论文标题
基于块坐标下降的投影梯度算法，用于正交非负矩阵分解
A Block Coordinate Descent-based Projected Gradient Algorithm for Orthogonal Non-negative Matrix Factorization
论文作者
论文摘要
本文利用预计的梯度方法（PG）来解决非负矩阵分解问题（NMF），其中一个或两个矩阵因子必须具有正生柱或行。我们惩罚正常限制，并通过块坐标下降方法应用PG方法。这意味着，在某个时候，一个矩阵因子是固定的，另一个基质因子通过沿惩罚目标函数计算出的最陡峭的下降方向进行更新，并投射到非阴性矩阵的空间上。 我们的方法对两组合成数据进行了测试，以实现各种惩罚参数值。将性能与Ding（2006）的众所周知的乘法更新（MU）方法进行了比较，并与Mirzal（2014）最近提出的MU算法的修改了全局收敛变体。我们提供了广泛的数值结果以及适当的可视化，这表明我们的方法非常有竞争力，并且通常比其他两种方法都优于其他两种方法。
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.
