Translation non-negative matrix factorization with fast optimization

Non-negative matrix factorization (NMF) reconstructs the original samples in a lower dimensional space and has been widely used in pattern recognition and data mining because it usually yields sparse representation. Since NMF leads to unsatisfactory reconstruction for the datasets that contain translations of large magnitude, it is required to develop translation NMF (TNMF) to first remove the translation and then conduct a decomposition. However, existing multiplicative update rule based algorithm for TNMF is not efficient enough. In this paper, we reformulate TNMF and show that it can be efficiently solved by using the state-of-the-art solvers such as NeNMF. Experimental results on face image datasets confirm both efficiency and effectiveness of the reformulated TNMF.