Checking the Sufficiently Scattered Condition using a Global Non-Convex
  Optimization Software
Nicolas Gillis Robert Luce
The sufficiently scattered condition (SSC) is a key condition in the study of
identifiability of various matrix factorization problems, including
nonnegative, minimum-volume, symmetric, simplex-structured, and polytopic
matrix factorizations. The SSC allows one to guarantee that the computed matrix
factorization is unique/identifiable, up to trivial ambiguities. However, this
condition is NP-hard to check in general. In this paper, we show that it can
however be checked in a reasonable amount of time in realistic scenarios, when
the factorization rank is not too large. This is achieved by formulating the
problem as a non-convex quadratic optimization problem over a bounded set. We
use the global non-convex optimization software Gurobi, and showcase the
usefulness of this code on synthetic data sets and on real-world hyperspectral
images.