Nonnegative matrix factorization
Exercise from Convex Optimization & Euclidean Distance Geometry, ch.4:
Given rank-2 nonnegative matrix find a nonnegative factorization by solving
which follows from the fact, at optimality,
Use the known closed-form solution for a direction vector to regulate rank (rank constraint is replaced) by Convex Iteration;
set to a nonincreasingly ordered diagonalization and , then
In summary, initialize then alternate solution of
Global convergence occurs, in this example, in only a few iterations.