l2, 1 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 justified from the viewpoint of half-quadratic (HQ) optimization, which facilitates convergence study and algorithmic development. In particular, a general formulation is accordingly proposed to unify l1-norm and l2,1-norm minimization 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 proposed method to obtain an appearance-based model, called Sparse-Fisherfaces. Extensive experiments show that our method can select robust and sparse features, and outperforms several state-of-the-art subspace methods on largescale and open face recognition datasets.