Online graph regularized non-negative matrix factorization for large-scale datasets

Non-negative matrix factorization (NMF) has been widely used to reduce dimensionality of data in image processing and various applications. Incorporating the geometric structure into NMF, graph regularized non-negative matrix factorization (GNMF) has shown significant performance improvement in comparison to conventional NMF. However, both NMF and GNMF require the data matrix to reside in the memory, which gives rise to tremendous pressure for computation and storage. Moreover, this problem becomes more serious if the scale of datasets increases dramatically. In this paper, we propose an online GNMF (OGNMF) method to process the incoming data in an incremental manner, i.e., OGNMF processes one data point or one chunk of data points one by one. By utilizing buffering and random projection tree strategy, OGNMF scales gracefully to large-scale datasets. Experimental results on popular text corpora and image databases demonstrate that OGNMF achieves better performance than the existing online NMF algorithms in terms of both accuracy and normalized mutual information, and outperforms the existing batch GNMF algorithms in terms of scalability.