The matrix completion problem is restoring a given matrix with missing entries when handling incomplete data. In many existing researches, rank minimization plays a central role in matrix completion. In this paper, noticing that the locally linear reconstruction can be used to approximate the missing entries, we view the problem from a new perspective and propose an algorithm called locally linear approximation (LLA). The LLA method tries to keep the local structure of the data space while restoring the missing entries from row angle and column angle simultaneously. The experimental results have demonstrated the effectiveness of the proposed method.

中文翻译：

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不完整数据的局部线性逼近方法


矩阵补全问题是在处理不完整数据时恢复缺少条目的给定矩阵。在许多现有的研究中，秩最小化在矩阵补全中起着核心作用。在本文中，注意到局部线性重建可以用来近似缺失的条目，我们从一个新的角度看待这个问题，并提出了一种称为局部线性近似（LLA）的算法。 LLA方法试图保持数据空间的局部结构，同时从行角度和列角度恢复丢失的条目。实验结果证明了该方法的有效性。