高秩矩阵补全的格拉斯曼代理融合
High Rank Matrix Completion via Grassmannian Proxy Fusion
AI总结：
本文提出一种基于格拉斯曼代理融合的高秩矩阵补全方法，通过聚类和优化子空间距离，提升低采样率下的补全性能。
摘要：
本文通过填充数据矩阵中缺失的条目来处理高秩矩阵补全（HRMC）问题，其中列接近多个子空间的并集，对这些列进行聚类，并识别底层子空间。当前方法往往缺乏理论支持，产生不可解释的结果，并且需要比理论上必要的更多样本。我们提出通过将代理子空间分组来聚类不完整的向量，并在格拉斯曼流形上最小化两个准则：(a) 每个点与其对应子空间之间的弦距离，以及 (b) 所有数据点子空间之间的测地距离。在合成和真实数据集上的实验表明，我们的方法在高采样率下与领先方法表现相当，在低采样率下显著更好，从而缩小了HRMC的理论采样限制与实际性能之间的差距。
英文摘要：
This paper approaches high-rank matrix completion (HRMC) by filling missing entries in a data matrix where columns lie near a union of subspaces, clustering these columns, and identifying the underlying subspaces. Current methods often lack theoretical support, produce uninterpretable results, and require more samples than theoretically necessary. We propose clustering incomplete vectors by grouping proxy subspaces and minimizing two criteria over the Grassmannian: (a) the chordal distance between each point and its corresponding subspace and (b) the geodesic distances between subspaces of all data points. Experiments on synthetic and real datasets demonstrate that our method performs comparably to leading methods in high sampling rates and significantly better in low sampling rates, thus narrowing the gap to the theoretical sampling limit of HRMC.
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。
