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arXiv · 1910.09092

Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion

Dimitris Bertsimas·Michael Lingzhi Li
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Abstract

We formulate the problem of matrix completion with and without side information as a non-convex optimization problem. We design fastImpute based on non-convex gradient descent and show it converges to a global minimum that is guaranteed to recover closely the underlying matrix while it scales to matrices of sizes beyond $10^5 \times 10^5$. We report experiments on both synthetic and real-world datasets that show fastImpute is competitive in both the accuracy of the matrix recovered and the time needed across all cases. Furthermore, when a high number of entries are missing, fastImpute is over $75\%$ lower in MAPE and $15$ times faster than current state-of-the-art matrix completion methods in both the case with side information and without.

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BibTeXRIS

Dimitris Bertsimas, Michael Lingzhi Li. 2019-10-21. Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion. https://arxiv.org/abs/1910.09092

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