# Means and Issues for Adjusting Principal Component Analysis Results
## 4 Discussion  
In this analysis, PCA revealed two principal directions: PC1, which represented water-soluble ions that permeated the ground in a specific direction, and PC2, which represented a water-insoluble ion that remained on the surface. The samples were differentiated based on their respective depths within the soil, while forested areas that had not been treated were distinctly separated from the treated regions. The application of artificial rotation enhanced the clarity of this representation.  
The results of the rotated PCA, albeit by a small angle, were more understandable. This somewhat compromises the priority of higher levels of PCs, but if the angle is not too large, the damage will not be too great. Understanding PCA plots can often be challenging, as PCA merely provides a summary, without revealing the specifics. Interpretation of the plot is left to the analyst. In this regard, enhanced readability could be highly appreciated. Notably, PCA is sensitive to noise. If this effect could be easily mitigated, this technique would be worth considering. To address this, it would be advisable to employ outlier detection methods provided by exploratory data analysis (EDA) [14,15]. This approach could potentially eliminate the need for artificial rotation, which would be a preferable outcome. In any case, introducing rotation complicates the process and reduces its objectivity. Unless there is a clear and compelling justification for its use, it would be more prudent to avoid it altogether.  
It should be noted that this constitutes an active intervention by the analyst, potentially compromising PCA's objectivity. The beauty of PCA lies in its impartiality. Diluting this aspect would be regrettable and might even lead to data manipulation. If such adjustments were made, it would be essential to keep the original, unadjusted plot available. This original information is also necessary for others to check whether a rotation was necessary. Alternatively, the rotated plot could serve as supplementary material for explaining the results. Although this analysis focuses primarily on the two main principal components (PCs), there may be instances where it is necessary to rotate subordinate PCs as well. However, this would further diminish the objectivity of the results. In such cases, it is  
Figure 3: Contribution of each method. The original PCA is the most ideal diagram, with the greatest concentration on PC1; adjusting by 14\({}^{\circ}\) rotation weakens this concentration somewhat; finally, rotating by 45\({}^{\circ}\), 4/\(\pi\), the advantage of PC1 disappears and becomes the same contribution as that of PC2. Rotation by 90 degrees, not shown here, replaces PC1 and PC2.  
recommended to present visual representations, such as those illustrated in Figure 3, to provide a clear and transparent depiction of the data.  
The following supporting information can be downloaded at [[https://www.mdpi.com/article/10.3390/a18030129/s1](https://www.mdpi.com/article/10.3390/a18030129/s1)]([https://www.mdpi.com/article/10.3390/a18030129/s1](https://www.mdpi.com/article/10.3390/a18030129/s1)): Rscript.txt: R code; and test.txt: the sample data.  
This research received no external funding.  
The sample data and R codes are supplied in the Supplementary Data.  
The author declares no conflicts of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} PC & Principal component \\ PCA & Principal component analysis \\ SVD & Singular value decomposition \\ \end{tabular}