Structured low-rank approximation with missing data

Abstract

The approach of SIAM J. Matrix Anal. Appl., 26(4):1083--1099 for solving structured total least squares problems is generalized to weighted structured low-rank approximation with missing data. The method proposed is based on elimination of the correction matrix and solution of the resulting nonlinear least squares problem by local optimization methods. The elimination step is a singular linear least-norm problem, which admits an analytic solution. Two approaches are proposed for the nonlinear least-squares minimization: minimization subject to equality constraints and unconstrained minimization with regularized cost function. The method is generalized to weighted low-rank approximation with singular weight matrix and is illustrated on 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.

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