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Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data
Joel A Tropp · Alp Yurtsever · Madeleine Udell · Volkan Cevher

Tue Dec 05 06:30 PM -- 10:30 PM (PST) @ Pacific Ballroom #20 #None

Several important applications, such as streaming PCA and semidefinite programming, involve a large-scale positive-semidefinite (psd) matrix that is presented as a sequence of linear updates. Because of storage limitations, it may only be possible to retain a sketch of the psd matrix. This paper develops a new algorithm for fixed-rank psd approximation from a sketch. The approach combines the Nyström approximation with a novel mechanism for rank truncation. Theoretical analysis establishes that the proposed method can achieve any prescribed relative error in the Schatten 1-norm and that it exploits the spectral decay of the input matrix. Computer experiments show that the proposed method dominates alternative techniques for fixed-rank psd matrix approximation across a wide range of examples.

Author Information

Joel A Tropp (Caltech)

Joel A. Tropp is Professor of Applied & Computational Mathematics at California Institute of Technology. He earned the Ph.D. degree in Computational Applied Mathematics from the University of Texas at Austin in 2004. Prof. Tropp’s work lies at the interface of applied mathematics, electrical engineering, computer science, and statistics. The bulk of this research concerns the theoretical and computational aspects of sparse approximation, compressive sampling, and randomized linear algebra. He has also worked extensively on the properties of structured random matrices. Prof. Tropp has received several major awards for young researchers, including the 2007 ONR Young Investigator Award and the 2008 Presidential Early Career Award for Scientists and Engineers. He is also winner of the 32nd annual award for Excellence in Teaching from the Associated Students of the California Institute of Technology.

Alp Yurtsever (EPFL)
Madeleine Udell (Cornell)
Volkan Cevher (EPFL)

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