Analysis of floating-point round-off error in linear algebra routines for graph clustering

Abstract

We explore the various ways rounding errors can impact the power method for calculating the Fielder vector for graph clustering. A rounding error analysis reveals that the best eigenpair that is computable with a certain floating point precision type has a worst-case error that scales to its unit round-off. Although rounding errors can accumulate in the power method at the worst-case bound, this behavior is not reflected in some practical examples. Furthermore, our numerical experiments show that rounding errors from the power method may satisfy the conditions necessary for the bounding of the mis-clustering rate and that the approximate eigenvectors with errors close to half precision unit round-off can yield sufficient clustering results for partitioning stochastic block model graphs.