Non-negative matrix factorisation (NMF) has been extensively applied to the problem of corrupted image data. Standard NMF approach minimises Euclidean distance between data matrix and factorised approximation. The traditional NMF technique is sensitive to outliers since it utilises the squared error of each data point, despite the fact that this method has proven effective. In this study, we theoretically examine the robustness of the traditional NMF, HCNMF, and L2,1-NMF algorithms and execute sets of experiments to demonstrate the robustness on ORL and Extended YaleB datasets. Our research indicates that each algorithm requires a different number of iterations to converge. Due to the computational cost of these approaches, our final models, such as the HCNMF and L2,1-NMF model, fail to converge within the iteration parameters of this work. Nonetheless, the experimental results illustrate, to some extent, the robustness of the aforementioned techniques.

翻译：非负矩阵分解（NMF）已被广泛应用于图像数据受损问题。标准NMF方法通过最小化数据矩阵与分解近似之间的欧氏距离进行求解。尽管传统NMF技术已被证明有效，但由于其利用每个数据点的平方误差，该方法对异常值较为敏感。本研究从理论上考察了传统NMF、HCNMF和L2,1-NMF算法的鲁棒性，并通过在ORL和Extended YaleB数据集上开展系列实验验证其鲁棒性。研究表明，每种算法达到收敛所需的迭代次数不同。由于这些方法的计算成本，本文所采用的最终模型（如HCNMF和L2,1-NMF模型）在设定的迭代参数范围内未能收敛。尽管如此，实验结果在一定程度上仍展示了上述技术的鲁棒性。