Initializations for the Nonnegative Matrix Factorization

The need to process and conceptualize large sparse matrices effectively and efficiently (typically via low-rank approximations) is essential for many data mining applications, including document and image analysis, recommendation systems, and gene expression analysis. The nonnegative matrix factorization (NMF) has many advantages to alternative techniques for processing such matrices, but its use comes with a caveat: the NMF must be initialized and the initialization selected is crucial to getting good solutions. It is well-known that good initializations can improve the speed and accuracy of the solutions of many NMF algorithms [43]. Add to this the fact that many NMF algorithms are sensitive with respect to the initialization of one or both NMF factors, and the impact of initializations becomes very important. In this paper, we compare the results of six initialization procedures (two standard and four new) on two alternating least squares algorithms, which we presented in [27].