The NMF problem of the form

$$X \simeq WH$$

is a constrained biconvex optimization problem, and is often solved by alternating updates schemes. For example, the multiplicative update rules use analytic solutions to update the two variables $\textbf{W, H}$ alternatively.

\begin{align} For \quad & i=1...niter \\ & Update \quad W\\ & Update \quad H \end{align}

My equation is: can we use a hybrid optimization scheme instead. For example, for $W$ we choose a multiplicative update rule and for $H$ we choose a projected gradient descent method ?


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