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arXiv · 1209.0001

An Improved Bound for the Nystrom Method for Large Eigengap

Mehrdad Mahdavi·Tianbao Yang·Rong Jin
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Abstract

We develop an improved bound for the approximation error of the Nystr\"{o}m method under the assumption that there is a large eigengap in the spectrum of kernel matrix. This is based on the empirical observation that the eigengap has a significant impact on the approximation error of the Nystr\"{o}m method. Our approach is based on the concentration inequality of integral operator and the theory of matrix perturbation. Our analysis shows that when there is a large eigengap, we can improve the approximation error of the Nystr\"{o}m method from $O(N/m^{1/4})$ to $O(N/m^{1/2})$ when measured in Frobenius norm, where $N$ is the size of the kernel matrix, and $m$ is the number of sampled columns.

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Mehrdad Mahdavi, Tianbao Yang, Rong Jin. 2012-08-30. An Improved Bound for the Nystrom Method for Large Eigengap. https://arxiv.org/abs/1209.0001

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