Deep Autoencoder-like Nonnegative Matrix Factorization for Community Detection

Community structure is found everywhere from simple networks to real world complex networks. The problem of community detection is to predict clusters of nodes that are densely connected among themselves. The task of community detection has a wide variety of applications ranging from recommendation systems, advertising, marketing, epidemic spreading, cancer detection etc. The two mainly existing approaches for community detection, namely, stochastic block model and modularity maximization model focus on building a low dimensional network embedding to reconstruct the original network structure. However the mapping to low dimensional space in these methods is purely linear. Understanding the fact that real world networks contain non-linear structures in abundance, aforementioned methods become less practical for real world networks. Considering the nonlinear representation power of deep neural networks, several solutions based on autoencoders are being proposed in the recent literature. In this work, we propose a deep neural network architecture for community detection wherein we stack multiple autoencoders and apply parameter sharing. This method of training autoencoders has been successfully applied for the problems of link prediction and node classification in the literature. Our enhanced model with modified architecture produced better results compared to many other existing methods. We tested our model on a few benchmark datasets and obtained competitive results.

Balancing topology structure and node attribute in evolutionary multi-objective community detection for attributed networks

Community detection in networks plays a key role in understanding their structures, and the application of clustering algorithms in community detection tasks in complex networks has attracted intensive attention in recent years. In this paper, based on the definition of uncertainty of node community belongings, the node density is proposed first. After that, the DD (the combination of node density and node degree centrality) is proposed for initial node selection in community detection. Finally, based on the DD and k-means clustering algorithm, we proposed a community detection approach, the density-degree centrality-jaccard-k-means method (DDJKM). The DDJKM algorithm can avoid the problem of random selection of initial cluster centers in conventional k-means clustering algorithms, so that isolated nodes will not be selected as initial cluster centers. Additionally, DDJKM can reduce the iteration times in the clustering process and the over-short distances between the initial cluster centers can be avoided by calculating the node similarity. The proposed method is compared with state-of-the-art algorithms on synthetic networks and real-world networks. The experimental results show the effectiveness of the proposed method in accurately describing the community. The results also show that the DDJKM is practical a approach for the detection of communities with large network datasets.

Identification of semantic community structures is important for understanding the interactions and sentiments of different groups of people and predicting the social emotion. A robust community detection method needs to autonomously determine the number of communities and community structure for a given network. Nonnegative matrix factorization (NMF), a component decomposition approach for latent sentiment discovery, has been extensively used for community detection. However, the existing NMF-based methods require the number of communities to be determined a priori , limiting their applicability in practice of affective computing. Here, we develop a novel NMF-based method to autonomously determine the number of semantic communities and community structure simultaneously. In our method, we use an initial number of semantic communities, larger than the actual number, in the NMF formulation, and then suppress some of the communities by introducing an adaptively weighted group-sparse low-rank regularization to derive the target number of communities and at the same time the corresponding community structure. Our method not only maintains the efficiency without increasing the complexity compared to the original NMF method but also can be straightforwardly extended to handle the non-network data. We thoroughly examine the new method, showing its superior performance over several competing methods on synthetic and large real-world social networks.

Graph clustering, often addressed as community detection, is a prominent task in the domain of graph data mining with dozens of algorithms proposed in recent years. In this paper, we focus on several popular community detection algorithms with low computational complexity and with decent performance on the artificial benchmarks, and we study their behaviour on real-world networks. Motivated by the observation that there is a class of networks for which the community detection methods fail to deliver good community structure, we examine the assortativity coefficient of ground-truth communities and show that assortativity of a community structure can be very different from the assortativity of the original network. We then examine the possibility of exploiting the latter by weighting edges of a network with the aim to improve the community detection outputs for networks with assortative community structure. The evaluation shows that the proposed weighting can significantly improve the results of community detection methods on networks with assortative community structure.

Due to the power of learning representations from unlabeled graphs, graph contrastive learning (GCL) has shown excellent performance in community detection tasks. Existing GCL-based methods on the community detection usually focused on learning attribute representations of individual nodes, which, however, ignores structure semantics of communities (e.g., nodes in the same community should be structurally cohesive). Therefore, in this paper, we consider the community detection under the community structure semantics and propose an effective framework for graph contrastive learning under structure semantics (GCLS2) to detect communities. To seamlessly integrate interior dense and exterior sparse characteristics of communities with our contrastive learning strategy, we employ classic community structures to extract high-level structural views and design a structure semantic expression module to augment the original structural feature representation. Moreover, we formulate the structure contrastive loss to optimize the feature representation of nodes, which can better capture the topology of communities. To adapt to large-scale networks, we design a high-level graph partitioning (HGP) algorithm that minimizes the community detection loss for GCLS2 online training. It is worth noting that we prove a lower bound on the training of GCLS2 from the perspective of the information theory, explaining why GCLS2 can learn a more accurate representation of the structure. Extensive experiments have been conducted on various real-world graph datasets and confirmed that GCLS2 outperforms nine state-of-the-art methods, in terms of the accuracy, modularity, and efficiency of detecting communities.

