L 1/2 regularization

被引：354

作者：

Xu ZongBen ^{[1
]}

Zhang Hai ^{[1
,2
]}

Wang Yao ^{[1
]}

Chang XiangYu ^{[1
]}

Liang Yong ^{[3
]}

机构：

[1] Xi An Jiao Tong Univ, Inst Informat & Syst Sci, Xian 710049, Peoples R China

[2] NW Univ Xian, Dept Math, Xian 710069, Peoples R China

[3] Univ Sci & Technol, Macau 999078, Peoples R China

来源：

SCIENCE CHINA-INFORMATION SCIENCES | 2010年 / 53卷 / 06期

基金：

中国国家自然科学基金;

关键词：

machine learning; variable selection; regularizer; compressed sensing; UNCERTAINTY PRINCIPLES; SELECTION; LASSO;

D O I：

10.1007/s11432-010-0090-0

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页码：1159 / 1169

页数：11

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