论文标题
NMF乘以$β$ -Diverences的乘法更新，这是不相交平等约束的
Multiplicative Updates for NMF with $β$-Divergences under Disjoint Equality Constraints
论文作者
论文摘要
非负矩阵分解（NMF）是近似输入非负矩阵$ v $的问题，作为两个较小的非负矩阵的产物，$ w $和$ h $。在本文中，我们介绍了一个通用框架，以基于$β$ -Diverences（$β$ -NMF）设计乘法更新（MU），并具有不相关的平等约束，并且在目标函数中具有惩罚项。通过脱节，我们的意思是每个变量最多出现在一个平等约束中。在优化过程中每次更新变量之后，我们的MU满足了一组约束，同时确保目标函数单调下降。我们在三种NMF型号上展示了此框架，并表明它具有良好的竞争：（1）〜$β$ -NMF，对$ h $，（2）最低限制$β$ -nmf的列的列对一个列的列约束，并在$ w $ $ w $ $ w $的列表上进行一定的约束，以及（3）$ w $ - 3） - 3）在$ w $的列中。
Nonnegative matrix factorization (NMF) is the problem of approximating an input nonnegative matrix, $V$, as the product of two smaller nonnegative matrices, $W$ and $H$. In this paper, we introduce a general framework to design multiplicative updates (MU) for NMF based on $β$-divergences ($β$-NMF) with disjoint equality constraints, and with penalty terms in the objective function. By disjoint, we mean that each variable appears in at most one equality constraint. Our MU satisfy the set of constraints after each update of the variables during the optimization process, while guaranteeing that the objective function decreases monotonically. We showcase this framework on three NMF models, and show that it competes favorably the state of the art: (1)~$β$-NMF with sum-to-one constraints on the columns of $H$, (2) minimum-volume $β$-NMF with sum-to-one constraints on the columns of $W$, and (3) sparse $β$-NMF with $\ell_2$-norm constraints on the columns of $W$.
