I have a sparse symmetric adjacency matrix $\mathbf{A} \in \{0,1\}^{n \times n}$ that denotes an undirected graph.
How can I densify the matrix? I mean, how can I find a non-sparse matrix?
Is it OK to optimize the following objective function to find a dense matrix $\mathbf{U}$:
$\min\limits_{\mathbf{U}>0} {\lVert \mathbf{A} - \mathbf{UU}^T \rVert}_F^2+\lambda {\lVert \mathbf{U} \rVert}_1$
where $\mathbf{U} \in \mathbb{R}^{n \times n}$ and $\lambda$ is a regularization parameter, ${\lVert . \rVert}_F$ denotes frobenius norm and ${\lVert . \rVert}_1$ represents $L_1$-norm.
Can anyone help me?
Thank you :)