Co-clustering of Nonsmooth Graphons

TL;DR

This paper establishes performance bounds for co-clustering bipartite graph data generated from nonsmooth graphons, demonstrating the theoretical accuracy of blockmodel approximations in population settings.

Contribution

It provides the first theoretical bounds for co-clustering methods applied to nonsmooth graphons, including extensions to degree-corrected models and random dot product graphs.

Findings

Co-clusters can be extended to population-level distributions.

Estimated blockmodels approximate the true graphon with error $O_P(n^{-1/2})$.

Performance bounds depend on latent space dimensionality.

Abstract

Performance bounds are given for exploratory co-clustering/ blockmodeling of bipartite graph data, where we assume the rows and columns of the data matrix are samples from an arbitrary population. This is equivalent to assuming that the data is generated from a nonsmooth graphon. It is shown that co-clusters found by any method can be extended to the row and column populations, or equivalently that the estimated blockmodel approximates a blocked version of the generative graphon, with estimation error bounded by $O_P(n^{-1/2})$. Analogous performance bounds are also given for degree-corrected blockmodels and random dot product graphs, with error rates depending on the dimensionality of the latent variable space.