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Riemannian optimization with subspace tracking for low-rank recovery | IEEE Conference Publication | IEEE Xplore

Riemannian optimization with subspace tracking for low-rank recovery


Abstract:

Low-rank matrix recovery (MR) has been widely used in data analysis and dimensionality reduction. As a direct heuristic to MR, convex relaxation is usually degraded by th...Show More

Abstract:

Low-rank matrix recovery (MR) has been widely used in data analysis and dimensionality reduction. As a direct heuristic to MR, convex relaxation is usually degraded by the repeated calling of singular value decomposition (SVD), especially in large-scale applications. In this paper, we propose a novel Riemannian optimization method (ROAM) for MR problem by exploiting the Riemannian geometry of the searching space. In particular, ROAM utilizes an efficient subspace tracking schema that automatically detects the unknown rank to identify the preferable geometry space. Moreover, a gradient-based optimization algorithm is proposed to obtain the latent low-rank component, which avoids the expensive full dimension of SVD. More significantly, ROAM algorithm is proved to converge under mild assumptions, which also verifies the effectiveness of ROAM. Extensive empirical results demonstrate the improved accuracy and efficiency of ROAM over convex-relaxation approaches.
Date of Conference: 24-29 July 2016
Date Added to IEEE Xplore: 03 November 2016
ISBN Information:
Electronic ISSN: 2161-4407
Conference Location: Vancouver, BC, Canada

References

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