论文标题
低级矩阵完成理论通过PLUCKER坐标
Low-rank matrix completion theory via Plucker coordinates
论文作者
论文摘要
尽管低级矩阵的完成程度很高，但其大多数理论还是在随机观察模式的假设下开发了，而对实际相关的非随机模式的情况知之甚少。具体而言，一个基本但大量开放的问题是描述允许独特或有限完成的模式。本文为任何等级提供了两个这样的模式系列。实现这一目标的关键是一种新颖的表述，以拔出器坐标为角度，这是计算机视觉中的传统工具。这种连接对于具有不完整数据的广泛矩阵和子空间学习问题具有潜在的意义。
Despite the popularity of low-rank matrix completion, the majority of its theory has been developed under the assumption of random observation patterns, whereas very little is known about the practically relevant case of non-random patterns. Specifically, a fundamental yet largely open question is to describe patterns that allow for unique or finitely many completions. This paper provides two such families of patterns for any rank. A key to achieving this is a novel formulation of low-rank matrix completion in terms of Plucker coordinates, the latter a traditional tool in computer vision. This connection is of potential significance to a wide family of matrix and subspace learning problems with incomplete data.
