In the NMF framework, whenever I want to get a sparse component, I set the rank to 1 (lowest possible) and get the W and H matrices of the low-rank component by doing a multiplication of the resulting W and H matrices.
Then, to get the sparse component, I simply subtract the low-rank matrix obtained from the one used in the NMF (the mixture):
sparse = mixture - low_rank;
Now, my question is how would I get the sparse component factors W and H ?
With these factors, I can also reconstruct the sparse component with them, but I need them to do some processing before reconstruction. Is that possible at all? I cannot find anything on Google related to this scenario.
In other words, the full scenario looks like this: mixture = low_rank(W * H) + sparse(W * H); but how would I get the sparse W and H?