Principal component analysis PCA scores

PCR creates a quantitative model in a two-step process (1) the so-called principal components analysis (PCA) scores (they are described just below), T, of the I calibration samples are calculated for A factors and then (2) the scores are regressed against the analyte concentration. 

Fig. 9.8.7 Principal components analysis (PCA) scores plot of derivative data for 30% samples.

The data dispersion is shown in principal component analysis (PCA) scores plot (Figure 8.3). The projection in the two first components plane of the PCA highlights the effect of the variability of the operating conditions on the data. 

Figure 5.6 Principal components analysis (PCA) score plot for Raman spectra of (A) A549, (B) BEAS2B and (C) HaCaT cell lines. Percentage labels on each axis denote the variance described by that PC. There is clear separation of cellular spectra fixed with Meth-Ac and Carnoy s fixative relative to live and formalin fixed spectra. A degree of similarity between the spectral content of formalin fixed and live cell spectra is implied by the proximity of their clusters. (Reproduced from reference [52].)...

FIGURE 23.5 Effect of feeding captive male ring-necked pheasant (Ph. colchicus) young a high- or low-protein feed for the first three weeks of life on the expression of wattle coloration (mean+SE) at 20 (open circles) and 40 (filled circles) weeks of age. Coloration was determined using a principal components analysis (PCA) of tristimulus scores (hue, saturation, and brightness) obtained with a Colortron II reflectance spectrophotometer. 

Principal component analysis (PCA) of the soil physico-chemical or the antibiotic resistance data set was performed with the SPSS software. Before PCA, the row MPN values were log-ratio transformed (ter Braak and Smilauer 1998) each MPN was logio -transformed, then, divided by sum of the 16 log-transformed values. Simple linear regression analysis between scores on PCs based on the antibiotic resistance profiles and the soil physico-chemical characteristics was also performed using the SPSS software. To find the PCs that significantly explain variation of SFI or SEF value, multiple regression analysis between SFI or SEF values and PC scores was also performed using the SPSS software. The stepwise method at the default criteria (p=0.05 for inclusion and 0.10 for removal) was chosen. 

For principal component analysis (PCA), the criterion is maximum variance of the scores, providing an optimal representation of the Euclidean distances between the objects. 

Principal Component Analysis (PCA) is the most popular technique of multivariate analysis used in environmental chemistry and toxicology [313-316]. Both PCA and factor analysis (FA) aim to reduce the dimensionality of a set of data but the approaches to do so are different for the two techniques. Each provides a different insight into the data structure, with PCA concentrating on explaining the diagonal elements of the covariance matrix, while FA the off-diagonal elements [313, 316-319]. Theoretically, PCA corresponds to a mathematical decomposition of the descriptor matrix,X, into means (xk), scores (fia), loadings (pak), and residuals (eik), which can be expressed as... 

Principal component analysis (PCA) was employed to identify the underlying motive dimensions. K-means cluster analysis was used to classify the respondents according to their travel experience levels. A number of checks on the importance of the items contributing to the travel experience levels were also conducted (Lee Pearce, 2002). The factor scores from the PCA analysis results were computed and independent t-tests were... 

Figure 4 shows the distribution of the ketones in the two dimensional score space (h, t2), resulting from the principal component analysis (PCA) of the table of 78 ketones described by the 11 structure descriptor variables derived from IR, NMR spectra and other properties such as density, molecular weight and so on [31]. The figure also shows 9 compounds selected by a D-optimal design to well span this score space. Figure 5 shows the same score space but with another selection of 12 compounds, claimed to be superior. 

Preference mapping can be accomplished with projection techniques such as multidimensional scaling and cluster analysis, but the following discussion focuses on principal components analysis (PCA) [69] because of the interpretability of the results. A PCA represents a multivariate data table, e.g., N rows ( molecules ) and K columns ( properties ), as a projection onto a low-dimensional table so that the original information is condensed into usually 2-5 dimensions. The principal components scores are calculated by forming linear combinations of the original variables (i.e., properties ). These are the coordinates of the objects ( molecules ) in the new low-dimensional model plane (or hyperplane) and reveal groups of similar... 

Because almost all materials used in the pharmaceutical industry have NIR spectra, the use of NIR for assuring blend homogeneity may prove to be a valuable application. Ciurczak [24,25] reported some of the first work on this subject. His work involved the use of a fiber probe to collect spectra from various locations in the mixer. Spectral matching and principal component analysis (PCA) were used to measure how similar the powder mix in a particular portion of the blender was to a predetermined good, or complete, mix. The match index or PCA scores were plotted versus time to assess the optimal blending time. 

On the other hand, successful identification of bacterial spores has been demonstrated by using Fourier transform infrared photoacoustic and transmission spectroscopy " in conjunction with principal component analysis (PCA) statistical methods. In general, PCA methods are used to reduce and decompose the spectral data into orthogonal components, or factors, which represent the most coimnon variations in all the data. As such, each spectrum in a reference library has an associated score for each factor. These scores can then be used to show clustering of spectra that have common variations, thus forming a basis for group member classification and identification. 

FIGURE 16 Principal component analysis (PCA) of the transformed spectra can be viewed as a three-dimensional scores plot. The data from each active and placebo dosage form fall into a separate cluster. 

Drug space map coordinates are the t-scores extracted via Principal Component Analysis. PCA was performed on a total set of423 satellite and core structures described by 72 descriptors representing size, lipophilicity, polarizability, charge, flexibility, rigidity, and hydrogen bond capacity. 

In practice, for spectra exploitation, the main procedure is the principal component analysis (PCA), identifying a set of few factors (the first eigenvectors of the matrix), used for the interpretation of data. Then, any spectrum can be explained as a linear combination of these factors (as a decomposition step), the coefficients of which are the PCA scores. 

In principal component analysis (PCA), a matrix is decomposed as a sum of vector products, as shown in Figure 1.6. The vertical vectors (following the object way) are called scores and the horizontal vectors (following the variable way) are called loadings. A similar decomposition is given for three-way arrays. Here, the array is decomposed as a sum of triple products of vectors as in Figure 1.7. This is the PARAFAC model. The vectors, of which there are three different types, are called loadings. 

Other whole molecule descriptors that do not require alignment include the Weighted Holistic Invariant Molecular (WHIM) indices developed by Todeschini et al. [70]. These indices are calculated from the 3D coordinates, which are weighted and centered to make them invariant to translation principal component analysis (PCA) is applied to obtain three principal components. These are used to produce new coordinates, which can be analyzed to obtain a series of 10 descriptors based on eigenvalues and the third-order and fourth-order moments of the three score column vectors. These descriptors are related to molecular size, shape, symmetry, and atom distribution and density. 

A Result of a principal component analysis (PCA) over all desciptors Scores for PC2 plotted vs those of PCI. PCI accounts for 50 % of the variance, PC2 for further 10%. 

Fig. (4). Principal component analysis (PCA) with respect to the occurrence of various potential reactive sites in 4861 STL. Scores (A) and loadings (B) of the first three PCs are plotted in X, Y and Z direction. The scores show the clustering of the compounds into 16 major groups while the loadings show the influence of the variables on the position of these clusters in feature space and the distinction between the clusters.

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