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 L1 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.