Non-negative matrix factorization and its extensions were applied to various areas (i.e., dimensionality reduction, clustering, etc.). When the original data are corrupted by outliers and noise, most of non-negative matrix factorization methods cannot achieve robust factorization and learn a subspace with binary codes. This paper puts forward a robust semi-supervised non-negative matrix factorization method for binary subspace learning, called RSNMF, for image clustering. For better clustering performance on the dataset contaminated by outliers and noise, we propose a weighted constraint on the noise matrix and impose manifold learning into non-negative matrix factorization. Moreover, we utilize the discrete hashing learning method to constrain the learned subspace, which can achieve a binary subspace from the original data. Experimental results validate the robustness and effectiveness of RSNMF in binary subspace learning and image clustering on the face dataset corrupted by Salt and Pepper noise and Contiguous Occlusion.

非负矩阵分解及其扩展已应用于各个领域（例如，降维，聚类等）。当原始数据被异常值和噪声破坏时，大多数非负矩阵分解方法都无法实现鲁棒的分解并学习带有二进制代码的子空间。提出了一种鲁棒的半监督非负矩阵分解方法，用于二值子空间学习，即图像聚类。为了在离群值和噪声污染的数据集上实现更好的聚类性能，我们提出了对噪声矩阵的加权约束，并将流形学习强加到非负矩阵分解中。此外，我们利用离散哈希学习方法来约束学习的子空间，这可以从原始数据中获得一个二进制子空间。