# Nonnegative matrix factorization

### From Wikimization

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- | + | Exercise from [http://meboo.convexoptimization.com/Meboo.html Convex Optimization & Euclidean Distance Geometry], ch.4: | |

Given rank-2 nonnegative matrix | Given rank-2 nonnegative matrix | ||

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<math>Y\!=U^\star U^{\star\rm T}.</math> | <math>Y\!=U^\star U^{\star\rm T}.</math> | ||

+ | Global convergence should occur, in this example, in only a few iterations. |

## Revision as of 14:48, 28 September 2009

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 an ordered diagonalization and , then

In summary, initialize then alternate solution of

with

Global convergence should occur, in this example, in only a few iterations.