Abstract
This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both matrix factors must have orthonormal columns or rows. We penalize the orthonormality constraints and apply the PG method via a block coordinate descent approach. This means that at a certain time one matrix factor is fixed and the other is updated by moving along the steepest descent direction computed from the penalized objective function and projecting onto the space of non-negative matrices. Our method is tested on two sets of synthetic data for various values of penalty parameters. The performance is compared to the well-known multiplicative update (MU) method from Ding (2006), and with a modified global convergent variant of the MU algorithm recently proposed by Mirzal (2014). We provide extensive numerical results coupled with appropriate visualizations, which demonstrate that our method is very competitive and usually outperforms the other two methods.
Highlights
We demonstrate, how the projected gradient method (PG) method described in Section 3, performs compared to the multiplicative update (MU)-based algorithms of Ding and Mirzal, which were described in Sections 2.1 and 2.2, respectively
We presented a projected gradient method to solve the orthogonal non-negative matrix factorization problem
We penalized the deviation from orthonormality with some positive parameters and added the resulted terms to the objective function of the standard non-negative matrix factorization problem
Summary
Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva ulica 6, SI-1000 Ljubljana, Slovenia
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have