论文标题
非convex正规化器的秩最小化的低级别分解
Low-Rank Factorization for Rank Minimization with Nonconvex Regularizers
论文作者
论文摘要
最小化是在机器学习应用中感兴趣的，例如推荐系统和可靠的主组件分析。将凸的放松最小化到最小化问题，即核定常，是一种有效的技术，可以通过强大的性能保证来解决该问题。但是，非凸弛豫的估计偏差较小，而不是核定常，并且可以更准确地降低噪声对测量的影响。 我们基于迭代重量重量的核标准方案开发了有效的算法，同时还利用Burer和Monteiro提出的半决赛计划的低等级分解。我们证明了收敛性并在计算上显示了优于凸松弛和交替最小化方法的优势。此外，我们算法的每种迭代的计算复杂性与其他最先进的算法相当，从而使我们能够快速找到解决大矩阵秩最小化问题的解决方案。
Rank minimization is of interest in machine learning applications such as recommender systems and robust principal component analysis. Minimizing the convex relaxation to the rank minimization problem, the nuclear norm, is an effective technique to solve the problem with strong performance guarantees. However, nonconvex relaxations have less estimation bias than the nuclear norm and can more accurately reduce the effect of noise on the measurements. We develop efficient algorithms based on iteratively reweighted nuclear norm schemes, while also utilizing the low rank factorization for semidefinite programs put forth by Burer and Monteiro. We prove convergence and computationally show the advantages over convex relaxations and alternating minimization methods. Additionally, the computational complexity of each iteration of our algorithm is on par with other state of the art algorithms, allowing us to quickly find solutions to the rank minimization problem for large matrices.
