I am trying to approximate a square symmetric nonnegative matrix $A \in \mathbb{R_+}^{n \times n}$ using the following matrix factorization
$$A \approx \hat{A} = P P^T$$
with $P \in \mathbb{R_+}^{n \times r}$ and $r << n$.
There are some novel papers on this factorization, e.g. Efficient and Non-Convex Coordinate Descent for Symmetric Nonnegative Matrix Factorization with code available. I tried to implement the $\alpha$-SNMF and $\beta$-SNMF Newton like methods from Symmetric Nonnegative Matrix Factorization: Algorithms and Applications to Probabilistic Clustering. But the errors in approximation are around 30%, which seems very high to me. Are there no methods in order to achieve an approximation with an error less than that?