Robust Manhattan non-negative matrix factorization for image recovery and representation

Abstract

Existing robust non-negative matrix factorization methods fail to achieve data recovery and learn a robust representation. This is because these methods suppose that outliers and noise of the original data are the Gaussian distribution. In this paper, we propose a robust non-negative matrix model, called robust Manhattan non-negative matrix factorization, which can handle various noise (e.g. Gaussian noise, Salt and Pepper noise or Contiguous Occlusion). Different from previous robust non-negative matrix factorization models, we utilize mean filter and matrix completion as additional constraints to recover the corrupted data from normal data or neighbouring corrupted data, and achieve a robust low-dimensional representation by Manhattan non-negative matrix factorization. We theoretically compare the robustness of our proposed model with other non-negative matrix factorization models and theoretically prove the effectiveness of the proposed algorithm. Extensive experimental results on the image dataset containing noise and outliers validate the robustness and effectiveness of our proposed model for image recovery and representation.