  This article utilizes 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 penalise 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 penalised 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.
