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Works (12)
Updated: April 5th, 2024 12:15
2024 journal article
A Theoretical Analysis of DeepWalk and Node2vec for Exact Recovery of Community Structures in Stochastic Blockmodels
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 46(2), 1065–1078.
author keywords: Stochastic blockmodel; network embedding; perfect community recovery; node2vec; DeepWalk; matrix factorization
TL;DR:
These results guarantee that with large enough window size and vertex number, applying the matrix factorization-based node2vec embeddings can correctly recover the memberships of all vertices in a network generated from the stochastic blockmodel (or its degree-corrected variants).
(via Semantic Scholar)
Source: Web Of Science
Added: February 12, 2024
2023 journal article
Hypothesis testing for equality of latent positions in random graphs
BERNOULLI, 29(4), 3221–3254.
author keywords: Asymptotic normality; generalized random dot product graphs; model selection; spectral embedding; stochastic block models
TL;DR:
This work considers the hypothesis testing problem that two vertices of a generalized random dot product graph have the same latent positions, possibly up to scaling, and proposes several test statistics based on the empirical Mahalanobis distances between the adjacency or the normalized Laplacian spectral embedding of the graph.
(via Semantic Scholar)
arxiv.org (repository)
Source: Web Of Science
Added: March 18, 2024
2022 article
A statistical interpretation of spectral embedding: The generalised random dot product graph
Rubin-Delanchy, P., Cape, J., Tang, M., & Priebe, C. E. (2022, June 3). JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY.
author keywords: graph embedding; networks; spectral clustering; stochastic block model
TL;DR:
A generalisation of the latent position network model known as the random dot product graph is proposed, to allow interpretation of those vector representations as latent position estimates, and the potential to uncover richer latent structure is uncovered.
(via Semantic Scholar)
Source: Web Of Science
Added: June 13, 2022
2022 journal article
Asymptotically efficient estimators for stochastic blockmodels: The naive MLE, the rank-constrained MLE, and the spectral estimator
BERNOULLI, 28(2), 1049–1073.
author keywords: Asymptotic efficiency; random dot product graph; stochastic blockmodels; asymptotic normality; spectral embedding
TL;DR:
The results indicate, in the context of stochastic blockmodel graphs, that spectral embedding is not just computationally tractable, but that the resulting estimates are also admissible, even when compared to the purportedly optimal but computationally intractable maximum likelihood estimation under no rank assumption.
(via Semantic Scholar)
Source: Web Of Science
Added: March 28, 2022
2022 article
Numerical Tolerance for Spectral Decompositions of Random Matrices and Applications to Network Inference
Athreya, A., Lubberts, Z., Priebe, C. E., Park, Y., Tang, M., Lyzinski, V., … Lewis, B. W. (2022, July 18). JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS.
author keywords: Optimal termination; Spectral decomposition; Statistical error
TL;DR:
It is demonstrated that terminating an eigendecomposition algorithm when the numerical error and statistical error are of the same order results in computational savings with no loss of accuracy.
(via Semantic Scholar)
Source: Web Of Science
Added: July 26, 2022
2022 article
Popularity Adjusted Block Models are Generalized Random Dot Product Graphs
Koo, J., Tang, M., & Trosset, M. W. (2022, June 25). JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS.
author keywords: Block models; Community detection; Generalized random dot product graphs; Network analysis; Sparse subspace clustering
TL;DR:
This work connects two random graph models by demonstrating that the PABM is a special case of the GRDPG in which communities correspond to mutually orthogonal subspaces of latent vectors and derives asymptotic properties of these algorithms.
(via Semantic Scholar)
Source: Web Of Science
Added: July 11, 2022
2022 journal article
Valid two-sample graph testing via optimal transport Procrustes and multiscale graph correlation with applications in connectomics
STAT, 11(1).
author keywords: brain networks; distance correlation; Drosophila mushroom body; random dot product graph
TL;DR:
It is demonstrated that substituting the MMD test with the multiscale graph correlation (MGC) test leads to a more powerful test both in synthetic and in simulated data and there is not sufficient evidence to reject the null hypothesis that the two hemispheres are equally distributed.
(via Semantic Scholar)
Source: Web Of Science
Added: February 14, 2022
2022 article
Vertex Nomination Between Graphs via Spectral Embedding and Quadratic Programming
Zheng, R., Lyzinski, V., Priebe, C. E., & Tang, M. (2022, May 13). JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS.
author keywords: Correlated graphs; Generalized random dot product graphs; Point set registration; Vertex nomination
TL;DR:
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 is proposed and shown to lead to accurate nomination under a generative model.
(via Semantic Scholar)
Source: Web Of Science
Added: May 23, 2022
2021 article
Eigenvalues of Stochastic Blockmodel Graphs and Random Graphs with Low-Rank Edge Probability Matrices
Athreya, A., Cape, J., & Tang, M. (2021, November 3). SANKHYA-SERIES A-MATHEMATICAL STATISTICS AND PROBABILITY.
author keywords: Random graphs; Stochastic blockmodels; Asymptotic normality; Eigenvalues distribution
Source: Web Of Science
Added: November 15, 2021
2021 journal article
On Estimation and Inference in Latent Structure Random Graphs
STATISTICAL SCIENCE, 36(1), 68–88.
author keywords: Latent structure random graphs; manifold learning; spectral graph inference; efficiency
TL;DR:
The latent structure model formulation is used to test bilateral homology in the Drosophila connectome and spectral estimates of the latent positions of an RDPG can be used for efficient estimation of the paramaters of the LSM.
(via Semantic Scholar)
Source: Web Of Science
Added: February 8, 2021
2020 journal article
Central limit theorems for classical multidimensional scaling
ELECTRONIC JOURNAL OF STATISTICS, 14(1), 2362–2394.
author keywords: Classical multidimensional scaling; dissimilarity matrix; perturbation analysis; central limit theorem
TL;DR:
It is shown that the resulting embedding gives rise to a central limit theorem for noisy dissimilarity measurements, and compelling simulation and real data illustration of this CLT for CMDS are provided.
(via Semantic Scholar)
Source: Web Of Science
Added: August 3, 2020
2019 journal article
On spectral embedding performance and elucidating network structure in stochastic blockmodel graphs
NETWORK SCIENCE, 7(3), 269–291.
author keywords: stochastic blockmodel; Laplacian matrix; adjacency matrix; spectral embedding; network structure; core-periphery; Chernoff information
TL;DR:
The findings support the claim that, for a particular notion of sparsity, “Laplacian spectral embedding favors relatively sparse graphs, whereas adjacency spectral embeddedding favors not-too-sparse graphs,” and provide evidence in support of the claims that “adjacency spectral embeding favors core-periphery network structure.”
(via Semantic Scholar)
Source: Web Of Science
Added: November 4, 2019
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