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Can the NNMF algorithm handle an error matrix of the original data?

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Can the NNMF algorithm handle an error matrix of the original data? E.g. instead of:
A=W x H + D, where D is minimized
Q is minimized, based on the error matrix (sij) of the original data (aij), which could for example be the measurement precision
min Q = sum(sum(dij/sij)^2))

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