hey eric,

the statement has been heard before ;),

The paper definately raises more questions and possibilities than it tries to answer.

that said,

the algorithm does not assume anything about the symmetric nature of noise, this is a choice made by the algorithm about the nature of the data that he is trying to analyse.

as for uses, I have used the lee and seung's approach to do decompose an image into its dominant color channels. This requires that both the A and V matrices be positive, since the color model is additive. As you would guess the algorithm is susceptible to local minima, but it does work most of the times.

have a look at

http://rick.ucsd.edu/~sagarwal/results.html