Science China Information Sciences

, Volume 53, Issue 6, pp 1159–1169 | Cite as

L1/2 regularization

  • ZongBen Xu
  • Hai Zhang
  • Yao Wang
  • XiangYu Chang
  • Yong Liang
Research Papers


In this paper we propose an L 1/2 regularizer which has a nonconvex penalty. The L 1/2 regularizer is shown to have many promising properties such as unbiasedness, sparsity and oracle properties. A reweighed iterative algorithm is proposed so that the solution of the L 1/2 regularizer can be solved through transforming it into the solution of a series of L 1 regularizers. The solution of the L 1/2 regularizer is more sparse than that of the L 1 regularizer, while solving the L 1/2 regularizer is much simpler than solving the L 0 regularizer. The experiments show that the L 1/2 regularizer is very useful and efficient, and can be taken as a representative of the L p (0 > p > 1)regularizer.


machine learning variable selection regularizer compressed sensing 


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Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • ZongBen Xu
    • 1
  • Hai Zhang
    • 1
    • 2
  • Yao Wang
    • 1
  • XiangYu Chang
    • 1
  • Yong Liang
    • 3
  1. 1.Institute of Information and System ScienceXi’an Jiaotong UniversityXi’anChina
  2. 2.Department of MathematicsNorthwest UniversityXi’anChina
  3. 3.University of Science and TechnologyMacauChina

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