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Structured Low-Rank Approximation as Optimization on a Grassmann Manifold
Published on Aug 26, 20134481 Views
Many data modeling problems can be posed and solved as a structured low-rank approximation problem. Using the variable projection approach, the problem is reformulated as optimization on a Grassmann m
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Chapter list
Structured low-rank approximation as optimization on a Grassmann manifold00:00
Structured low-rank approximation problem00:28
Hankel matrices - 102:44
Hankel matrices - 204:30
Low-rank Hankel matrices: examples - 105:30
Low-rank Hankel matrices: examples - 207:33
Block-Hankel matrices09:09
Sylvester matrices11:17
Other structures12:29
Structured low-rank approximation: formulation13:48
Weighted semi-norm: examples16:17
Reparameterization of the problem17:38
Inner minimization problem20:16
Outer minimization problem21:26
Constrained minimization22:09
Retraction-based methods22:52
Parametrizations with permutation matrices24:09
Optimization with permutations - 125:34
Optimization with permutations - 225:42
Optimization with switching permutations26:10
Comparison of the methods26:41
Conclusions27:02
References28:01
Thank you!28:15