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The Nystrom method is a popular technique that uses a small number oflandmark points to compute a fixed-rank approximation of large kernel matricesthat arise in machine learning problems. In practice, to ensure high qualityapproximations, the number of landmark points is chosen to be greater than thetarget rank. However, for simplicity the standard Nystrom method uses asub-optimal procedure for rank reduction. In this paper, we examine thedrawbacks of the standard Nystrom method in terms of poor performance and lackof theoretical guarantees. To address these issues, we present an efficientmodification for generating improved fixed-rank Nystrom approximations.Theoretical analysis and numerical experiments are provided to demonstrate theadvantages of the modified method over the standard Nystrom method. Overall,the aim of this paper is to convince researchers to use the modified method, asit has nearly identical computational complexity, is easy to code, has greatlyimproved accuracy in many cases, and is optimal in a sense that we makeprecise.

Improved Fixed-Rank Nystr\"om Approximation via QR Decomposition: Practical and Theoretical Aspects