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Register a new userScalable and Robust Community Detection with Randomized Sketching
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Added by
Andre Beckus
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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This paper explores and analyzes the unsupervised clustering of large partially observed graphs. We propose a scalable and provable randomized framework for clustering graphs generated from the stochastic block model. The clustering is first applied to a sub-matrix of the graphs adjacency matrix associated with a reduced graph sketch constructed using random sampling. Then, the clusters of the full graph are inferred based on the clusters extracted from the sketch using a correlation-based retrieval step. Uniform random node sampling is shown to improve the computational complexity over clustering of the full graph when the cluster sizes are balanced. A new random degree-based node sampling algorithm is presented which significantly improves upon the performance of the clustering algorithm even when clusters are unbalanced. This algorithm improves the phase transitions for matrix-decomposition-based clustering with regard to computational complexity and minimum cluster size, which are shown to be nearly dimension-free in the low inter-cluster connectivity regime. A third sampling technique is shown to improve balance by randomly sampling nodes based on spatial distribution. We provide analysis and numerical results using a convex clustering algorithm based on matrix completion.
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A common goal in network modeling is to uncover the latent community structure present among nodes. For many real-world networks, observed connections consist of events arriving as streams, which are then aggregated to form edges, ignoring the temporal dynamic component. A natural way to take account of this temporal dynamic component of interactions is to use point processes as the foundation of the network models for community detection. Computational complexity hampers the scalability of such approaches to large sparse networks. To circumvent this challenge, we propose a fast online variational inference algorithm for learning the community structure underlying dynamic event arrivals on a network using continuous-time point process latent network models. We provide regret bounds on the loss function of this procedure, giving theoretical guarantees on performance. The proposed algorithm is illustrated, using both simulation studies and real data, to have comparable performance in terms of community structure in terms of community recovery to non-online variants. Our proposed framework can also be readily modified to incorporate other popular network structures.
Fitting large Bayesian network models quickly become computationally infeasible when the number of nodes grows into the hundreds of thousands and millions. In particular, the mixed membership stochastic blockmodel (MMSB) is a popular Bayesian network model used for community detection. In this paper, we introduce a scalable inference method that leverages nodal information that often accompanies real-world networks. Conditioning on this extra information leads to a model that admits a parallel variational inference algorithm. We apply our method to a citation network with over two million nodes and 25 million edges. Our method recovers parameters and achieves convergence better on simulated networks generated according to the MMSB.
A distinguishing property of communities in networks is that cycles are more prevalent within communities than across communities. Thus, the detection of these communities may be aided through the incorporation of measures of the local richness of the cyclic structure. In this paper, we introduce renewal non-backtracking random walks (RNBRW) as a way of quantifying this structure. RNBRW gives a weight to each edge equal to the probability that a non-backtracking random walk completes a cycle with that edge. Hence, edges with larger weights may be thought of as more important to the formation of cycles. Of note, since separate random walks can be performed in parallel, RNBRW weights can be estimated very quickly, even for large graphs. We give simulation results showing that pre-weighting edges through RNBRW may substantially improve the performance of common community detection algorithms. Our results suggest that RNBRW is especially efficient for the challenging case of detecting communities in sparse graphs.
We study the community detection problem on a Gaussian mixture model, in which vertices are divided into $kgeq 2$ distinct communities. The major difference in our model is that the intensities for Gaussian perturbations are different for different entries in the observation matrix, and we do not assume that every community has the same number of vertices. We explicitly find the threshold for the exact recovery of the maximum likelihood estimation. Applications include the community detection on hypergraphs.
Community detection is a key task to further understand the function and the structure of complex networks. Therefore, a strategy used to assess this task must be able to avoid biased and incorrect results that might invalidate further analyses or applications that rely on such communities. Two widely used strategies to assess this task are generally known as structural and functional. The structural strategy basically consists in detecting and assessing such communities by using multiple methods and structural metrics. On the other hand, the functional strategy might be used when ground truth data are available to assess the detected communities. However, the evaluation of communities based on such strategies is usually done in experimental configurations that are largely susceptible to biases, a situation that is inherent to algorithms, metrics and network data used in this task. Furthermore, such strategies are not systematically combined in a way that allows for the identification and mitigation of bias in the algorithms, metrics or network data to converge into more consistent results. In this context, the main contribution of this article is an approach that supports a robust quality evaluation when detecting communities in real-world networks. In our approach, we measure the quality of a community by applying the structural and functional strategies, and the combination of both, to obtain different pieces of evidence. Then, we consider the divergences and the consensus among the pieces of evidence to identify and overcome possible sources of bias in community detection algorithms, evaluation metrics, and network data. Experiments conducted with several real and synthetic networks provided results that show the effectiveness of our approach to obtain more consistent conclusions about the quality of the detected communities.
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