8 problems

Let $A\in\mathbb{R}_{\geq 0}^{m\times r}$ and consider the cone toolkit, in which rows of $A$ determine facets of the associated cone and its extreme rays provide candidate vectors…

The displayed examples consist of $15$ nonnegative matrix factorizations, each expressing a nonnegative matrix as a product of two nonnegative matrices. Global rigidity conjecture.…

Two-endmember conjecture. A combination of only two endmembers suffices to meet the APMRC in Theorem.

Automatic regularization conjecture. By automatically deciding how much regularized NMF should rely on the prior, it should not be necessary to manually change the regularization-p…

Let $P$ and $Q$ be the outer and inner polytopes associated with the nested polytope problem NPP($\mathcal{P}^{\bar{\alpha}}(M)$), and let $m$ and $n$ denote the dimensions governi…

Let $M$ satisfy … and suppose that $\operatorname{conv}(\theta(\mathcal{P}(M)))$ has at least $k+1$ vertices. Let $\bar{\alpha}$ be defined as in Equation. The arbitrary-rank finit…

Let $A$ be a matrix, let $M$ and $N$ be row and column index sets, and let $p=\min(|M|,|N|)$. After optimizing the rank-one approximation variables, define … where…

Let $A$ be a nonnegative matrix, let $M$ and $N$ be row and column index sets, and define … where $\gamma$ is a penalty parameter, $\mathbf{u}$ and $\mathbf{v}$ are vectors, and…