Many papers suggest doing clustering not on the (n x p)raw data but on the n x n or p x p matrices computed according to determined similarity measures (eg, correlation, cosine, point mutual information, etc).
This is useful for sparse data, and personally, I find it also useful to switch categorical data in continuous one that works way better with classic clustering methods.
My problem is the interpretation though: doing the clustering on the n x p, n x n, p x p matrices will give you different results. Especially the differences in clustering between the n x p and n x n are hard to explain.
I would say that:
- clusters on n x p (along n) identify groups of observations (n) that tend in having similar values in their p features.
- clusters on n x n identify observations that have similar similarity patterns to other observations (tricky!).
- clusters on p x p identify features that have similar similarity patterns to other features (even more tricky!).
I can write these things up, but I'm not sure I'm grasping the deep meaning and implications of the differences.