Fixed Points of the EM Algorithm and Nonnegative Rank Boundaries

Matrices of nonnegative rank r represent mixtures of r independent distributions. Likelihood inference for this model leads to problems in real algebraic geometry that are addressed here for the first time. We characterize the fixed point locus of Expectation Maximization, and we study the boundary of the space of matrices with nonnegative rank at most 3. Both of these are algebraic varieties with many irreducible components.