Sampling Techniques For The Nystrom Method

Abstract

The Nystrom method is an efficient technique to generate low-rank matrix approximations and is used in several large-scale learning applications. A key aspect of this method is the distribution according to which columns are sampled from the original matrix. In this work, we present an analysis of different sampling techniques for the Nystrom method. Our analysis includes both empirical and theoretical components. We first present novel experiments with several real world datasets, comparing the performance of the Nystrom method when used with uniform versus non-uniform sampling distributions. Our results suggest that uniform sampling without replacement, in addition to being more efficient both in time and space, produces more effective approximations. This motivates the theoretical part of our analysis which gives the first performance bounds for the Nystrom method precisely when used with uniform sampling without replacement.