In order to save space, here we just list the iterative update algorithms of INMF in (8):
Bucak and Gunsel  introduced an incremental nonnegative matrix factorization algorithm (INMF) which imposed the NMF algorithm into incremental study, so INMF inherits the disadvantage of the NMF algorithm; that is, it does not consider the geometric structure in the data.
In this section, the FERET database [23, 24] and CMU-PIE database  are selected to evaluate the performance of our IGNMF and B-IGNMF algorithms, along with two canonical face recognition algorithms: supervised GNMF (GNMF-S) and unsupervised GNMF (GNMF-U) and three incremental algorithms: INMF, CINMF, and IOPNMF.
Our experiments are performed as follows: first, GNMF and NMF are chosen for initialization; second, IGNMF and INMF are performed to incremental study; GNMF and NMF are also performed by rerunning GNMF and NMF every time when new image comes.
Figures 3 and 4 illustrate the curves of recognition rates for INMF, IGNMF, NMF, and GNMF during incremental study.