The Annals of Statistics

Co-clustering of nonsmooth graphons

David Choi

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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.

Article information

Source
Ann. Statist., Volume 45, Number 4 (2017), 1488-1515.

Dates
Received: July 2015
Revised: March 2016
First available in Project Euclid: 28 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.aos/1498636864

Digital Object Identifier
doi:10.1214/16-AOS1497

Mathematical Reviews number (MathSciNet)
MR3670186

Zentralblatt MATH identifier
06773281

Subjects
Primary: 62G05: Estimation
Secondary: 05C80: Random graphs [See also 60B20] 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52)

Keywords
Graphon bipartite graph co-clustering statistical network analysis stochastic blockmodel degree-corrected blockmodel random dot product graph

Citation

Choi, David. Co-clustering of nonsmooth graphons. Ann. Statist. 45 (2017), no. 4, 1488--1515. doi:10.1214/16-AOS1497. https://projecteuclid.org/euclid.aos/1498636864


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Supplemental materials

  • Supplement to “Co-clustering of nonsmooth graphons”. The supplementary material contains a proof of Lemma 7 and Theorem 2.