Structured low-rank approximation with missing data

Ivan Markovsky, Konstantin Usevich

Research output: Contribution to journalArticlepeer-review

52 Citations (Scopus)


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 languageEnglish
Pages (from-to)814-830
Number of pages17
JournalSIAM J. Matrix Anal. Appl.
Publication statusPublished - 1 Feb 2013


  • low-rank approximation
  • missing data
  • variable projection
  • system identification
  • approximate matrix completion


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