L21 regularized correntropy for robust feature selection

In this paper, we study the problem of robust feature extraction based on l2,1 regularized correntropy in both theoretical and algorithmic manner. In theoretical part, we point out that an l2,1-norm minimization can be justi-fied from the viewpoint of half-quadratic (HQ) optimiza-tion, which facilitates convergence study and algorithmic development. In particular, a general formulation is ac-cordingly proposed to unify l1-norm and l2,1-norm mini-mization within a common framework. In algorithmic part, we propose an l2,1 regularized correntropy algorithm to extract informative features meanwhile to remove outliers from training data. A new alternate minimization algorithm is also developed to optimize the non-convex correntropy objective. In terms of face recognition, we apply the pro