A late fusion scheme for multi-graph regularized NMF

Guangyan Ji, Gui-Fu Lu

Abstract: Graph regularized non-negative matrix factorization (GNMF), which is an important extension of NMF, shows good clustering performance on some datasets. However, GNMF only uses one graph to simulate the manifold structure of the data, which may be not accurate enough. Then, some scholars proposed multi-graph regularized NMF(MGNMF). MGNMF first combines multiple graphs into one graph through a linear combination method, and then obtains a low-dimensional representation of the data. However, the representation ability of MGNMF is limited and cannot fully make use of the multi-graph information since MGNMF first combines multiple graphs into one graph and then obtains only one low-dimensional representation of the data, which makes clustering performance unsatisfactory enough. Therefore, we propose an innovative method, i.e., a late fusion scheme for multi-graph regularized NMF(LFS/MGNMF). Different from the existing algorithms, LFS/MGNMF does not directly combine multiple graphs into a graph, but first obtains their own low-dimensional representation matrices, and then uses self-expressiveness property of data to obtain the self-representation matrices of all the low-dimensional representations and removes noise simultaneously. In addition, by using the tensor low-rank constraint, i.e., tensor nuclear norm constraint, LFS/MGNMF can explore higher-order information among different self-representation matrices. Finally, LFS/MGNMF fuses the self-representation matrices for clustering. Therefore, we believe the proposed method is a late fusion scheme and can make full use of the multi-graph information. As far as we know, LFS/MGNMF is the first late fusion method for multi-graph regularized methods. The Augmented Lagrange Multiplier method is exploited to solve LFS/MGNMF, and the experimental results on four datasets are very promising and fully demonstrate the superiority of LFS/MGNMF.