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A reasonable way to factor a non-negative matrix $A$ into two non-negative matrices $M$ and $N$ can be done by minimizing the squared Frobenius norm, $||A - (M^2) (N^2)||_F^2$, where $M^2$ is the operation of squaring each entry of the matrix $M$ element wise (likewise with $N^2$). The final factorization of $A$ is given by $A = WH$, where $W = M^2$ and $H = N^2$, and squaring is done element-wise as before.

I tried to search for information about this method, but I could not find anything. I am specifically interested in how this method relates to non-negative matrix factorization (NMF), and the pros and cons of factorizing a matrix by the method described above over using NMF.

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