Nonnegative matrix rank and the EM algorithm

We consider the mixture model of two discrete random variables, i.e.
matrices of nonnegative rank at most r. For r=3, we give a
quantifier-free formula of this semialgebraic set and describe its
boundary using nested polygons. We study minimal primes of the ideal of
the EM fixed points and recognize the boundary components among them.

This talk is based on joint work with Elina Robeva and Bernd Sturmfels.