Discrete Aware Matrix Completion via Convexized ℓ0-Norm Approximation
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Abstract (arXiv)
We consider a novel algorithm, for the completion of partially observed low-rank matrices in a structured setting where each entry can be chosen from a finite discrete alphabet set, such as in common recommender systems. The proposed low-rank matrix completion (MC) method is an improved variation of state-of-the-art (SotA) discrete aware matrix completion method which we previously proposed, in which discreteness is enforced by an ℓ0-norm regularizer, not by replaced with the ℓ1-norm, but instead approximated by a continuous and differentiable function normalized via fractional programming (FP) under a proximal gradient (PG) framework. Simulation results demonstrate the superior performance of the new method compared to the SotA techniques as well as the earlier ℓ1-norm-based discrete-aware matrix completion approach.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 8 of its 32 references that are in the map. First posted on arXiv 3 May 2024.
Builds on
8 of 32 references.
References · 8
- 2018Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overviewcited by 159
- 2014Guaranteed Matrix Completion via Non-convex Factorizationcited by 81
- 2019Low-Rank Matrix Completion: A Contemporary Surveycited by 43
- 2015Matrix Completion with Noisy Entries and Outlierscited by 7
- 2016The Non-convex Geometry of Low-rank Matrix Optimizationcited by 6
- 2016Link Prediction via Matrix Completioncited by 4
- 2018Proximal Gradient Algorithms: Applications in Signal Processingcited by 3
- 2020Discrete-Aware Matrix Completion via Proximal Gradientcited by 2
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Citing papers per year: 2026: 1.
1 paper.
- 2026Low Rank Tensor Completion via Adaptive ADMMcited by 0
- 2026Low Rank Tensor Completion via Adaptive ADMM5 May 2026