1,323 research outputs found
Universally Consistent Latent Position Estimation and Vertex Classification for Random Dot Product Graphs
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. from some distribution. If
class labels are observed for a number of vertices tending to infinity, then we
show that the remaining vertices can be classified with error converging to
Bayes optimal using the -nearest-neighbors classification rule. We evaluate
the proposed methods on simulated data and a graph derived from Wikipedia
A nonparametric two-sample hypothesis testing problem for random dot product graphs
We consider the problem of testing whether two finite-dimensional random dot
product graphs have generating latent positions that are independently drawn
from the same distribution, or distributions that are related via scaling or
projection. We propose a test statistic that is a kernel-based function of the
adjacency spectral embedding for each graph. We obtain a limiting distribution
for our test statistic under the null and we show that our test procedure is
consistent across a broad range of alternatives.Comment: 24 pages, 1 figure
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