The naive Nystrom extension forms a low-rank approximation to a positive-semidefinite matrix by uniformly randomly sampling from its columns. This paper provides the first relative-error bound on the spectral norm error incurred in this process. This bound follows from a natural connection between the Nystrom extension and the column subset selection problem. The main tool is a matrix Chernoff bound for sampling without replacement.
Categories: math.NA cs.NA
