PCA loading plots

Figure 8.7 PCA loading plot of GC/MS data for the 53 samples of waterproofing material...

The ethanol concentration in the medium of a Saccharomyces cerevisiae cultivation can be monitored from its content in the gas phase by directly recording the current from a chemical MOS sensor [28]. The accuracy of such a measurement was significantly improved by using an electronic nose with five sensors in the array and recognizing the response pattern with ANN [29, 30]. The sensors were a combination of MOS and MOSFET sensors selected from a PCA loading plot. Data sets from three cultivations were used to train the ANN. When the trained net was applied on new cultivations the ethanol was predicted with a mean square error (RMSE) of 4.6% compared to the off-line determined ethanol (Fig. 6). With only one sensor the RMSE was 18%. 

Figure 22.26 PCA loadings plots of factor 1 and factor 2 of the results shown in Figure 22.25 [24].

A second piece of important information obtained by PCA is the loadings, which are denoted by PI, P2, etc. They indicate which variables influence a model and how the variables are correlated In algebraic terms the loadings indicate how the variables are combined to build the scores. Figure 9-8 shows a loading plot each point is a feature of the data set, and features that are close in the plot are correlated. 

To investigate the variance structure in the raw physical/chemical data material a PCA was performed on the autoscaled Y-data. Figure 3 shows a loading plot of the Y-data as a function of the two first PC s describing together 57 % of the total variance. 

Since U and V express one and the same set of latent vectors, one can superimpose the score plot and the loading plot into a single display as shown in Fig. 31,2e. Such a display was called a biplot (Section 17.4), as it represents two entities (rows and columns of X) into a single plot [10]. The biplot plays an important role in the graphic display of the results of PCA. A fundamental property of PCA is that it obviates the need for two dual data spaces and that instead of these it produces a single space of latent variables. 

Figure 33-1 presents the plot of the PLS loadings. Paul and Susan each computed both loadings. Note that the first loading is indistinguishable to the eye from the first PCA loading (see our original column on this topic [1]). 

PCA results are summarized in Fig. 5, which shows the loading plots characterizing the main contamination patterns in every analyzed data set and their explained... 

The described projection method with scores and loadings holds for all linear methods, such as PCA, LDA, and PLS. These methods are capable to compress many variables to a few ones and allow an insight into the data structure by two-dimensional scatter plots. Additional score plots (and corresponding loading plots) provide views from different, often orthogonal, directions. 

Factor analysis with the extraction of two factors and varimax rotation can be carried out in R as described below. The factor scores are estimated with a regression method. The resulting score and loading plots can be used as in PCA. 

Loadings Plot (Model and Variable Diagnostic) The loading plot in Figure 4.64 reveals that the first and se< ond loadings have nonrandom features, while the third is random in nature. This suggests a two-principal component model consistent with the percent variance explained, residuals plots, and mSECV PCA results... 

Figure 4.84. Loadings plot for the PCA model of TEA. Solid, PC1 dashed, PC2 dotted, PCS.

Therefore, it is possible to select, by means of the loading plot related to the PCA of all the available data (Fig. 19.3), a minimal number of variables (analytical indexes) capable of characterizing the cheeses. 

Figure 13.2 Analysis of raspberries by NIR imaging (third PC image) showing a grading in the maturity (Berries i = low maturity ii = medium maturity iii = ripe), (a) The figure shows the third PC image and (b) is a plot of the raw spectrum and the third PCA loading. From Walloon Agricultural Research Centre, Belgium.

Repeat the PCA in step 4, but remove the first three points in time. Compute the scores and loadings plots of PC2 versus PCI. Why has the scores plot dramatically changed in appearance compared with that obtained in question 2 Interpret this new plot. 

Perform PCA on the dataset, but standardise the intensities at each mass, and retain two PCs. Present the scores plot of PC2 versus PCI, labelling all the points in time, starting from 1 the lowest to 25 the highest. Produce a similar loadings plot, also labelling the points and comment on the correspondence between these graphs. 

Repeat this but sum the intensities at each point in time to 1 prior to standardising and performing PCA and produce scores plot of PC2 versus PCI, and comment. Why might it be desirable to remove points 1-3 in time Repeat the procedure, this time using only points 4-25 in time. Produce PC2 versus PCI scores and loadings plots and comment. 

Perform PCA, standardised, again on the reduced 25 x 10 dataset consisting of die best 10 masses according to the criterion of question 4, and present the labelled scores and loadings plots. Comment. Can you assign m /z values to the components in die mixture ... 

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