L21 Regularized Correntropy for Robust Feature Selection

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Ran He, Tieniu Tan, Liang Wang and Wei-Shi Zheng. L21 Regularized Correntropy for Robust Feature Selection. In IEEE CVPR,2012.
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We study the problem of robust feature extraction based on L21 regularized correntropy in both theoretical and algorithmic manner. In theoretical part, we point out that an L21-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 L21-norm minimization within a common framework. In algorithmic part, we propose an L21 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.
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