A spectral method for community detection in moderately sparse degree-corrected stochastic block models

Gulikers, Lennart; Lelarge, Marc; Massoulié, Laurent

doi:10.1017/apr.2017.18

Cited by 48 publications

(34 citation statements)

References 32 publications

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“…Empirically, the larger class of DCBMs is able to provide possibly much better fits to many real world network datasets [23]. Since the proposal of the model, there have been various methods proposed for community detection in DCBMs, including but not limited to spectral clustering [24,18,15,11] and modularity based approaches [17,28,3,5]. On the theoretical side, [10] provides an information-theoretic characterization of the impossibility region of community detection for DCBMs with two clusters, and sufficient conditions have been given in [28,5] for strongly and weakly consistent community detection.…”

Section: Introductionmentioning

confidence: 99%

Community detection in degree-corrected block models

Gao¹,

Ma²,

Zhang³

et al. 2018

Ann. Statist.

120

102

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Community detection is a central problem of network data analysis. Given a network, the goal of community detection is to partition the network nodes into a small number of clusters, which could often help reveal interesting structures. The present paper studies community detection in Degree-Corrected Block Models (DCBMs). We first derive asymptotic minimax risks of the problem for a misclassification proportion loss under appropriate conditions. The minimax risks are shown to depend on degree-correction parameters, community sizes, and average within and between community connectivities in an intuitive and interpretable way. In addition, we propose a polynomial time algorithm to adaptively perform consistent and even asymptotically optimal community detection in DCBMs.

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Section: Introductionmentioning

confidence: 99%

Community detection in degree-corrected block models

Gao¹,

Ma²,

Zhang³

et al. 2018

Ann. Statist.

120

102

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“…Clustering is asymptotically trivial when the weights C ab differ by O(1), as a vanishing error classification rate is easily guaranteed [6]. We shall instead consider the regime where the clustering performance is not asymptotically perfect.…”

Section: A Model and Assumptionsmentioning

confidence: 99%

Random matrix improved community detection in heterogeneous networks

Ali¹,

Couillet²

2016

2016 50th Asilomar Conference on Signals, Systems and Computers

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Abstract-This article proposes a new spectral method for community detection in large dense networks following the degree-corrected stochastic block model. We theoretically support and analyze an approach based on a novel "α-regularization" of the modularity matrix. We provide a consistent estimator for the choice of α inducing the most favorable community detection in worst case scenarios. We further prove that spectral clustering ought to be performed on a 1 − α regularization of the dominant eigenvectors (rather than on the eigenvectors themselves) to compensate for biases due to degree heterogeneity. Although focused on dense graph models, our clustering method is shown to be very promising on real world networks with competitive performances versus state-of-the-art spectral techniques developed for sparse homogeneous networks.

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“…We thus consider here the non-trivial regime where C ab = O(1) but differ only by O(n − 1 2 ). Spectral clustering on the adjacency matrix of a DC-SBM however fails to cluster the nodes as the leading eigenvectors tend to follow a mixture of the degree distribution and class-wise canonical vectors, instead of purely aligning to the latter, therefore leading to ambiguities in classification and a trend to over-clustering (see top of Figure 1 and [7]). We thus work here on a normalized version L of the adjacency (precisely the modularity) matrix defined, for 1 We shall see (as already observed in [7]) that the dominant eigenvectors of L are strongly aligned to the class-wise canonical eigenvectors, thus recover the lost clustering ability of A (see bottom of Figure 1).…”

Section: Introductionmentioning

confidence: 99%

Performance analysis of spectral community detection in realistic graph models

Tiomokoali

Couillet

2016

2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This article proposes a spectral analysis of dense random graphs generated by (a modified version of) the degree-corrected stochastic block model, for a setting where the inter block probabilities differ by O(n − 1 2) with n the number of nodes. We study a normalized version of the graph modularity matrix which is shown to be asymptotically well approximated by an analytically tractable (spiked) random matrix. The analysis of the latter allows for the precise evaluation of (i) the transition phase where clustering becomes asymptotically feasible and (ii) the alignment between the dominant eigenvectors and the block-wise canonical basis, thus enabling the estimation of misclassification rates (prior to post-processing) in simple scenarios.

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A spectral method for community detection in moderately sparse degree-corrected stochastic block models

Cited by 48 publications

References 32 publications

Community detection in degree-corrected block models

Community detection in degree-corrected block models

Random matrix improved community detection in heterogeneous networks

Performance analysis of spectral community detection in realistic graph models

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