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- W1921737982 abstract "Matrix sketching schemes and the Nystrom method have both been extensively used to speed up large-scale eigenvalue computation and kernel learning methods. Matrix sketching methods produce accurate matrix approximations, but they are only computationally efficient on skinny matrices where one of the matrix dimensions is relatively small. In particular, they are not efficient on large square matrices. The Nystrom method, on the other hand, is highly efficient on symmetric (and thus square) matrices, but can only achieve low matrix approximation accuracy. In this paper we propose a novel combination of the sketching method and the Nystrom method to improve their efficiency/effectiveness, leading to a novel approximation which we call the Sketch-Nystrom method. The Sketch-Nystrom method is computationally nearly as efficient as the Nystrom method on symmetric matrices with approximation accuracy comparable to that of the sketching method. We show theoretically that the Sketch-Nystrom method can potentially solve eigenvalue problems and kernel learning problems in linear time with respect to the matrix size to achieve $1+epsilon$ relative-error, whereas the sketch methods and the Nystrom method cost at least quadratic time to attain comparable error bound. Our technique can be straightforwardly applied to make the CUR matrix decomposition more efficiently computed without much affecting the accuracy. Empirical experiments demonstrate the effectiveness of the proposed methods." @default.
- W1921737982 created "2016-06-24" @default.
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- W1921737982 date "2015-03-29" @default.
- W1921737982 modified "2023-09-27" @default.
- W1921737982 title "Towards More Efficient Symmetric Matrix Sketching and the CUR Matrix Decomposition" @default.
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