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In this work we show that, using the eigen-decomposition of the adjacency matrix, we can consistently estimate latent positions for random dot product graphs provided the latent positions are i.i.d.
The rotation of eigenvectors by a pertubation. III
C. Davis and W. Kahan · 1970
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Consistent nonparametric regression
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D.J. Aldous · 1981
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P. W. Holland, K. Laskey, and S. Leinhardt · 1983
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A probabilistic theory of pattern recognition
L. Devroye, L. Györfi, and G. Lugosi · 1996
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Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure
T. A. B. Snijders and K. Nowicki · 1997
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Latent Space Approaches to Social Network Analysis
P. D. Hoff, A. E. Raftery, and M. S. Handcock · 2002
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E. M. Airoldi, D. M. Blei, S. E. Fienberg, and E. P. Xing · 2008
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Concentration of the adjacency matrix and of the laplacian in random graphs with independent edges
R. I. Oliveira · 2009
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The method of moments and degree distributions for network models
P. J. Bickel, A. Chen, and E. Levina · 2011
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Vertex nomination via attributed random dot product graphs
D. Marchette, C. E. Priebe, and G. Coppersmith · 2011
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Spectral clustering and the high-dimensional stochastic blockmodel
K. Rohe, S. Chatterjee, and B. Yu · 2011
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Stochastic blockmodels with a growing number of classes
D. S. Choi, P. J. Wolfe, and E. M. Airoldi · 2012
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A nonparametric view of network models and Newman-Girvan and other modularities
P. J. Bickel and A. Chen · 2009
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A consistent adjacency spectral embedding for stochastic blockmodel graphs
D. L. Sussman, M. Tang, D. E. Fishkind, and C. E. Priebe
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D. E. Fishkind, D. L. Sussman, M. Tang, J.T. Vogelstein, and C.E. Priebe · 2012
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Z. Ma, D. J. Marchette, and C. E. Priebe · 2012
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