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Robust PCA is a standard tool for learning a linear subspace in the presenceof sparse corruption or rare outliers. What about robustly learning manifoldsthat are more realistic models for natural data, such as images? There havebeen several recent attempts to generalize robust PCA to manifold settings. Inthis paper, we propose $\ell_1$- and scaling-invariant $\ell_1/\ell_2$-robustautoencoders based on a surprisingly compact formulation built on the intuitionthat deep autoencoders perform manifold learning. We demonstrate on severalstandard image datasets that the proposed formulation significantly outperformsall previous methods in collectively removing sparse corruption, without cleanimages for training. Moreover, we also show that the learned manifoldstructures can be generalized to unseen data samples effectively.

Robust Autoencoders for Collective Corruption Removal