A Limit Theorem for Scaled Eigenvectors of Random Dot Product Graphs

被引：0

作者：

Athreya A. ^{[1
]}

Priebe C.E. ^{[1
]}

Tang M. ^{[1
]}

Lyzinski V. ^{[2
]}

Marchette D.J. ^{[3
]}

Sussman D.L. ^{[4
]}

机构：

[1] Department of Applied Mathematics and Statistics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, 21218, MD

[2] Human Language Technology Center of Excellence, Johns Hopkins University, Stieff Building, 810 Wyman Park Drive, Baltimore, 21211, MD

[3] Naval Surface Warfare Center, 17320 Dahlgren Road, Dahlgren, 22448, VA

[4] Department of Statistics, Harvard University, Science Center, Floor 7, One Oxford St, Cambridge, 02138, MA

来源：

Sankhya A | 2016年 / 78卷 / 1期

关键词：

Random dot product graph; Central limit theorem; Model-based clustering; Primary 62E20; Secondary 05C80; 60F05;

D O I：

10.1007/s13171-015-0071-x

中图分类号：

学科分类号：

摘要：

We prove a central limit theorem for the components of the largest eigenvectors of the adjacency matrix of a finite-dimensional random dot product graph whose true latent positions are unknown. We use the spectral embedding of the adjacency matrix to construct consistent estimates for the latent positions, and we show that the appropriately scaled differences between the estimated and true latent positions converge to a mixture of Gaussian random variables. We state several corollaries, including an alternate proof of a central limit theorem for the first eigenvector of the adjacency matrix of an Erdos-Rényi random graph. © 2015, Indian Statistical Institute.

引用

页码：1 / 18

页数：17

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