论文标题
通过平均场理论的非负矩阵的快速排名降低
Fast Rank Reduction for Non-negative Matrices via Mean Field Theory
论文作者
论文摘要
我们为非阴性矩阵提出了有效的矩阵降低方法，其时间复杂性在矩阵的行数或列中是二次的。我们的关键见解是通过在结构化样本空间上通过对数线性模型对矩阵进行建模，将降低作为平均场近似值，这使我们能够将等级还原作为凸优化。该公式的亮点是，可以以封闭形式分析计算与给定矩阵的KL差异最小化的最佳解决方案。我们从经验上表明，我们的排名降低方法比NMF及其受欢迎的变体LRANMF快，同时在合成和现实世界数据集中达到了竞争性的低等级近似误差。
We propose an efficient matrix rank reduction method for non-negative matrices, whose time complexity is quadratic in the number of rows or columns of a matrix. Our key insight is to formulate rank reduction as a mean-field approximation by modeling matrices via a log-linear model on structured sample space, which allows us to solve the rank reduction as convex optimization. The highlight of this formulation is that the optimal solution that minimizes the KL divergence from a given matrix can be analytically computed in a closed form. We empirically show that our rank reduction method is faster than NMF and its popular variant, lraNMF, while achieving competitive low rank approximation error on synthetic and real-world datasets.
