Improved Sparse Low-Rank Matrix Estimation

Abstract

We address the problem of estimating a sparse low-rank matrix from its noisy observation. We propose an objective function consisting of a data-fidelity term and two parameterized non-convex penalty functions. Further, we show how to set the parameters of the non-convex penalty functions, in order to ensure that the objective function is strictly convex. The proposed objective function better estimates sparse low-rank matrices than a convex method which utilizes the sum of the nuclear norm and the ${\ell }_1$ norm. We derive an algorithm (as an instance of ADMM) to solve the proposed problem, and guarantee its convergence provided the scalar augmented Lagrangian parameter is set appropriately. We demonstrate the proposed method for denoising an audio signal and an adjacency matrix representing protein interactions in the `Escherichia coli' bacteria.

10 pages, 10 figures

References in corpus (6)

• Operator norm consistent estimation of large-dimensional sparse covariance matrices
• Global Convergence of ADMM in Nonconvex Nonsmooth Optimization
• Total Variation Denoising via the Moreau Envelope
• Enhanced Low-Rank Matrix Approximation
• Background Subtraction via Generalized Fused Lasso Foreground Modeling
• Link Prediction in Graphs with Autoregressive Features

Cited by in corpus (2)

• Reduce the rank calculation of a high-dimensional sparse matrix based on network controllability theory
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