
A consistent adjacency spectral embedding for stochastic blockmodel graphs
We present a method to estimate block membership of nodes in a random gr...
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The multilayer random dot product graph
We present an extension of the latent position network model known as th...
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Latent structure blockmodels for Bayesian spectral graph clustering
Spectral embedding of network adjacency matrices often produces node rep...
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Outofsample extension of graph adjacency spectral embedding
Many popular dimensionality reduction procedures have outofsample exte...
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Semiparametric spectral modeling of the Drosophila connectome
We present semiparametric spectral modeling of the complete larval Droso...
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Spectral embedding of regularized block models
Spectral embedding is a popular technique for the representation of grap...
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Multilayer Graph Clustering with Optimized Node Embedding
We are interested in multilayer graph clustering, which aims at dividing...
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Spectral embedding for dynamic networks with stability guarantees
We consider the problem of embedding a dynamic network, to obtain timeevolving vector representations of each node, which can then be used to describe the changes in behaviour of a single node, one or more communities, or the entire graph. Given this openended remit, we wish to guarantee stability in the spatiotemporal positioning of the nodes: assigning the same position, up to noise, to nodes behaving similarly at a given time (crosssectional stability) and a constant position, up to noise, to a single node behaving similarly across different times (longitudinal stability). These properties are defined formally within a generic dynamic latent position model. By showing how this model can be recast as a multilayer random dot product graph, we demonstrate that unfolded adjacency spectral embedding satisfies both stability conditions, allowing, for example, spatiotemporal clustering under the dynamic stochastic block model. We also show how alternative methods, such as omnibus, independent or timeaveraged spectral embedding, lack one or the other form of stability.
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