In this preliminary study, we have investigated the human eye as an important part of face for personal authentication under certain restricted circumstances related to face occlusion, individual privacy concerns and religious practices. Although this part of face is not as unique as full-face, but it offers much higher computational efficiency with minimum processing steps, and minimum storage capacity as compared to full-face. In our experiments, the frontal human eye images are generated from Essex dataset with 153 subjects. The images are tested with non-negative matrix factorization (NMF), local NMF (LNMF) and spatially confined NMF (SFNMF) respectively. Our experiments show that LNMF performs most optimally to attain 95.12% recognition rate, follow by SFNMF and NMF, which achieve 94.48% and 93.23%, respectively. It is evidenced that LNMF and SFNMF performs better than sole plain NMF. Besides, another goal of this paper is to study the influence of r, to which degree the basis number is sufficient to achieve the optimal recognition rate.