l_2,p Matrix Norm and Its Application in Feature Selection
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Recently, l_2,1 matrix norm has been widely applied to many areas such as computer vision, pattern recognition, biological study and etc. As an extension of l_1 vector norm, the mixed l_2,1 matrix norm is often used to find jointly sparse solutions. Moreover, an efficient iterative algorithm has been designed to solve l_2,1-norm involved minimizations. Actually, computational studies have showed that l_p-regularization (0<p<1) is sparser than l_1-regularization, but the extension to matrix norm has been seldom considered. This paper presents a definition of mixed l_2,p (p∈ (0, 1]) matrix pseudo norm which is thought as both generalizations of l_p vector norm to matrix and l_2,1-norm to nonconvex cases (0<p<1). Fortunately, an efficient unified algorithm is proposed to solve the induced l_2,p-norm (p∈ (0, 1]) optimization problems. The convergence can also be uniformly demonstrated for all p∈ (0, 1]. Typical p∈ (0,1] are applied to select features in computational biology and the experimental results show that some choices of 0<p<1 do improve the sparse pattern of using p=1.
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