A Novel Monotonic Fixed-Point Algorithm for l1-Regularized Least Square Vector and Matrix Problem

  • Jiaojiao Jiang
  • Haibin Zhang
  • Shui Yu
Part of the Communications in Computer and Information Science book series (CCIS, volume 163)


Least square problem with l 1 regularization has been proposed as a promising method for sparse signal reconstruction (e.g., basis pursuit de-noising and compressed sensing) and feature selection (e.g., the Lasso algorithm) in signal processing, statistics, and related fields. These problems can be cast as l 1-regularized least-square program (LSP). In this paper, we propose a novel monotonic fixed point method to solve large-scale l 1-regularized LSP. And we also prove the stability and convergence of the proposed method. Furthermore we generalize this method to least square matrix problem and apply it in nonnegative matrix factorization (NMF). The method is illustrated on sparse signal reconstruction, partner recognition and blind source separation problems, and the method tends to convergent faster and sparser than other l 1-regularized algorithms.


l1-regularized LSP fixed point method signal reconstruction NMF 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jiaojiao Jiang
    • 1
  • Haibin Zhang
    • 1
  • Shui Yu
    • 2
  1. 1.College of Applied SciencesBeijing University of TechnologyChina
  2. 2.School of Information TechnologyDeakin UniversityBurwoodAustralia

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