Non-negative Matrix Factorization (NMF) has been used for source separation in various fields. However, the existing methods have ignored the presence of interactions among sources/measurements which leads to incorrect results. Interactions are common in a multivariate process where the variables are physically related/correlated with one another (for example: pressure-temperature dependency in an industrial process). In this work, conventional methods are extended to take into account the interactions. The contributions of this work are as follows: (i) an augmented NMF method to correctly determine the number of sources in the presence of multiple interactions; (ii) an algorithm to identify the correct signatures of the physical sources. The conventional method of NMF is shown to be a special case of the proposed method. Simulation studies are presented to demonstrate the practicality and utility of the proposed method. © 2009 Elsevier Inc. All rights reserved.