A Survey of Algorithms for Dense Subgraph Discovery

Lee, Victor E.; Ruan, Ning; Jin, Ruoming; Aggarwal, Charų C.

doi:10.1007/978-1-4419-6045-0_10

Cited by 178 publications

(115 citation statements)

References 46 publications

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“…where G t i \u and C t i \u are defined as above, but excluding the contribution from node u. Node i updates R t i→u by acquiring messages from its neighbours, except u, and aggregating them according to (7). If node u is isolated, i.e., δu = ∅, there are no updates for this node.…”

Section: Belief Propagation Algorithm For Detection With Perfect Sidementioning

confidence: 99%

The Power of Side-Information in Subgraph Detection

Kadavankandy

Avrachenkov

Cottatellucci

et al. 2018

IEEE Trans. Signal Process.

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Abstract:In this work, we tackle the problem of hidden community detection. We consider Belief Propagation (BP) applied to the problem of detecting a hidden Erdős-Rényi (ER) graph embedded in a larger and sparser ER graph, in the presence of side-information. We derive two related algorithms based on BP to perform subgraph detection in the presence of two kinds of sideinformation. The first variant of side-information consists of a set of nodes, called cues, known to be from the subgraph. The second variant of side-information consists of a set of nodes that are cues with a given probability. It was shown in past works that BP without side-information fails to detect the subgraph correctly when an effective signal-to-noise ratio (SNR) parameter falls below a threshold. In contrast, in the presence of non-trivial side-information, we show that the BP algorithm achieves asymptotically zero error for any value of the SNR parameter. We validate our results through simulations on synthetic datasets as well as on a few real world networks.

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Section: Belief Propagation Algorithm For Detection With Perfect Sidementioning

confidence: 99%

The Power of Side-Information in Subgraph Detection

Kadavankandy

Avrachenkov

Cottatellucci

et al. 2018

IEEE Trans. Signal Process.

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“…Besides, [11,5] propose a rank-one nonnegative matrix factorization method to extract maximum biclique/clique. Other related problems with size restrictions have also been studied, such as k-clique [23], k-core [19] and k-plex problem [15].…”

Section: Related Workmentioning

confidence: 99%

HiDDen: Hierarchical Dense Subgraph Detection with Application to Financial Fraud Detection

Zhang¹,

Zhou²,

Yildirim³

et al. 2017

Proceedings of the 2017 SIAM International Conference on Data Mining

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Dense subgraphs are fundamental patterns in graphs, and dense subgraph detection is often the key step of numerous graph mining applications. Most of the existing methods aim to find a single subgraph with a high density. However, dense subgraphs at different granularities could reveal more intriguing patterns in the underlying graph. In this paper, we propose to hierarchically detect dense subgraphs. The key idea of our method (HiDDen) is to envision the density of subgraphs as a relative measure to its background (i.e., the subgraph at the coarse granularity). Given that the hierarchical dense subgraph detection problem is essentially a nonconvex quadratic programming problem, we propose effective and efficient alternative projected gradient based algorithms to solve it. The experimental evaluations on real graphs demonstrate that (1) our proposed algorithms find subgraphs with an up to 40% higher density in almost every hierarchy; (2) the densities of different hierarchies exhibit a desirable variety across different granularities; (3) our projected gradient descent based algorithm scales linearly w.r.t the number of edges of the input graph; and (4) our methods are able to reveal interesting patterns in the underlying graphs (e.g., synthetic ID in financial fraud detection).

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“…The problem of finding a dense subgraph from a large input graph has been widely studied [19]. Generally speaking, such a problem aims at finding a subgraph of a given input graph that maximizes some notion of density.…”

Section: Related Workmentioning

confidence: 99%

“…Finding dense subgraphs in large graphs has emerged as a key primitive in a variety of real-world application domains [19], ranging from biology [13,18] to finance [12]. In the Web domain, Gibson et al [14] have observed that dense subgraphs might correspond to thematic group of pages or * Partially funded by a Google Faculty Research Award.…”

Section: Introductionmentioning

confidence: 99%

Finding Subgraphs with Maximum Total Density and Limited Overlap

Balalau

Bonchi

Chan

et al. 2015

Proceedings of the Eighth ACM International Conference on Web Search and Data Mining

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Finding dense subgraphs in large graphs is a key primitive in a variety of real-world application domains, encompassing social network analytics, event detection, biology, and finance. In most such applications, one typically aims at finding several (possibly overlapping) dense subgraphs which might correspond to communities in social networks or interesting events. While a large amount of work is devoted to finding a single densest subgraph, perhaps surprisingly, the problem of finding several dense subgraphs with limited overlap has not been studied in a principled way, to the best of our knowledge. In this work we define and study a natural generalization of the densest subgraph problem, where the main goal is to find at most k subgraphs with maximum total aggregate density, while satisfying an upper bound on the pairwise Jaccard coefficient between the sets of nodes of the subgraphs. After showing that such a problem is NP-Hard, we devise an efficient algorithm that comes with provable guarantees in some cases of interest, as well as, an efficient practical heuristic. Our extensive evaluation on large realworld graphs confirms the efficiency and effectiveness of our algorithms.

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A Survey of Algorithms for Dense Subgraph Discovery

Cited by 178 publications

References 46 publications

The Power of Side-Information in Subgraph Detection

The Power of Side-Information in Subgraph Detection

HiDDen: Hierarchical Dense Subgraph Detection with Application to Financial Fraud Detection

Finding Subgraphs with Maximum Total Density and Limited Overlap

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