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I have a compositional data matrix V, whose i-th row is the element ratio of the i-th sample. Finding a matrix decomposition as follows:

enter image description here

How can i solve this question use Non-negative matrix factorization (NMF or NNMF)?

Jean-François Corbett
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Vector Zhao
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  • Your image link is incorrect or broken. – Gambit1614 Oct 30 '17 at 09:20
  • I can open it. Image link:https://i.stack.imgur.com/1WjL0.png – Vector Zhao Oct 30 '17 at 12:49
  • With sklearn's NMF? You can't. This should be clear after reading their objective function. – sascha Oct 30 '17 at 13:46
  • Thanks for you answer. How should I do? Is there a Python model to deal with it? – Vector Zhao Oct 30 '17 at 14:06
  • Not that i know of. You probably have to build your own optimizer (probably based on alternative minimization with projections). – sascha Oct 30 '17 at 14:11
  • On a second look the projection looks non-trivial (not sure if valuable to pursue). Look up anything you can find on *constrained* nmf (in vector-terms the projection would be one to the probability-simplex; but in your case it's more complex as those are matrices). – sascha Oct 30 '17 at 14:23
  • i read the paper: http://www.sciencedirect.com/science/article/pii/S016794739800098X – Vector Zhao Oct 31 '17 at 11:12
  • I think it would help me solve this question, but i still have no ideas about the paper. so sad. – Vector Zhao Oct 31 '17 at 11:18

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