A unified algorithm for mixed -minimizations and its application in feature selection

Recently, matrix norm has been widely applied to feature selection in many areas such as computer vision, pattern recognition, biological study and etc. As an extension of norm, matrix norm is often used to find jointly sparse solution. Actually, computational studies have showed that the solution of -minimization () is sparser than that of -minimization. The generalized -minimization () is naturally expected to have better sparsity than -minimization. This paper presents a type of models based on matrix norm which is non-convex and non-Lipschitz continuous optimization problem when is fractional (). For all in , a unified algorithm is proposed to solve the -minimization and the convergence is also uniformly demonstrated. In the practical implementation of algorithm, a gradient projection technique is utilized to reduce the computational cost. Typically different are applied to select features in computational biology.