Loading factors

Ambient temperature 20°C. For outdoor temperature —18°, multiply load value in table by correction factor. Loads based on ANSI Schedule 40 pipe for pressures up to 16bar. Schedule 80 pipe for pressures above 16bar, except Schedule 120 above 40bar in sizes 125mm and over. 

The theory of the non-linear PCA biplot has been developed by Gower [49] and can be described as follows. We first assume that a column-centered measurement table X is decomposed by means of classical (or linear) PCA into a matrix of factor scores S and a matrix of factor loadings L ... 

The biplot in Fig. 37.3 has been constructed from the factor scores of the 12 compounds and the factor loadings of the five physicochemical and biological variables [42,43]. (The biplot graphic technique is explained in Section 31.2.) It is... 

The principle of FA and PCA consists in an orthogonal decomposition of the original n x m data matrix X into a product of two matrixes, F (nxk matrix of factor scores, common factors) and L (kxm matrix of factor loadings)... 

The factor extraction according to Eq. (8.20) in the course of which the number of common factors are estimated by rank analysis and coefficients of the factors (factor loadings) are calculated. 

Factor Variance in % Essential factor loadings by Genesis... 

Fig. 3. Biplots of log-ratio factor loading for Aegean Sea sediments. Upper plot, complete dataset lower plot, offshore samples. Percentages indicate variance accounted for by factor.

The second step in factor analysis is interpretation of the principal components or factors. This is accomplished by examining the contribution that each of the original measured variables makes to the linear combination describing the factor axis. These contributions are called the factor loadings. When several variables have large loadings on a factor they may be identified as being associated. From this association one may infer chemical or physical interactions that may then be interpreted in a mechanistic sense. 

Two factors characterized most of the waters sampled in the monitoring program. The factor loadings for Factor one indicate that the following chemical species participate in correlated behavior that permits the separations and distinctions described above alkalinity, bicarbonate, B, Cl, conductance, F, Li, Mo, and Na. To simplify discussions in the plots shown earlier this group of species was called the salinity factor. Specific conductance in natural waters usually correlates well with hardness and not as well with bicarbonate, but the current study finds specific conductance closely related to bicarbonate and unrelated to hardness (Ca, Mg, sulfate). This indicates that the ions responsible for increased conductance are probably not calcium or magnesium, rather they are more likely sodium, fluoride, and chloride. 

The values of the factor loadings, a.., rather than the factors themselves are of primary interest The total variance of the variable accounted for the combination of all common factors is termed the commonality of the variable and may be calculated from the factor loadings. 

The factor loadings also represent correlations between factors and variables and may be used to obtain the correlations between variables in the factor model. These calculated correlations should be close to the observed correlations. 

With the molecular descriptors as the X-block, and the senso scores for sweet as the Y-block, PLS was used to calculate a predictive model using the Unscrambler program version 3.1 (CAMO A/S, Jarleveien 4, N-7041 Trondheim, Norway). When the full set of 17 phenols was us, optimal prediction of sweet odour was shown with 1 factor. Loadings of variables and scores of compounds on the first two factors are shown in Fig es 1 and 2 respectively. Figure 3 shows predicted sweet odour score plotted against that provid by the sensory panel. Vanillin, with a sensory score of 3.3, was an obvious outlier in this set, and so the model was recalculated without it. Again 1 factor was r uired for optimal prediction, shown in Figure 4. 

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... 

For Koch-Sulzer packing, Neo-Kloss packing, and Leva film trays, a preliminary estimate can be made by dividing the pressure drop per foot of packing at a typical or expected F factor loading from Fig. 2, 3, or 4 by an assumed HETS (in feet). 

Finally, a similar approach was undertaken to evaluate the origin of factor 3 in Fig. 15.3c whose score image reveals several small-localized pockets in the epidermis. The loading from factor 3 (Fig. 15.3b) depicts one broad feature at 1090cm 1 not present in the other factor loadings. Based on both the position of this particular band and the spatial distribution of the factor score, the band probably arises from a phosphodiester mode of DNA [30, 31] present in the nuclei of keratinocytes or other cells. An additional feature at 780 cm 1 in both spectra and factors (not shown) arises from cytosine in DNA [32] and is consistent with this interpretation. 

Fig. 15.5. Factor analysis results for the C-H stretching region (2800-3050 cm 1 region) in human skin and in cultured skin model (Epiderm ). Data from human skin (8 x 12 pixels) and cultured skin (7 x 12 pixels) have been concatenated. Pixels marked with x s were excluded from the analysis, a Factor loadings for the methylene stretching region. The dashed vertical line marks 2876 cm-1 and emphasizes the shift in frequency between factors 1 and 2. b Score plots for factor 1 are depicted for human skin in the left set of 8 X 12 pixels and for cultured skin in the right set of 7 x 12 pixels, c Score plots for factor 2 are depicted for human skin in the left set of 8 x 12 pixels and for cultured skin in the right set of 7 x 12 pixels...

Fig. 15.11. a Factor loadings constructed from Raman spectra specific to the general area of the wound. The amide I and III contours of factors 1 and 2 are characteristic of high collagen and high keratin levels, respectively, b Factor score images reveal that collagen (factor 1) in the wounded area is pressed up from the dermis, while the keratin (factor 2) in the non-wounded area arises from the SC and from the viable epidermis... 

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