A Block Coordinate Descent-Based Projected Gradient Algorithm for Orthogonal Non-Negative Matrix Factorization

This article uses the projected gradient method (PG) for a non-negative matrix factorization problem (NMF), where one or both factors must have orthonormal columns rows. We penalize orthonormality constraints and apply PG via block coordinate descent approach. means that at certain time factor is fixed other updated by moving along steepest direction computed from penalized objective function projecting onto space of matrices. Our tested on two sets synthetic data various values penalty parameters. The performance compared to well-known multiplicative update (MU) Ding (2006), with modified global convergent variant MU algorithm recently proposed Mirzal (2014). provide extensive numerical results coupled appropriate visualizations, which demonstrate our very competitive usually outperforms methods.