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arXiv · 1805.09978

Distributed Cartesian Power Graph Segmentation for Graphon Estimation

Shitong Wei·Oscar Hernan Madrid-Padilla·James Sharpnack
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Abstract

We study an extention of total variation denoising over images to over Cartesian power graphs and its applications to estimating non-parametric network models. The power graph fused lasso (PGFL) segments a matrix by exploiting a known graphical structure, $G$, over the rows and columns. Our main results shows that for any connected graph, under subGaussian noise, the PGFL achieves the same mean-square error rate as 2D total variation denoising for signals of bounded variation. We study the use of the PGFL for denoising an observed network $H$, where we learn the graph $G$ as the $K$-nearest neighborhood graph of an estimated metric over the vertices. We provide theoretical and empirical results for estimating graphons, a non-parametric exchangeable network model, and compare to the state of the art graphon estimation methods.

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BibTeXRIS

Shitong Wei, Oscar Hernan Madrid-Padilla, James Sharpnack. 2018-05-25. Distributed Cartesian Power Graph Segmentation for Graphon Estimation. https://arxiv.org/abs/1805.09978

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