# Nonnegative matrix factorization

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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

with

Global convergence occurs, in this example, in only a few iterations.