Chemometrics linear discriminant analysis

While principal components models are used mostly in an unsupervised or exploratory mode, models based on canonical variates are often applied in a supervisory way for the prediction of biological activities from chemical, physicochemical or other biological parameters. In this section we discuss briefly the methods of linear discriminant analysis (LDA) and canonical correlation analysis (CCA). Although there has been an early awareness of these methods in QSAR [7,50], they have not been widely accepted. More recently they have been superseded by the successful introduction of partial least squares analysis (PLS) in QSAR. Nevertheless, the early pattern recognition techniques have prepared the minds for the introduction of modem chemometric approaches. 

Figure 7.4 shows the results of applying stepwise linear discriminant analysis (SLDA) to the same samples used in the previous chemometric procedures. 

Table 7.1 Authentication of the geographical origin of virgin olive oil samples comparative results of SEXIA expert system, neural networks and the supervised chemometric procedure of stepwise linear discriminant analysis. Samples collected in the regions of Jaen (Spain)...

Table 7.2 Authentication of mono varietal virgin olive oils comparative results of fuzzy logic algorithms (Calvente and Aparicio, 1995) and the supervised chemometric procedure of linear discriminant analysis. Chemical compounds used linolenic acid, 24-methylen-cycloarthanol sterol and copaene hydrocarbon...

The SIMCA method, first advocated by the S. Wold in tire early 1970s, is regarded by many as a form of soft modelling used in chemical pattern recognition. Although there are some differences with linear discriminant analysis as employed in traditional statistics, the distinction is not as radical as many would believe. However, SIMCA has an important role in the history of chemometrics so it is important to understand the main steps of the method. 

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). 

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). 

Chemometric tools/analysis Statistical tools such as principal component analysis (PCA), linear discriminant analysis (LDA), hierarchical cluster analysis (HCA), or artificial neural networks (ANNs), which aid in the interpretation of patterns obtained in differential sensing. 

The first phase of data evaluation was to determine plasma concentration of sterols analyzed as described earlier. The standard addition method was used, calibration curves were constructed, and plasma sterol concentrations were determined. The second phase of data evaluation was to look for characteristic biomarkers and separate patient groups based on sterol concentrations. This was done by applying chemometrics (e.g., linear discriminant analysis) with sufficient validation. It was found that sterol concentration ratios are much more characteristic disease markers than the individual concentrations. Eor example, the concentration ratio of desmosterol to sitosterol was a much better marker of cholesterol-related disorders than the cholesterol concentration itself, and the concentration ratio of lathosterol to total plasma cholesterol was an excellent marker of statin treatment. Application of these analytical results by biochemists and medical doctors will hopefully result in better treatment of patients. 

Fig. 4 Different chemometric tools used in the development of BioETs clear bars) in comparison with those mostly used for generic ET systems dark bars). PCA principal component analysis, LDA linear discriminant analysis, ANN artificial neural network, PLS partial least squares, PCR. principal component regression, k-NN k-nearest neighbours, MCR multiple component regression. Data obtained from the literature search on the period 1996-2015 using SCOPUS database (Elsevier)...

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. 

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. 

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