This paper presents 3 main methods to obtain the NMF. An interesting thing is that the ALS is the easiest and fastest method which is used in the 1994 pioneering paper, but it is not used in the famous paper in Nature 1999.
Though this paper looks like an overview, its content is a little flat. I can hardly see or remember any convergent property of the NMF methods after reading the paper. Two examples used in the paper are not very common and NMF is not totally successful and the performance of other factorizations are not presented. To me, showing some simple application where the NMF works perfectly is more exciting. One good thing is that a public library is mentioned so maybe we can learn more from the library :).
Another thing is the NMF is getting popular in computer graphics. Many data in graphics are always non-negative: BRDF, visibility, etc. Also if NMF is used, the positive factorizations can be processed on GPU, which is optimized to handle positive numbers.
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