If I understand correctly, this method, versus a simple method such as k-means, doesn't only examine the closeness of points in phase space. For example, Figure 1 of the ArXiv paper shows NMF clustering of interior and exterior points. (I don't understand the details, but I'm trying to get a grip on the results.)

If this works, can we use NMF based clustering to identify outliers in datasets? I ask this because this is a significant element of my work. I have large datasets with sometimes questionable data and we want to early on identify outliers that don't fit with the rest. Typically we need to work through a series of regressions prior to identifying those samples that aren't with the program.

What else can we do with these?

Also, will NMF clustering methods reproduce the simple clustering. I mean, if we were to replace across the board all our clustering methods with this, would there be any disadvantages?