
On estimation and inference in latent structure random graphs
We define a latent structure model (LSM) random graph as a random dot pr...
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Link prediction in dynamic networks using random dot product graphs
The problem of predicting links in large networks is a crucial task in a...
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Spectral embedding for dynamic networks with stability guarantees
We consider the problem of embedding a dynamic network, to obtain timee...
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Statistical inference on random dot product graphs: a survey
The random dot product graph (RDPG) is an independentedge random graph ...
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Outofsample extension of graph adjacency spectral embedding
Many popular dimensionality reduction procedures have outofsample exte...
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BiasVariance Tradeoffs in Joint Spectral Embeddings
Latent position models and their corresponding estimation procedures off...
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Learning Gridlike Units with Vector Representation of SelfPosition and Matrix Representation of SelfMotion
This paper proposes a model for learning gridlike units for spatial awa...
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The multilayer random dot product graph
We present an extension of the latent position network model known as the generalised random dot product graph to accommodate multiple graphs with a common node structure, based on a matrix representation of the natural thirdorder tensor created from the adjacency matrices of these graphs. Theoretical results concerning the asymptotic behaviour of the node representations obtained by spectral embedding are established, showing that after the application of a linear transformation these converge uniformly in the Euclidean norm to the latent positions with a Gaussian error. The flexibility of the model is demonstrated through application to the tasks of latent position recovery and twograph hypothesis testing, in which it performs favourably compared to existing models. Empirical improvements in link prediction over single graph embeddings are exhibited in a cybersecurity example.
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