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August 2017 Co-clustering of nonsmooth graphons
David Choi
Ann. Statist. 45(4): 1488-1515 (August 2017). DOI: 10.1214/16-AOS1497

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.

Citation

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David Choi. "Co-clustering of nonsmooth graphons." Ann. Statist. 45 (4) 1488 - 1515, August 2017. https://doi.org/10.1214/16-AOS1497

Information

Received: 1 July 2015; Revised: 1 March 2016; Published: August 2017
First available in Project Euclid: 28 June 2017

zbMATH: 06773281
MathSciNet: MR3670186
Digital Object Identifier: 10.1214/16-AOS1497

Subjects:
Primary: 62G05
Secondary: 05C80 , 60B20

Keywords: Bipartite graph , co-clustering , degree-corrected blockmodel , graphon , random dot product graph , statistical network analysis , stochastic blockmodel

Rights: Copyright © 2017 Institute of Mathematical Statistics

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Vol.45 • No. 4 • August 2017
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