Community detection in complex networks using edge-deleting with restrictions

Feature extraction is an important research topic in hyper-spectral image (HSI) classification. However, most of feature extraction methods only extract low-level features, which makes them not perform well in the applications of HSI. In this paper, we have proposed a non-negative matrix factorization (NMF) based deep feature extraction algorithm, namely deep NMF. Deep NMF tries to construct a deep feature representation by cascading multiple NMFs. Reconstruction residual of NMF is passed layer by layer to reduce information loss. Meanwhile, passing residuals between layers can construct a feature hierarchy from coarse to fine. Furthermore, activation functions are applied between adjacent layers to enhance the ability of non-linear feature extraction. Experimental results have also shown that our algorithm is computationally efficient and effective for HSI classification.

Scaling up algorithms or applications in data mining studies for massive datasets to improve the computing performance is becoming crucial since we've stepped into Big Data era. For community detection, which is one of the most important topics in data mining, numerous algorithms were proposed for a better exploration of the complex networks in real world and researchers keep working on improving their computing performance by parallel programming. Speaker-listener Label Propagation Algorithm (SLPA) is a sequential linear time algorithm for overlapping community detection. In this work, we proposed a new approach to parallelize and optimize SLPA. We make it more efficient through reducing the computational complexity of one of its computing kernels and providing with a better way to get memory access during parallel execution. Evaluation of abundant experiments demonstrates our implementation's better scalability on multi-core CPUs than prior work.

Community detection can exhibit the aggregation behavior of complex networks. Network motifs are the fundamental building blocks which can reveal the higher-order structure of complex networks. Label propagation algorithm has the advantage of approximately linear time complexity, unfortunately, the randomness of label update is a major but unsolved issue. For these reasons, this paper proposes a novel community detection method, named motif-based embedding label propagation algorithm (MELPA). First, complex network topology is reconstructed by merging higher-order topology with lower-order connectivity features, where higher-order topology is captured by mining network motifs. Second, We design a label propagation characteristic model according to nodes influence, then a new label update rule is formulated based on reconstructed weighted network, the rule integrates frequency among neighbor labels, influence of nodes, propagation characteristics and closeness of nodes to update the node label, the purpose is to overcome the randomness of label selection and identify a better and more stable community structure. Finally, extensive experiments on synthetic networks and real-world complex networks are conducted to verify the effectiveness of MELPA, especially for the complex networks with unobvious community structure, MELPA will get unexpected results.

Community detection in networks involves grouping nodes on a graph into clusters such that connections between groups are sparse while nodes within groups are densely connected. Despite the success of clustering based community detection methods, there have been few efforts to devise similarity metrics between nodes for clustering algorithms that measures the likeliness of two nodes belonging to the same community. In this paper we present a new similarity measure based on the density of a sub-graph constructed by common neighbors of two nodes in question. The proposed metric is referred to as common neighborhood sub-graph density (CND) and is combined with affinity propagation to detect communities from network data. We apply community detection algorithms with CND to real-world benchmark data sets to demonstrate its useful behavior in the task of community detection in networks.KeywordsSimilarity MeasureCommunity DetectionCommon NeighborCollege FootballResistance DistanceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Community detection is one of the popular research topics in the field of complex networks analysis. It aims to identify communities, represented as cohesive subgroups or clusters, where nodes in the same community link to each other more densely than others outside. Due to the interpretability, simplicity, flexibility, and generality, nonnegative matrix factorization (NMF) has become a very ideal model for community detection and lots of related methods have been presented. To facilitate research on NMF-based community detection, in this article, we make a comprehensive review on NMF-based methods for community detection, especially the state-of-the-art methods presented in high prestige journals or conferences. First, we introduce the basic principles of NMF and explain why NMF can detect communities and design a general framework of NMF-based community detection. Second, according to the applicable network types, we propose a taxonomy to divide the existing NMF-based methods for community detection into six categories, namely, topology networks, signed networks, attributed networks, multilayer networks, dynamic networks, and large-scale networks. We deeply analyze representative methods in every category. Finally, we summarize the common problems faced by all methods and potential solutions and propose four promising research directions. We believe that this survey can fully demonstrate the versatility of NMF-based community detection and serve as a useful guideline for researchers in related fields.

Digging into it: Community detection via hidden attributes analysis

The task of community detection in a graph formalizes the intuitive task of grouping together subsets of vertices such that vertices within clusters are connected tighter than those in disparate clusters. This paper approaches community detection in graphs by constructing Markov random walks on the graphs. The mixing properties of the random walk are then used to identify communities. We use coupling from the past as an algorithmic primitive to translate the mixing properties of the walk into revealing the community structure of the graph. We analyze the performance of our algorithms on specific graph structures, including the stochastic block models (SBM) and LFR random graphs.

Community detection is one of the most important problems in network analysis. Among many algorithms proposed for this task, methods based on statistical inference are of particular interest: they are mathematically sound and were shown to provide partitions of good quality. Statistical inference methods are based on fitting some random graph model (a.k.a. null model) to the observed network by maximizing the likelihood. The choice of this model is extremely important and is the main focus of the current study. We provide an extensive theoretical and empirical analysis to compare several models: the widely used planted partition model, recently proposed degree-corrected modification of this model, and a new null model having some desirable statistical properties. We also develop and compare two likelihood optimization algorithms suitable for the models under consideration. An extensive empirical analysis on a variety of datasets shows, in particular, that the new model is the best one for describing most of the considered real-world complex networks according to the likelihood of observed graph structures.