Simultaneous Dimensionality and Complexity Model Selection for Spectral Graph Clustering

Yang, Congyuan; Priebe, Carey E.; Park, Youngser; Marchette, David J.

doi:10.48550/arxiv.1904.02926

Cited by 2 publications

(3 citation statements)

References 62 publications

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“…k is used in this paper. Additionally, as a second di erence from Yang et al (2019), the full model proposed here will also incorporate a second-level community cluster structure on these vectors of variances, which will be introduced in Section 5.…”

Section: A Bayesian Model For Sbm Embeddingsmentioning

confidence: 99%

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Bayesian estimation of the latent dimension and communities in stochastic blockmodels

Passino,

Heard

2019

Preprint

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Spectral embedding of adjacency or Laplacian matrices of undirected graphs is a common technique for representing a network in a lower dimensional latent space, with optimal theoretical guarantees. The embedding can be used to estimate the community structure of the network, with strong consistency results in the stochastic blockmodel framework. One of the main practical limitations of standard algorithms for community detection from spectral embeddings is that the number of communities and the latent dimension of the embedding must be speci ed in advance. In this article, a novel Bayesian model for simultaneous and automatic selection of the appropriate dimension of the latent space and the number of blocks is proposed. Extensions to directed and bipartite graphs are discussed. The model is tested on simulated and real world network data, showing promising performance for recovering latent community structure.

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Section: A Bayesian Model For Sbm Embeddingsmentioning

confidence: 99%

“…The method is tested on simulated data and applied to real world computer and transportation networks. It should be noted that Yang et al (2019) have simultaneously and independently proposed a similar inferential procedure within a frequentist framework.…”

Section: Introductionmentioning

confidence: 99%

Bayesian estimation of the latent dimension and communities in stochastic blockmodels

Passino,

Heard

2019

Preprint

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“…After the first four greatest eigenvalues, the rest are small enough to cause Λ to produce behavior similar to that which a lower rank matrix would produce. Rigorous analysis of the optimal embedding dimension is beyond the scope of this present paper; see [61] for principled methodology.…”

Section: More Simulation Experimentsmentioning

confidence: 99%

Vertex nomination: The canonical sampling and the extended spectral nomination schemes

Yoder¹,

Chen²,

Pao³

et al. 2018

Preprint

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Suppose that one particular block in a stochastic block model is of interest, but block labels are only observed for a few of the vertices in the network. Utilizing a graph realized from the model and the observed block labels, the vertex nomination task is to order the vertices with unobserved block labels into a ranked nomination list with the goal of having an abundance of interesting vertices near the top of the list. There are vertex nomination schemes in the literature, including the optimally precise canonical nomination scheme L C and the consistent spectral partitioning nomination scheme L P . While the canonical nomination scheme L C is provably optimally precise, it is computationally intractable, being impractical to implement even on modestly sized graphs.With this in mind, an approximation of the canonical scheme-denoted the canonical sampling nomination scheme L CS -is introduced; L CS relies on a scalable, Markov chain Monte Carlo-based approximation of L C , and converges to L C as the amount of sampling goes to infinity. The spectral partitioning nomination scheme is also extended to the extended spectral partitioning nomination scheme, L EP , which introduces a novel semisupervised clustering framework to improve upon the precision of L P . Real-data and simulation experiments are employed to illustrate the precision of these vertex nomination schemes, as well as their empirical computational complexity.

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Simultaneous Dimensionality and Complexity Model Selection for Spectral Graph Clustering

Cited by 2 publications

References 62 publications

Bayesian estimation of the latent dimension and communities in stochastic blockmodels

Bayesian estimation of the latent dimension and communities in stochastic blockmodels

Vertex nomination: The canonical sampling and the extended spectral nomination schemes

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