Journal
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
Volume 34, Issue 2, Pages 814-830Publisher
SIAM PUBLICATIONS
DOI: 10.1137/120883050
Keywords
low-rank approximation; missing data; variable projection; system identification; approximate matrix completion
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Funding
- European Research Council under the European Union's Seventh Framework Programme (FP7)/ERC [258581]
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We consider low-rank approximation of affinely structured matrices with missing elements. The method proposed is based on reformulation of the problem as inner and outer optimization. The inner minimization is a singular linear least-norm problem and admits an analytic solution. The outer problem is a nonlinear least-squares problem and is solved by local optimization methods: minimization subject to quadratic equality constraints and unconstrained minimization with regularized cost function. The method is generalized to weighted low-rank approximation with missing values and is illustrated on approximate low-rank matrix completion, system identification, and data-driven simulation problems. An extended version of this paper is a literate program, implementing the method and reproducing the presented results.
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