I would like to group principal components based on sample values. That is, for a matrix with columns (PC1, PC2, ... , PCn), and rows with transformed values, I want to group PCs with similar values.
I'm working on a spatial problem, and some PCs produce similar patterns in space. E.g PC3, PC5, and PC18 pick out the same spatial feature, and so these could be grouped.
I have tried hierarchical column-wise clustering to solve this problem. However Euclidean distance doesn't seem appropriate (because PCA produces orthogonal vectors that are ~equidistant?).
I have tried mahalonobis distances with Ward linkage, and produced something that might be appropriate, but need advice from someone with proper mathematical background! How should I group based on PC?