribution and in the case of high-dimensional data, being a compromise between LDA and QDA (Friedman, 1989). 

Sometimes canonical correlation or canonical analysis is referred to as a central technique with factor and correspondence analysis considered in one branch (having no causal concepts) and multivariate regression and discriminant analysis in the other branch (based on causal concepts). 

In discriminant analysis, in a manner similar to factor analysis, new synthetic features have to be created as linear combinations of the original features which should best indicate the differences between the classes, in contrast with the variances within the classes. These new features are called discriminant functions. Discriminant analysis is based on the same matrices B and W as above. The above tested groups or classes of data are modeled with the aim of reclassifying the given objects with a low error risk and of classifying ( discriminating ) another objects using the model functions. 

At this stage, however, discriminant analysis as well as factor analysis, do not provide a real reduction in dimensions from the practical (experimental) point of view because in the linear combinations used in both methods we still need all the original features. 

There are many other statistical models which can be used for the evaluation of DICE studies. Inclusion of not only a group factor, but also a time factor in the experiment methods of the analysis of variance (ANOVA) can be applied to find expression changes within the temporal course of the protein expression or to find interactions between the group and time factor. Several multivariate statistical methods are of use, too. Spots with similar expression profiles can be grouped by cluster analysis or, on the other hand, new spots can be assigned to existing groups by the methods of discriminant analysis. 

Chemometrics is a branch of science and technology dealing with the extraction of useful information from multidimensional measurement data using statistics and mathematics. It is applied in numerous scientific disciplines, including the analysis of food [313-315]. The most common techniques applied to multidimensional analysis include principal components analysis (PCA), factor analysis (FA), linear discriminant analysis (LDA), canonical discriminant function analysis (DA), cluster analysis (CA) and artificial neurone networks (ANN). 

Least squares models, 39, 158 Linear combination, normalized, 65 Linear combination of variables, 64 Linear discriminant analysis, 134 Linear discriminant function, 132 Linear interpolation, 47 Linear regression, 156 Loadings, factor, 74 Lorentzian distribution, 14... 

Screening of estuarine and marine sediment samples by automated pyrolysis mass spectrometry combined with factor-discriminant analysis leads to a useful classification related to the geographical position and the sources of the organic matter. The mass spectral data give preliminary information about the organic matter composition. Analysis of the characteristic mass peaks m/z=86 and 100 by PMSMS and PGCMS points to bacterial poly-alkanoates in the mud fraction of the river sediments. 

The pyrolysis methods applied in this study are used as a tool for a general characterization of the organic matter from the sediments. We describe here the results from screening of estuarine and open sea sediment samples by automated pyrolysis low voltage mass spectrometry combined with factor-discriminant analysis. Characteristic mass peaks resulting from this procedure were investigated in more detail by pyrolysis-tandem mass spectrometry and pyrolysis-photoionization GCMS. 

Pyrolysis Mass Spectrometry and Multivariant Data Analysis. The automated pyrolysis mass spectrometer and the multivariant data analysis by factor-discriminant analysis (f.d.a.) procedure used have been... 

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