In general, in unbalanced problems you are looking for a solution with more rows than columns (i.e. more data than variables, in the statistical sense). So the problem does not have a closed form solution, but needs to be solved via iterative methods. The balanced case is solved by performing one SVD, and the unbalanced problem needs roughly one SVD per iteration, and in ill conditioned problems this might mean a large number of SVD's.
Together with a colleague we have studied a new method for this (cited in the docs), and I had to test it against other previously developed methods, so I had to implement the scikit for my research purposes. From what I gather, in Psychometrics it might be useful to use the unbalanced problem if you are looking to find redundancies in the variables, for example.
- Melissa