Teaching Principal Component Analysis Using a Free and Open Source Software Program and Exercises Applying PCA to Real-World Examples

Abstract

Principal component analysis (PCA) is one of the most important and powerful methods in chemometrics as well as in a wealth of other areas. Running a PCA results in two main elements, the score plot and the loading plot; the score plot provides the location of the samples, and the loading plot indicates correlations among variables, the trends in the grouping of samples, and the most important variables. In the past 10 years teaching chemometrics, we have struggled with not having free software with an easy to use graphical user interface for data handling and calculations. In this paper, we provide a series of examples that students used to carry PCA in R-Project, a free and open source software program. In the first example, students used PCA to find correlations among chemical properties of chemical elements and relate these properties with the periodic distribution of the elements. In the second example, meat samples were grouped using 14 variables, and students could observe how outlier samples might influence the PCA model; in this case, they were also taught how to use the t test to choose the variables that were significant to the PCA model. In the third example, healthy patients were differentiated from diabetic patients using 163 lipid concentrations. In the fourth example, Atlantic salmon samples were differentiated from catfish samples. In the fifth and sixth examples, students were able to observe how data treatment affects the classification of natural products and edible oils, respectively.

Quantification of Nitrite in Food and Water Samples Using the Griess Assay and Digital Images Acquired Using a Desktop Scanner

“…Variances were compared using F test, and average values were compared using t test. Hypothesis tests were carried out using spreadsheets, as described in our previous papers. , …”

Principal Component Analysis (PCA) and Statistical Tests Using Factoshiny and R Commander.

“…In the loading plot (Figure 1), correlations among variables were observed in the loading plot, positively correlated variables were located close together, and inversely correlated variables were at 180° to one another, 2,32 for example, fixed acidity and citric acid are directly correlated, both variables were inversely correlated to pH. Total sulfur dioxide and free sulfur dioxide were directly correlated.…”

“…The PCA employs a mathematical procedure that transforms a set of possibly correlated variables into a new set of uncorrelated variables, called principal components, PCs. 2,31 The amount of each of the original variables included in the PC is described by the loading (Figure 1). By plotting the loadings for the two PCs, it was possible to assess the relative importance of each of the variables in the PCA model, variables with higher impact have larger vectors than variables with lower impact.…”

“…1 We did not have any free software with an easy-to-use graphical interface for data handing, so we published our first paper describing how to do principal component analysis (PCA) with Factoshiny. 2 After that, we had to do statistical tests and plots which were difficult to do with spreadsheets, such as one-way ANOVA, boxplot, plot of means and histograms. Therefore, we have released this manuscript that demonstrates how to do statical tests and graphs using R Commander and Factoshiny.…”

The Metabolite Fingerprints, Antimalarial Activities and Toxicities of Artocarpus Champeden Stembark From Various Regions in Indonesia

“…In order to visualize the significant metabolites affected to metabolite fingerprinting of A. champeden from five different locations, the score plots and the loading plots of PCA were used. The score plots reflected the significant samples whilst the loading plots reflected the significant variable (Bro & Smilde, 2014;Sidou & Borges, 2020). There were three significant metabolites affected in loading plots i.e.…”