论文标题
统一的优化框架，用于低级诱发惩罚
A Unified Optimization Framework for Low-Rank Inducing Penalties
论文作者
论文摘要
在本文中，我们研究了新功能的凸信封。使用这种方法，我们能够从公正的非凸式制剂和加权核定常惩罚中统一两个重要的正规化器类别。这为结合两全其美的可能性开放，并利用每种方法在仅执行其中一名正规机构不足的情况下做出的贡献。 我们表明，提出的正规化器可以纳入标准分裂方案中，例如乘数的交替方向方法（ADMM）和其他亚级别方法。此外，我们提供了一种计算近端运算符的有效方法。 最后，我们显示了实际的非刚性结构 - 触发器（NRSFM）数据集，这些问题是使用加权核标准惩罚引起的问题，以及如何使用我们提出的方法对此进行修复。
In this paper we study the convex envelopes of a new class of functions. Using this approach, we are able to unify two important classes of regularizers from unbiased non-convex formulations and weighted nuclear norm penalties. This opens up for possibilities of combining the best of both worlds, and to leverage each methods contribution to cases where simply enforcing one of the regularizers are insufficient. We show that the proposed regularizers can be incorporated in standard splitting schemes such as Alternating Direction Methods of Multipliers (ADMM), and other subgradient methods. Furthermore, we provide an efficient way of computing the proximal operator. Lastly, we show on real non-rigid structure-from-motion (NRSfM) datasets, the issues that arise from using weighted nuclear norm penalties, and how this can be remedied using our proposed method.
