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CO-CLUSTERING SEPARATELY EXCHANGEABLE NETWORK DATA
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DOI：10.1214/13-AOS1173.png)
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Abstract
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This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the condition of separate exchangeability. We provide oracle inequalities with rate of convergence O-P(n(-1/4)) corresponding to profile likelihood maximization and mean-square error minimization, and show that the blockmodel can be interpreted in this setting as an optimal piecewise-constant approximation to the generative nonparametric model. We also show for large sample sizes that the detection of co-clusters in such data indicates with high probability the existence of co-clusters of equal size and asymptotically equivalent connectivity in the underlying generative process.
Keywords:
Bipartite graph
network clustering
oracle inequality
profile likelihood
statistical network analysis
stochastic blockmodel and co-blockmodel
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