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L 1/2 regularization
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DOI：10.1007/s11432-010-0090-0.png)
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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.
Keyword:
machine learning
variable selection
regularizer
compressed sensing
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