Discriminant analysis score

FIGURE 4.12 Discriminant analysis score plot performed considering dough samples of different geographical origins considering both NMR and IRMS data (From Brescia et al., 2007.)... 

The VolSurf method was used to produce molecular descriptors, and PLS discriminant analysis (DA) was applied. The statistical model showed two significant latent variables after cross-validation. The 2D PLS score model offers a discrimination between the permeable and less permeable compounds. When the spectrum color is active (Fig. 17.2), red points refer to high permeability, whereas blue points indicate low permeability. There is a region in the central part of the plot with both red and blue compounds. In this region, and in between the two continuous lines, the permeability prediction is less reliable. The permeability model... 

Stepwise discriminant analysis was used to determine how tree chemical, phenologlcal, and physical parameters differed between sites (Table VII). Only seven of the 18 variables used were needed to completely differentiate the trees at the 2 sites (F/y ] 93) = 210.36 p < 0.001). The magnitudes of the standardized discriminant function coefficients for the Included variables Indicated that the differences between sites were largely due to terpene chemistry (Table VIII). The discriminant function contrasts primarily the relative concentration of alpha-plnene versus the concentration of several terpenes, particularly bornyl acetate and beta-plnene. Examination of the discriminant scores showed that the stressed trees loaded negatively on the function (x discriminant score = -2.23), while the non-stressed trees loaded positively (x discriminant score = 3.38). In other wards, trees from the stressed site were higher In alpha-plnene vdille the non-stressed trees contained more bornyl acetate, beta-plnene, and other terpenes In their young needles. 

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). 

Correlation of Analytical/Sensory Results. Sensory data was correlated with headspace data of tobacco volatiles by factor analysis (BMDP4M) and canonical correlation BMDP6M. Analytical data included factor scores and discriminant analyses scores sensory data included scores from the two MDS dimensions. Sorted rotated factor loadings of combined sensory/analytical data using factor analysis are shown in Table II. Factor one contained those variables from the analytical and sensory data which related to differences between bright (A), burley (B), and oriental (C) (Figure 10). These included dimension 1 in the... 

Initially an optimised model was constructed using the data collected as outlined above by constructing a principal component (PC)-fed linear discriminant analysis (LDA) model (described elsewhere) [7, 89], The linear discriminant function was calculated for maximal group separation and each individual spectral measurement was projected onto the model (using leave-one-out cross-validation) to obtain a score. The scores for each individual spectrum projected onto the model and colour coded for consensus pathology are shown in Fig. 13.3. The simulation experiments used this optimised model as a baseline to compare performance of models with spectral perturbations applied to them. The optimised model training performance achieved 93% accuracy overall for the three groups. 

Partial least square (PLS) regression model describes the dependences between two variables blocks, e.g. sensor responses and time variables. Let the X matrix represent the sensor responses and the Y matrix represent time, the X and Y matrices could be approximated to few orthogonal score vectors, respectively. These components are then rotated in order to get as good a prediction of y variables as possible [25], Linear discriminant analysis (LDA) is among the most used classification techniques. The method maximises the variance between... 

Figure 3 presents the reconstructed mass spectrum of the first discriminant function which separated the river and marine stations in the DiD2-map of Figure 1. The positive D-function describes the covariant mass peaks with higher intensities with respect to the zero point spectrum. All sample spectra with such characteristics will have positive score values. This spectrum is a representation of the characteristics of riverine material. The negative D-function spectrum in Figure 3 is indicative of the marine characteristics. The D spectrum shows a number of mass peaks indicative for carbohydrates, lignin and proteinaceous material (12). The mass peak m/z=86 and 100 are uncommon and a special characteristic of these fluvial samples. It can be speculated to be the molecular ion of (alkyl)thiadiazole (a metal binding pollutant), however a cyclic ketone, short chain alcohol or unsaturated acid are also possibilities. These mass peaks were chosen for further study because of their rare occurrence and their high discriminating power in the factor-discriminant analysis.

Fig. 1. Graphical representation of discriminant function D1 derived from the che-mometric analysis of mass spectral signatures of 30 microlayer and bulk seawater film extracts (FI). Intensities at each m/z represent the loadings for that particular m/z variable used to calculate the D1 discriminant function score. Prominent m/z variables include those representative of fatty acids, acyl lipids, sterols, poloxy-mers and humic compounds...

The adaptive least squares (ALS) method [396, 585 — 588] is a modification of discriminant analysis which separates several activity classes e.g. data ordered by a rating score) by a single discriminant function. The method has been compared with ordinary regression analysis, linear discriminant analysis, and other multivariate statistical approaches in most cases the ALS approach was found to be superior to categorize any numbers of classes of ordered data. ORMUCS (ordered multicate-gorial classification using simplex technique) [589] is an ALS-related approach which... 

Two studies have suggested that the IR spectra of synovial fluid specimens provide the basis to diagnose arthritis and to differentiate among its variants.A NIR study demonstrated that osteoarthritis, rheumatoid arthritis, and spondyloarthropathy could be distinguished on the basis of the synovial fluid absorption patterns in the range 2000-2400 nm.< In that case, the pool of synovial fluid spectra was subject to principal component analysis, and eight principal component scores for each spectrum were employed as the basis for linear discriminant analysis (LDA). On that basis, the optimal LDA classifier matched 105 of the 109 spectra to the correct clinical designation (see Table 7). 

Figure 10.13 Principal components analysis scores plots (a) using all three example variables (first two principal components discriminations of the varieties, particularly sample Le2, would be very difficult) (b) using the best two variables, unweighted w selected [equation (10.31) in text] (discrimination of the varieties is now possible using only the first principal component) (c) discarding the best variable, unweighted w selected (linear discrimination of the varieties would not appear to be possible from this chart). Details of the variables are given in Table 10.3.

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