The Power of Side-Information in Subgraph Detection

Kadavankandy, Arun; Avrachenkov, Konstantin; Cottatellucci, Laura; Sundaresan, Rajesh

doi:10.1109/tsp.2017.2786266

Cited by 15 publications

(22 citation statements)

References 37 publications

(95 reference statements)

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“…Similarly the supremum over s can be calculated via a derivative, finding s * = ( 1 T log( γ+β aT )) + , which is positive as long as β > T (a−b) 2 . Since s * = 0 leads to a trivial bound, consider β > T (a−b) 2 and substitute in (31).…”

Section: B Varying Number Of Fixed-quality Featuresmentioning

confidence: 99%

Community Detection With Side Information: Exact Recovery Under the Stochastic Block Model

Saad

Nosratinia

2018

IEEE J. Sel. Top. Signal Process.

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The community detection problem involves making inferences about node labels in a graph, based on observing the graph edges. This paper studies the effect of additional, non-graphical side information on the phase transition of exact recovery in the binary stochastic block model (SBM) with n nodes.When side information consists of noisy labels with error probability α, it is shown that phase transition is improved if and only if log( 1−α α ) = Ω(log(n)). When side information consists of revealing a fraction 1 − ǫ of the labels, it is shown that phase transition is improved if and only if log(1/ǫ) = Ω(log(n)).For a more general side information consisting of K features, two scenarios are studied: (1) K is fixed while the likelihood of each feature with respect to corresponding node label evolves with n, and (2) The number of features K varies with n but the likelihood of each feature is fixed. In each case, we find when side information improves the exact recovery phase transition and by how much. In the process of deriving inner bounds, a variation of an efficient algorithm is proposed for community detection with side information that uses a partial recovery algorithm combined with a local improvement procedure. DRAFT Side Information Observed Graph community − −−−− → detection error error True Labels Detected communities Side Information Graph + side information community − −−−− → detection True Labels Enhanced detection Fig. 1. (top) standard community detection (bottom) Community detection with side information Community detection outcomes fall into several broad categories in terms of residual error as the size of the graph n grows, enumerated here in increasing order of strength: Correlated recovery refers to community detection that performs better than random guessing [19]-[23]. Weak recovery means the fraction of misclassified labels in the graph vanishes with probability converging to one [24]-[26]. Exact recovery means correct recovery of all nodes with probability converging to one [18], [27], [28]. This paper concentrates on the exact recovery metric. 1 A few results have recently appeared in the literature on the broader community detection problem in the presence of additional (non-graphical) information. Mossel and Xu [29] studied the behavior of belief propagation detector in the presence of noisy label information. Cai et al. [30] studied the effect of knowing a growing fraction of labels on correlated and weak recovery. Neither of [29], [30] includes a converse, so they do not establish phase transition. Kadavankandy et al. [31] studied the single-community problem with noisy label observations,showing weak recovery in the sparse regime. Kanade et al. [32] showed that partial observation of labels is unhelpful to the correlated recovery phase transition if a vanishing portion of labels 1 Formally, let en denote the number of misclassified nodes. Then, correlated recovery means limn→∞ P( en n < 0.5) = 1. Weak recovery means limn→∞ P( en n < ε) = 1 for any positive ε. Exact recovery means limn→...

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Section: B Varying Number Of Fixed-quality Featuresmentioning

confidence: 99%

Community Detection With Side Information: Exact Recovery Under the Stochastic Block Model

Saad

Nosratinia

2018

IEEE J. Sel. Top. Signal Process.

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“…For example, [13] fused the vertex connection probability with the triangle subgraph to improve the detection performance of the algorithm and obtained the detection boundary of statistic through the emerging concentration measure theory. [14] applied the local belief propagation algorithm to collect the vertex neighborhood message to implement the subgraph detection in the Erdős-Rényi random graph models. To make full use of the structural information between vertices, [15] proposed an anomaly detection method in a strong noise environment by mapping the matrix of random graph into a higher-order tensor.…”

Section: Introductionmentioning

confidence: 99%

“…However, these methods have limitations in models and other aspects. For instance, [14] required a large amount of prior information, which makes the algorithm hard to implement in many real scenarios. In particular, most algorithms are only effective for special random graph model, i.e., Erdős-Rényi random graphs.…”

Section: Introductionmentioning

confidence: 99%

Anomalous Subgraph Detection in Given Expected Degree Networks With Deep Learning

et al. 2021

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Anomalous subgraph detection within networks is an important issue in many emerging applications. Existing algorithms, such as graph structure methods and spectral feature methods, usually focus on the special stochastic model (such as the Erdős-Rényi random graph) or may not efficiently extract the anomalous behaviors of the networks, which result in detection performance degradation. To mitigate the limitations, in this paper, we first present an anomalous subgraph detection framework associated with deep neural networks (DNN) for detecting anomalous behaviors within the networks. Furthermore, based on the developed framework, we propose a residual matrix-based convolutional neural network (RM-CNN) algorithm with respect to the given expected degree models, which are more general networks than the Erdős-Rényi random graphs. In particular, the trained RM-CNN can efficiently capture the anomalous changes of the network and then achieve the detection performance improvement. Simulation experiments display that the proposed RM-CNN algorithm is superior to the compared algorithms in both detection performance and detection speed.INDEX TERMS Anomalous subgraph detection, given expected degree models, deep learning, convolutional neural network.

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“…In practice, along with the hypergraph A, side information about node labels is usually available [23][24][25][26][27][28][29][30]. For example, in a co-authorship or co-citation network, the cluster labels of some authors are known [28].…”

Section: Introductionmentioning

confidence: 99%

Information Limits for Community Detection in Hypergraph with Label Information

2021

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In network data mining, community detection refers to the problem of partitioning the nodes of a network into clusters (communities). This is equivalent to identifying the cluster label of each node. A label estimator is said to be an exact recovery of the true labels (communities) if it coincides with the true labels with a probability convergent to one. In this work, we consider the effect of label information on the exact recovery of communities in an m-uniform Hypergraph Stochastic Block Model (HSBM). We investigate two scenarios of label information: (1) a noisy label for each node is observed independently, with 1−αn as the probability that the noisy label will match the true label; (2) the true label of each node is observed independently, with the probability of 1−αn. We derive sharp boundaries for exact recovery under both scenarios from an information-theoretical point of view. The label information improves the sharp detection boundary if and only if αn=n−β+o(1) for a constant β>0.

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The Power of Side-Information in Subgraph Detection

Cited by 15 publications

References 37 publications

Community Detection With Side Information: Exact Recovery Under the Stochastic Block Model

Community Detection With Side Information: Exact Recovery Under the Stochastic Block Model

Anomalous Subgraph Detection in Given Expected Degree Networks With Deep Learning

Information Limits for Community Detection in Hypergraph with Label Information

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