Symmetric NMF is a well know tool used for graph clustering applications.
Given a similarity matrix $X \in \mathcal{R}^{n\times n}$, symmetric NMF seek to factorize it into o production of the form $HH^T$ such that $X \approx HH^T$, where $H \in \mathcal{n \times r}$. The values of $X$ are reals between 0 and 1.
The optimization problem can be written follows:
$$min_{H}f(X, HH^T)$$ My question is, beside the Frobenius norm,i.e., $f(X, HH^T) = \|X-HH^T\|^2$ what are the possible divergences or norms that can be used as a function to measure the quality of the reconstruction $f$ ?
Thank you.