Abstract
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 the paper is a literate program, implementing the method and reproducing the presented results.
Original language | English |
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Pages (from-to) | 814-830 |
Number of pages | 17 |
Journal | SIAM J. Matrix Anal. Appl. |
Volume | 34 |
Publication status | Published - 1 Feb 2013 |
Keywords
- low-rank approximation
- missing data
- variable projection
- system identification
- approximate matrix completion