Online high-rank matrix completion

Abstract

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(n3) to O(r3), where n is the number of data points, r is the matrix rank in the feature space, and r ≪ 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.

Publication
CVPR 2019 (oral)
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Jicong Fan
Research Assistant Professor

My research interests include machine learning, computer vision, and optimization.