How To Interpret PCA Points Labeled With Specific Data Dimensions

Question

I've done some PCA on my own, and am familiar with the basic concepts of how PCA components are calculated and applied. However, I'm working on a research project and am confused as to how to interpret a common type of graph I've seen across many papers using SPME analysis of volatiles. None of the papers I'd read through elaborate on how to interpret these graphs specifically, and trying to find more information elsewhere just leads to general explanations of PCA interpretation, which isn't what I'm having trouble with.

Specifically, many researchers provide PCA graphs, where the points of the graph are labeled with specific compounds included in the analysis. For example, in an analysis of acids present in different vinegars the associated PCA chart has points labeled for each of those individual acids.

Should I interpret those labeled points as the location within the graph where that given compound would be at it's highest observed signal? So if some point at (0.75, -1.15) is labeled "but1one" that's where some hypothetical sample containing only but1one would appear?

Answer 1

Most likely what you're seeing is the following. PCA is clearly used to find the most dominant features within some provided dataset, where you can think of each feature as being part of a basis you might use to represent your dataset. Given your dataset is a bunch of points in $n$-dimensions and you use PCA to find $k \ll n$ features in that dataset, you are then able to project any piece of data you have from the original $n$ dimensional space to a lower $k$ dimensional space with some loss in accuracy, but hopefully not much because you chose features that carry a lot of the variance weight when describing your original dataset.

So what you likely are seeing above is the researchers took a variety of compounds, first represented them in the original (zero mean) $n$-dimension versions, and then use your $k$ features from PCA to project them into $k$ dimensional space, which in the above image is just $k=2$ dimensions using the two most dominant PCA features. Then they label them according to what each of those dimensionality reduces vectors corresponded to in the $n$ dimensional representation.