A three-stage method for batch-based incremental nonnegative matrix factorization

The main issue in incremental nonnegative matrix factorization (INMF) is how to update base matrix and coefficient matrix. The re-training scheme(RT-NMF) and the scheme proposed by Bucak and Gunsel(BG-INMF) are two common methods. However, both of them have problems in balancing root mean square error(RMSE) and time cost when incremental samples appear in a batch form. In this paper, a three-stage method(3S-INMF) is proposed to derive a good balance between RMSE and time cost. In the first stage, only the coefficient matrix of incremental samples is updated while the base matrix and the coefficient matrix of old samples are fixed. If the RMSE does not meet the required precision after this stage, the second stage, i.e. BG-INMF, is carried out. In the second stage, the base matrix and the coefficient matrix of incremental samples are updated alternatively while the coefficient matrix of old samples is fixed. If the RMSE still does not meet with the required precision after BG-INMF, the coefficient matrix of old samples will be updated in the third stage while the base matrix and the coefficient matrix of incremental samples are fixed. In the three consecutive stages, the initial values of base matrix and coefficient matrix in each stage are the corresponding output values in the previous stage. In addition, extensive experiments on the three popular datasets show that 3S-INMF obtains the best balance between RMSE and time cost compared with RT-NMF and BG-INMF. Furthermore, the 3S-INMF is extended to graph nonnegative matrix factorization(GNMF) and kernel nonnegative matrix factorization(KNMF), which also has a superior performance examined by further experiments. (C) 2020 Elsevier B.V. All rights reserved.