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.

现有的健壮的非负矩阵分解方法无法实现数据恢复，也无法学习健壮的表示形式。这是因为这些方法假定原始数据的离群值和噪声是高斯分布。在本文中，我们提出了一个鲁棒的非负矩阵模型，称为鲁棒的曼哈顿非负矩阵分解，它可以处理各种噪声（例如高斯噪声，盐和胡椒噪声或连续遮挡）。与以前的鲁棒非负矩阵分解模型不同，我们利用均值滤波器和矩阵完成作为附加约束，从正常数据或相邻的破坏数据中恢复损坏的数据，并通过曼哈顿非负矩阵分解实现鲁棒的低维表示。我们从理论上将我们提出的模型与其他非负矩阵分解模型的鲁棒性进行比较，并从理论上证明了该算法的有效性。在包含噪声和异常值的图像数据集上的大量实验结果验证了我们提出的图像恢复和表示模型的鲁棒性和有效性。