
Vertex Nomination, Consistent Estimation, and Adversarial Modification
Given a pair of graphs G_1 and G_2 and a vertex set of interest in G_1, ...
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Simultaneous Embedding of Colored Graphs
A set of colored graphs are compatible, if for every color i, the number...
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A Note on Toroidal MaxwellCremona Correspondences
We explore toroidal analogues of the MaxwellCremona correspondence. Eri...
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Change Detection in Noisy Dynamic Networks: A Spectral Embedding Approach
Change detection in dynamic networks is an important problem in many are...
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Vertex nomination: The canonical sampling and the extended spectral nomination schemes
Suppose that one particular block in a stochastic block model is deemed ...
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A Triclustering Approach for Time Evolving Graphs
This paper introduces a novel technique to track structures in time evol...
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Outofsample Extension for Latent Position Graphs
We consider the problem of vertex classification for graphs constructed ...
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Vertex nomination between graphs via spectral embedding and quadratic programming
Given a network and a subset of interesting vertices whose identities are only partially known, the vertex nomination problem seeks to rank the remaining vertices in such a way that the interesting vertices are ranked at the top of the list. An important variant of this problem is vertex nomination in the multigraphs setting. Given two graphs G_1, G_2 with common vertices and a vertex of interest x ∈ G_1, we wish to rank the vertices of G_2 such that the vertices most similar to x are ranked at the top of the list. The current paper addresses this problem and proposes a method that first applies adjacency spectral graph embedding to embed the graphs into a common Euclidean space, and then solves a penalized linear assignment problem to obtain the nomination lists. Since the spectral embedding of the graphs are only unique up to orthogonal transformations, we present two approaches to eliminate this potential nonidentifiability. One approach is based on orthogonal Procrustes and is applicable when there are enough vertices with known correspondence between the two graphs. Another approach uses adaptive point set registration and is applicable when there are few or no vertices with known correspondence. We show that our nomination scheme leads to accurate nomination under a generative model for pairs of random graphs that are approximately lowrank and possibly with pairwise edge correlations. We illustrate our algorithm's performance through simulation studies on synthetic data as well as analysis of a highschool friendship network and analysis of transition rates between web pages on the Bing search engine.
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