L (1/2) regularization

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.