Low-Rank Matrix Estimation From Rank-One Projections by Unlifted Convex Optimization

Sohail Bahmani; Kiryung Lee

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arXiv · 2004.02718

Low-Rank Matrix Estimation From Rank-One Projections by Unlifted Convex Optimization

Sohail Bahmani·Kiryung Lee

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Abstract

We study an estimator with a convex formulation for recovery of low-rank matrices from rank-one projections. Using initial estimates of the factors of the target $d_1\times d_2$ matrix of rank-$r$, the estimator admits a practical subgradient method operating in a space of dimension $r(d_1+d_2)$. This property makes the estimator significantly more scalable than the convex estimators based on lifting and semidefinite programming. Furthermore, we present a streamlined analysis for exact recovery under the real Gaussian measurement model, as well as the partially derandomized measurement model by using the spherical $t$-design. We show that under both models the estimator succeeds, with high probability, if the number of measurements exceeds $r^2 (d_1+d_2)$ up to some logarithmic factors. This sample complexity improves on the existing results for nonconvex iterative algorithms.

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BibTeX RIS

Sohail Bahmani, Kiryung Lee. 2020-04-06. Low-Rank Matrix Estimation From Rank-One Projections by Unlifted Convex Optimization. https://arxiv.org/abs/2004.02718

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