We examine three non-negative matrix factorization techniques; L2-norm, L1-norm, and L2,1-norm. Our aim is to establish the performance of these different approaches, and their robustness in real-world applications such as feature selection while managing computational complexity, sensitivity to noise and more. We thoroughly examine each approach from a theoretical perspective, and examine the performance of each using a series of experiments drawing on both the ORL and YaleB datasets. We examine the Relative Reconstruction Errors (RRE), Average Accuracy and Normalized Mutual Information (NMI) as criteria under a range of simulated noise scenarios.