Random matrix improved community detection in heterogeneous networks

Ali, Hafiz Tiomoko; Couillet, Romain

doi:10.1109/acssc.2016.7869603

Cited by 9 publications

(20 citation statements)

References 10 publications

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“…In Ali & Couillet (2018), the authors studied the existence of an optimal value α opt of the parameter α for community detection methods based on D −α AD −α . Recall that our SRSC and CRSC are designed based on…”

Section: Discussionmentioning

confidence: 99%

Impact of regularization on spectral clustering under the mixed membership stochastic block model

Qing,

Wang

2021

Preprint

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Mixed membership community detection is a challenge problem in network analysis. To estimate the memberships and study the impact of regularized spectral clustering under the mixed membership stochastic block (MMSB) model, this article proposes two efficient spectral clustering approaches based on regularized Laplacian matrix, Simplex Regularized Spectral Clustering (SRSC) and Cone Regularized Spectral Clustering (CRSC). SRSC and CRSC methods are designed based on the ideal simplex structure and the ideal cone structure in the variants of the eigendecomposition of the population regularized Laplacian matrix. We show that these two approaches SRSC and CRSC are asymptotically consistent under mild conditions by providing error bounds for the inferred membership vector of each node under MMSB. Through the theoretical analysis, we give the upper and lower bound for the regularizer τ . By introducing a parametric convergence probability, we can directly see that when τ is large these two methods may still have low error rates but with a smaller probability. Thus we give an empirical optimal choice of τ is O(log(n)) with n the number of nodes to detect sparse networks. The proposed two approaches are successfully applied to synthetic and empirical networks with encouraging results compared with some benchmark methods.

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Section: Discussionmentioning

confidence: 99%

Impact of regularization on spectral clustering under the mixed membership stochastic block model

Qing,

Wang

2021

Preprint

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“…It remains unsolved that whether there exists optimal parameter τ both theoretically and numerically. In [2], the authors studied the existence of an optimal value α opt of the parameter α for community detection methods based on D −α AD −α for community detection problem. Recall that our Mixed-ISC is designed based on…”

Section: Discussionmentioning

confidence: 99%

“…Consider an undirected, unweighted, no-self-loop network N and assume that there are K disjoint blocks C (1) , C (2) , . .…”

Section: Settings and Modelmentioning

confidence: 99%

An improved spectral clustering method for mixed membership community detection

Qing,

Wang

2020

Preprint

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Community detection has been well studied recent years, but the more realistic case of mixed membership community detection remains a challenge. Here, we develop an efficient spectral algorithm Mixed-ISC based on applying more than K eigenvectors for clustering given K communities for estimating the community memberships under the degree-corrected mixed membership (DCMM) model. We show that the algorithm is asymptotically consistent. Numerical experiments on both simulated networks and many empirical networks demonstrate that Mixed-ISC performs well compared to a number of benchmark methods for mixed membership community detection. Especially, Mixed-ISC provides satisfactory performances on weak signal networks.

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“…Guarantees independent of the coherence can be obtained for more advanced sampling methods. Perhaps the most well known method is that of leverage scores, where one draws m samples independently by selecting (with replacement) the i-th column with probability p i = V k (i, :) 2 2 /k, called leverage scores. Theorem 3.2 (Lemma 5 for q = 1 in [54]).…”

Section: Nyström-based Methodsmentioning

confidence: 99%

“…Let us denote by D the diagonal degree matrix such that D(i, i) = ∑ j W(i, j) is the (weighted) degree of node i. We define the combinatorial graph Laplacian matrix L = D − W, the normalized graph Laplacian matrix L n = I − D −1/2 WD −1/2 , and the random walk Laplacian L rw = I − D −1 W. Other popular choices include 3 the non-backtracking matrix [73], degree-corrected versions of the modularity matrix [2], the Bethe-Hessian matrix [114] or similar deformed Laplacians [34].…”

Section: Spectral Clusteringmentioning

confidence: 99%

Approximating Spectral Clustering via Sampling: A Review

Tremblay

Loukas

2019

Unsupervised and Semi-Supervised Learning

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Spectral clustering refers to a family of unsupervised learning algorithms that compute a spectral embedding of the original data based on the eigenvectors of a similarity graph. This non-linear transformation of the data is both the key of these algorithms' success and their Achilles heel: forming a graph and computing its dominant eigenvectors can indeed be computationally prohibitive when dealing with more that a few tens of thousands of points. In this paper, we review the principal research efforts aiming to reduce this computational cost. We focus on methods that come with a theoretical control on the clustering performance and incorporate some form of sampling in their operation. Such methods abound in the machine learning, numerical linear algebra, and graph signal processing literature and, amongst others, include Nyström-approximation, landmarks, coarsening, coresets, and compressive spectral clustering. We present the approximation guarantees available for each and discuss practical merits and limitations. Surprisingly, despite the breadth of the literature explored, we conclude that there is still a gap between theory and practice: the most scalable methods are only intuitively motivated or loosely controlled, whereas those that come with end-to-end guarantees rely on strong assumptions or enable a limited gain of computation time.

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Random matrix improved community detection in heterogeneous networks

Cited by 9 publications

References 10 publications

Impact of regularization on spectral clustering under the mixed membership stochastic block model

Impact of regularization on spectral clustering under the mixed membership stochastic block model

An improved spectral clustering method for mixed membership community detection

Approximating Spectral Clustering via Sampling: A Review

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