当前位置: X-MOL 学术Adv. Comput. Math. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
An efficient method for non-negative low-rank completion
Advances in Computational Mathematics ( IF 1.7 ) Pub Date : 2020-03-23 , DOI: 10.1007/s10444-020-09779-x
Nicola Guglielmi , Carmela Scalone

In this article, we propose a new method for low-rank completion of a large sparse matrix, subject to non-negativity constraint. As a challenging prototype of this problem, we have in mind the well-known Netflix problem. Our method is based on the derivation of a constrained gradient system and its numerical integration. The methods we propose are based on the constrained minimization of a functional associated to the low-rank completion matrix having minimal distance to the given matrix. In the main 2-level method, the low-rank matrix is expressed in the form of the non-negative factorization X = εUVT, where the factors U and V are assumed to be normalized with unit Frobenius norm. In the inner level—for a given ε—we minimize the functional; in the outer level, we tune the parameter ε until we reach a solution. Numerical experiments on well-known large test matrices show the effectiveness of the method when compared with other algorithms available in the literature.

中文翻译:

一种非负的低秩完成的有效方法

在本文中,我们提出了一种在非负约束条件下低秩完成大型稀疏矩阵的新方法。作为此问题的具有挑战性的原型,我们考虑了众所周知的Netflix问题。我们的方法基于约束梯度系统的推导及其数值积分。我们提出的方法基于与低阶完成矩阵相关联的函数的约束最小化,该函数与给定矩阵的距离最小。在主2层的方法,所述低秩矩阵在非负因子分解的形式表示X = ε ü V Ť,其中所述因素ùV假设已使用单位Frobenius范数标准化。在内部级别(对于给定的ε),我们将功能最小化;在最外层,我们调整参数ε直到找到一个解。与文献中提供的其他算法相比,在著名的大型测试矩阵上进行的数值实验证明了该方法的有效性。
更新日期:2020-03-23
down
wechat
bug