Interpretation of "low variance" in PCA I have a question to ask about the interpretation of the PCA result.
The context concerns biological samples (spectroscopically analyzed) divided into treated and untreated samples (control)
If the first principal components describe only a small part of the variance (eg 15-16%) it means that they are not able to represent the entire variance of the system. If no main component can explain a good part of the variance of the system, can it be said that no predictor has a strong influence on the system and that therefore no strong differences are observed between a treated and untreated?
I honestly believe I cannot draw this conclusion.
I think that "low variance" explained means that the items are not sufficient to explain the model.
Thank you!


can it be said that no predictor has a strong influence on the system

no. You could have strong influence, but in a way that cannot be well approximated linearly.
Imagine a situation where controls have a certain variabiliy, and treatment consistently and strongly reduces this variability, but does not shift the mean.

no strong differences are observed between a treated and untreated?

Again, no, see above. But even within the subset of linear differences, the difference due to treatment may be strong in an application sense, but still overwhelmed by noise from all kinds of sources.

(Close to) spherical noise as discussed by @psyguy in spectroscopy often points to instrument noise. One big advantage we have in spectroscopy is that you can have a look at the loadings from a spectroscopic point of view. If instrument noise indeed dominates, already the first PC loadings should look very noisy and not like spectra.
If they look like spectra, your spectroscopic knowledge may suggest what their meaning is, and that in turn may help to find out why you don't see the diffrence you are looking for.
Other noise sources (so-called chemical noise) often have a structure and lead to distinct loadings.

There is nothing very special in the treatment not showing up in the first few PCs, that is often the case for spectroscopic raw data. Fortunately, for many kinds of spectroscopy, we do know important influencing factors for the signal and can often correct them e.g. in appropriate pre-processing. This will lower total variance, and (hopefully) keep the control - treatment difference, thus enhancing the signal-to-noise-ratio wrt. the application.
OTOH, applying the wrong pre-processing can clean the signal out of your data, leaving only noise and thus also lead to a situation like you describe...
