Say I have four populations of samples, and I'd like to know if they are distinct or sampling the same process. Each sample is multivariate, and the distributions of the variables are non-normal. Furthermore the data set is quite noisy, so kernel-based PCA on all the samples gives no discernible structure.
I'd like to select those samples that best represent the underlying process(es), so I did the following: for each population I bootstrapped the mean for each variable, giving me a mean vector. To rate the samples, I computed the Pearson correlation coefficient between sample and corresponding mean vector.
My question is: Those samples that correlate the highest with their respective mean vectors, are they suitable for further analysis (e.g. clustering methods) or am I deluding myself?