Rank-One Matrix Completion with Automatic Rank Estimation via L1-Norm Regularization

Qiquan Shi, Haiping LU, Yiu Ming CHEUNG*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

34 Citations (Scopus)


Completing a matrix from a small subset of its entries, i.e., matrix completion is a challenging problem arising from many real-world applications, such as machine learning and computer vision. One popular approach to solve the matrix completion problem is based on low-rank decomposition/factorization. Low-rank matrix decomposition-based methods often require a prespecified rank, which is difficult to determine in practice. In this paper, we propose a novel low-rank decomposition-based matrix completion method with automatic rank estimation. Our method is based on rank-one approximation, where a matrix is represented as a weighted summation of a set of rank-one matrices. To automatically determine the rank of an incomplete matrix, we impose L1-norm regularization on the weight vector and simultaneously minimize the reconstruction error. After obtaining the rank, we further remove the L1-norm regularizer and refine recovery results. With a correctly estimated rank, we can obtain the optimal solution under certain conditions. Experimental results on both synthetic and real-world data demonstrate that the proposed method not only has good performance in rank estimation, but also achieves better recovery accuracy than competing methods.

Original languageEnglish
Article number8183435
Pages (from-to)4744-4757
Number of pages14
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number10
Publication statusPublished - Oct 2018

Scopus Subject Areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence

User-Defined Keywords

  • approximation
  • Low-rank decomposition
  • matrix completion
  • rank estimation
  • rank-one


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