Nonnegative matrix factorization (NMF) has become a widely used tool for the analysis of
high-dimensional data as it automatically extracts sparse and meaningful features from a set …

Identifying the underlying structure of a data set and extracting meaningful information is a
key problem in data analysis. Simple and powerful methods to achieve this goal are linear …

We construct a bipartite generalization of Alon and Szegedy's nearly orthogonal vectors,
thereby obtaining strong bounds for several extremal problems involving the Lovász theta …

Let A be an m× n matrix with nonnegative real entries. The psd rank of A is the smallest k for
which there exist two families (P 1,…, P m) and (Q 1,…, Q n) of positive semidefinite …

The hitting number of a polytope P is the smallest size of a subset of vertices of P such that
every facet of P has a vertex in the subset. We show that, if P is the base polytope of any …

Estimating the number of vertices of a two dimensional projection, called a shadow, of a
polytope is a fundamental tool for understanding the performance of the shadow simplex …

Abstract​​​​​​​ This paper proposes an optimization method for the Equality Set
Projection algorithm to compute the orthogonal projection of polytopes. However, its …

Given a non-negative real matrix M of non-negative rank at least r, can we witness this fact
by a small submatrix of M? While Moitra (SIAM J. Comput. 2013) proved that this cannot be …

Computational Approaches for Lower Bounds on the Nonnegative Rank Page 1
Computational Approaches for Lower Bounds on the Nonnegative Rank Julien Dewez …

We show that for every A⊆{0, 1} n, there exists a polytope P⊆ R n with P∩{0, 1} n= A and
extension complexity O (2 n/2), and that there exists an A⊆{0, 1} n such that the extension …