Symmetric Sparse Boolean Matrix Factorization and Applications. (arXiv:2102.01570v3 [cs.LG] UPDATED)

In this work, we study a variant of nonnegative matrix factorization where we
wish to find a symmetric factorization of a given input matrix into a sparse,
Boolean matrix. Formally speaking, given $\mathbf{M}\in\mathbb{Z}^{m\times m}$,
we want to find $\mathbf{W}\in\{0,1\}^{m\times r}$ such that $\| \mathbf{M} -
\mathbf{W}\mathbf{W}^\top \|_0$ is minimized among all $\mathbf{W}$ for which
each row is $k$-sparse. This question turns out to be closely related to a
number of questions like recovering a hypergraph from its line graph, as …

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