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Outliers due to occlusion, pixel corruption, and so on pose serious challenges to face recognition despite the recent progress brought by sparse representation. In this article, we show that robust statistics implemented by the state-of-the-art methods are insufficient for robustness against dense gross errors. By modeling the distribution of coding residuals with a Laplacian-uniform mixture, we obtain a sparse representation that is significantly more robust than the previous methods. The nonconvex error term of the implemented objective function is nondifferentiable at zero and cannot be properly addressed by the usual iteratively reweighted least-squares formulation. We show that an iterative robust coding algorithm can be derived by local linear approximation of the nonconvex error term, which is both effective and efficient. With iteratively reweighted $l_{1}$ minimization of the error term, the proposed algorithm is capable of handling the sparsity assumption of the coding errors more appropriately than the previous methods. Notably, it has the distinct property of addressing error detection and error correction cooperatively in the robust coding process. The proposed method demonstrates significantly improved robustness for face recognition against dense gross errors, either contiguous or discontiguous, as verified by extensive experiments. [ABSTRACT FROM AUTHOR]

We formulate a framework for applying errorcorrecting codes (ECCs) on multilabel classification problems. The framework treats some base learners as noisy channels and uses ECC to correct the prediction errors made by the learners. The framework immediately leads to a novel ECC-based explanation of the popular random k-label sets (RAKEL) algorithm using a simple repetition ECC. With the framework, we empirically compare a broad spectrum of off-the-shelf ECC designs for multilabel classification. The results not only demonstrate that RAKEL can be improved by applying some stronger ECC, but also show that the traditional binary relevance approach can be enhanced by learning more parity-checking labels. Our research on different ECCs also helps to understand the tradeoff between the strength of ECC and the hardness of the base learning tasks. Furthermore, we extend our research to ECC with either hard (binary) or soft (real-valued) bits by designing a novel decoder. We demonstrate that the decoder improves the performance of our framework. [ABSTRACT FROM AUTHOR]