线性模型的凸松弛鲁棒计算
Robust computation of linear models by convex relaxation
摘要：
考虑一个向量值观测数据集，该数据集由噪声内点组成，这些内点可以通过低维子空间很好地解释，还有一些离群点。这项工作描述了一个凸优化问题，称为REAPER，可以可靠地适合这种类型的数据的低维模型。这种方法使用正交投影仪来参数化线性子空间，并且它使用正交投影仪的集合的松弛来达到凸公式。本文给出了求解REAPER问题的一个有效算法，并通过数值实验证实了REAPER算法能够可靠地发现合成数据和自然数据中的线性结构。此外，当内点位于低维子空间附近时，有一个严格的理论描述了REAPER何时可以近似这个子空间。
英文摘要：
Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using orthogonal projectors, and it uses a relaxation of the set of orthogonal projectors to reach the convex formulation. The paper provides an efficient algorithm for solving the REAPER problem, and it documents numerical experiments which confirm that REAPER can dependably find linear structure in synthetic and natural data. In addition, when the inliers lie near a low-dimensional subspace, there is a rigorous theory that describes when REAPER can approximate this subspace.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
