Communications of the ACM· 2012Q1
Exact matrix completion via convex optimization
- 1,010citations
- Q1SCImago
- 2012year
Short summary
A convex optimization approach can perfectly recover missing entries of a low-rank matrix from a sufficiently large, randomly sampled subset of its entries.
AI-generated from the title and abstract; the full text is not read.
Key points
- Perfect matrix completion is possible for low-rank matrices from incomplete subsets of entries.
- The method involves solving a convex optimization problem minimizing the nuclear norm.
- Success depends on the size of the observed subset and the matrix being low-rank.
- Techniques are analogous to those used in compressed sensing for signal reconstruction.
AI-generated from the title and abstract; the full text is not read.
Abstract
Suppose that one observes an incomplete subset of entries selected from a low-rank matrix. When is it possible to complete the matrix and recover the entries that have not been seen? We demonstrate that in very general settings, one can perfectly recover all of the missing entries from most sufficiently large subsets by solving a convex programming problem that finds the matrix with the minimum nuclear norm agreeing with the observed entries. The techniques used in this analysis draw upon parallels in the field of compressed sensing, demonstrating that objects other than signals and images can be perfectly reconstructed from very limited information.
The authors' abstract, as published at the source. Communications of the ACM, 2012 · DOI ↗
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Field: Computational Mechanics
Computational MechanicsEngineering