Missing Data Recovery for High-Dimensional Signals With Nonlinear Low-Dimensional Structures
Missing Data Recovery for High-Dimensional Signals With Nonlinear Low-Dimensional Structures
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DOI：
10.1109/tsp.2017.2725227
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发表时间：
2017-10
影响因子：
5.4
通讯作者：
Pengzhi Gao;Meng Wang;J. Chow;M. Berger;Lee M. Seversky
中科院分区：
文献类型：
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作者：
Pengzhi Gao;Meng Wang;J. Chow;M. Berger;Lee M. Seversky
受电力系统监测中缺失数据恢复的启发，本文研究了具有低维非线性结构的高维信号的缺失条目恢复问题。我们提出了一个新的模型，称为“子空间的并和”，来描述实际的非线性数据集。在该模型中，每个数据点要么属于几个低维子空间中的一个，要么属于子空间的子集的总和。在此模型下，我们提出了基于凸优化的缺失条目恢复方法。我们从理论上分析了我们提出的方法在无噪声和有噪声测量下的恢复保证。通过对合成数据和电力系统仿真数据的数值实验，验证了所提方法的有效性。
Motivated by missing data recovery in power system monitoring, we study the problem of recovering missing entries of high-dimensional signals that exhibit low-dimensional nonlinear structures. We propose a novel model, termed as “union and sums of subspaces,” to characterize practical nonlinear datasets. In this model, each data point belongs to either one of a few low-dimensional subspaces or the sum of a subset of subspaces. We propose convex-optimization-based methods to recover missing entries under this model. We theoretically analyze the recovery guarantee of our proposed methods with both noiseless and noisy measurements. Numerical experiments on synthetic data and simulated power system data are conducted to verify the effectiveness of the proposed methods.