Online High Rank Matrix Completion
2019 IEEE/CVF CONFERENCE ON COMPUTER VISION AND PATTERN RECOGNITION (CVPR 2019)(2019)
摘要
Recent advances in matrix completion enable data imputation in full-rank matrices by exploiting low dimensional (nonlinear) latent structure. In this paper, we develop a new model for high rank matrix completion (HRMC), together with batch and online methods to fit the model and out-of-sample extension to complete new data. The method works by (implicitly) mapping the data into a high dimensional polynomial feature space using the kernel trick; importantly, the data occupies a low dimensional subspace in this feature space, even when the original data matrix is of full-rank. The online method can handle streaming or sequential data and adapt to non-stationary latent structure, and enjoys much lower space and time complexity than previous methods for HRMC. For example, the time complexity is reduced from $O(n^3)$ to $O(r^3)$, where $n$ is the number of data points, $r$ is the matrix rank in the feature space, and $r\ll n$. We also provide guidance on sampling rate required for these methods to succeed. Experimental results on synthetic data and motion data validate the performance of the proposed methods.
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关键词
rank matrix completion
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