Publication

Fixed-Rank Approximation of a Positive-Semidefinite Matrix from Streaming Data

Volkan Cevher, Alp Yurtsever
2017
Conference Papers

Abstract

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 Nystrom 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.

Official source

https://infoscience.epfl.ch/entities/publication/75d6930b-463a-4411-a162-a4012c15810b

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Volkan Cevher, Alp Yurtsever
2017
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/75d6930b-463a-4411-a162-a4012c15810b

About this result

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Eigenvalues and eigenvectors

In linear algebra, an eigenvector (ˈaɪgənˌvɛktər) or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is applied to it. The corresponding eigenvalue, often represented by , is the multiplying factor. Geometrically, a transformation matrix rotates, stretches, or shears the vectors it acts upon. The eigenvectors for a linear transformation matrix are the set of vectors that are only stretched, with no rotation or shear.

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