2.3.1.3. Limitation of PCA
From what has been discussed previously it can appear very appealing, but there are few drawbacks or at least limitations that can be raised:
This method is very sensitive to extreme points: correlation coefficient can be perturbed by them.
In the case of non-linear phenomenon, the very basic concept of PCA collapses. Imagine a simple circle-shaped set of points, there are no correlation between the two variables, so no smaller space can be found using linear combinations.
Even if the PCA is working smoothly, one has to be able to find an interpretation of the resulting linear combinations that have been defined to create the principle component. Moreover, it might not be possible to move along on more refined analysis, such as sensitivity analysis for instance.
