ziyin-dl
commented
5 years ago -
This is equivalent to the "symmetric model" in [Chatterjee, 2015]:
- X (in [Chatterjee, 2015]) = M+N where N is an IID noise matrix. Note E[Xij]=Mij.
- p=1, meaning every entry of X is observed.
- η -> 0 Under the three points we recover the 2*\sqrt{n}\sigma threshold for singular values. Note the following remark in [Chatterjee, 2015]: "One limitation of USVT is the requirement that the entries should lie in a bounded interval. One may relax this requirement by assuming, for example, that the errors xij −mij are distributed as normal random variables with mean zero and variance σ^2. If σ^2 is known, then I believe that one can modify the USVT algorithm by thresholding at (2 + η)σ√n and obtain the same theorems."
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I believe you might have used the wrong order for NMF in this case. I think the following procedures are reasonable:
- Do the spectral estimation first, on the original matrix (say, calculate SVD(\tilde M)=UDV^T).
- Apply the soft thresholding operator t on D, and get the "noise filtered" matrix \hat M= Ut(D)V^T
- Do a NMF on \hat M. In this case the spectral estimation part should be identical.
asadullah797
Great Work!! I am following this paper and its code and I have a question related to Spectral Estimation. How did you get this formula. The reference you have given from [Chatterjee, 2015], I even could not find it in paper. Also I want to use NMF(Non-negative matrix factorization) instead of SVD, when I use the spectral estimation formula in the paper, I got all the elements become zero. How could I overcome this issue. Thanks!