Graph Clustering Research Articles

Effective semi-supervised graph clustering with pairwise constraints

Semi-supervised graph clustering with constraints has received considerable attention in the last decade. They use pre-given constraints to guide the clustering process and improve the performance. Nonetheless, most of related research works still face two main issues: (1) cannot-link problem: how to ensure that instances under the cannot-link constraint are located in different clusters as much as possible. (2) The high computational cost caused by eigendecomposition. To tackle these problems, this paper proposes a novel method for directly solving the clustering indicator matrix without high complexity computational steps. Then, we propose an effective and simple algorithm guided by the pre-given constraints, which is able to simultaneously optimize the associated multiple pairs of constraints, allowing the associated constraints to achieve the related co-optimal solution. Extensive experiments are conducted to verify that our approach significantly reduces the violation rate of the prior constraints and the clustering performance of the proposed method outperforms seven other state-of-the-art semi-supervised clustering methods on 16 real benchmark datasets.

Diverse representation-guided graph learning for multi-view metric clustering

Multi-view graph clustering has garnered tremendous interest for its capability to effectively segregate data by harnessing information from multiple graphs representing distinct views. Despite the advances, conventional methods commonly construct similarity graphs straightway from raw features, leading to suboptimal outcomes due to noise or outliers. To address this, latent representation-based graph clustering has emerged. However, it often hypothesizes that multiple views share a fixed-dimensional coefficient matrix, potentially resulting in useful information loss and limited representation capabilities. Additionally, many methods exploit Euclidean distance as a similarity metric, which may inaccurately measure linear relationships between samples. To tackle these challenges, we develop a novel diverse representation-guided graph learning for multi-view metric clustering (DRGMMC). Concretely, raw sample matrix from each view is first projected into diverse latent spaces to capture comprehensive knowledge. Subsequently, a popular metric is leveraged to adaptively learn similarity graphs with linearity-aware based on attained coefficient matrices. Furthermore, a self-weighted fusion strategy and Laplacian rank constraint are introduced to output clustering results directly. Consequently, our model merges diverse representation learning, metric learning, consensus graph learning, and data clustering into a joint model, reinforcing each other for holistic optimization. Substantial experimental findings substantiate that DRGMMC outperforms most advanced graph clustering techniques.

Attributed graph clustering under the contrastive mechanism with cluster-preserving augmentation

Attributed graph clustering is a fundamental task in complex network analysis. Many existing graph clustering methods utilize graph representation learning techniques to learn node representations, subsequently applying K-means for clustering. Despite the significant attention and promising outcomes of graph contrastive learning in graph representation learning, we find two essential problems that need to be solved. (1) How to achieve augmentation for contrast that preserves the cluster structure of a given graph? (2) How to design an effective contrastive learning mechanism that collaborates with clustering? Therefore, we propose an attributed graph clustering method under the contrastive mechanism with cluster-preserving augmentation, integrating node representation learning and clustering into a unified framework. Specifically, we construct a contrasting view based on a generated kNN graph and edge betweenness centrality to preserve the cluster structure in the original graph. Meanwhile, a multilevel contrast mechanism based on pseudo-label-guided negative sampling is proposed to maximize the agreement between node representations in multiple latent spaces. We jointly optimize a specific clustering objective during the contrastive process, leading to refined cluster distribution directly in training. Extensive experiments on several datasets demonstrate that our proposed model consistently outperforms existing state-of-the-art methods on clustering.

Diverse joint nonnegative matrix tri-factorization for attributed graph clustering

Cluster analysis of attributed graphs is a demanding and challenging task in the analysis of network-structured data. It involves learning node representation by leveraging both node attributes and the topological structure of the graph, aiming to accomplish effective clustering. Typically, existing methods fuse the topological and non-topological information by learning a consensus representation, often resulting in redundancy and overlooking their inherent distinctions. To address this issue, this paper proposes the Diverse Joint Nonnegative Matrix Tri-Factorization (Div-JNMTF), an embedding based model to detect communities in attributed graphs. The novel JNMTF model attempts to extract two distinct node representations from topological and non-topological data. Simultaneously, a diversity regularization technique utilizing the Hilbert–Schmidt Independence Criterion (HSIC) is employed. Its objective is to reduce redundant information in the node representations while encouraging the distinct contributions of both types of information. In addition, two graph regularization terms are introduced to preserve the local structures in the topological and attribute representation spaces. The Div-JNMTF model is optimized by developing an iterative optimization approach. By conducting thorough experiments on four synthetic and eight real-world attributed graph datasets, it has been demonstrated that the proposed model excels in accurately detecting attributed communities and surpasses the performance of existing methods.

Improved Dual Correlation Reduction Network With Affinity Recovery.

Deep graph clustering, which aims to reveal the underlying graph structure and divide the nodes into different clusters without human annotations, is a fundamental yet challenging task. However, we observe that the existing methods suffer from the representation collapse problem and tend to encode samples with different classes into the same latent embedding. Consequently, the discriminative capability of nodes is limited, resulting in suboptimal clustering performance. To address this problem, we propose a novel deep graph clustering algorithm termed improved dual correlation reduction network (IDCRN) through improving the discriminative capability of samples. Specifically, by approximating the cross-view feature correlation matrix to an identity matrix, we reduce the redundancy between different dimensions of features, thus improving the discriminative capability of the latent space explicitly. Meanwhile, the cross-view sample correlation matrix is forced to approximate the designed clustering-refined adjacency matrix to guide the learned latent representation to recover the affinity matrix even across views, thus enhancing the discriminative capability of features implicitly. Moreover, we avoid the collapsed representation caused by the oversmoothing issue in graph convolutional networks (GCNs) through an introduced propagation regularization term, enabling IDCRN to capture the long-range information with the shallow network structure. Extensive experimental results on six benchmarks have demonstrated the effectiveness and efficiency of IDCRN compared with the existing state-of-the-art deep graph clustering algorithms. The code of IDCRN is released at https://github.com/yueliu1999/IDCRN. Besides, we share a collection of deep graph clustering, including papers, codes, and datasets at https://github.com/yueliu1999/Awesome-Deep-Graph-Clustering.

Structured Deep Graph Clustering Network Based on Consistency Constraint

Graph clustering is an essential task in data analysis. Recently, there has been a notable trend in the application of deep learning in graph clustering. However, it is worth noting that existing deep graph clustering methods primarily focus on the topological information of nodes while overlooking the use of attribute information in the learned feature representations. In addition, they do not address the consistency of the space distribution in attribute and structure clustering results. To tackle these critical issues, a novel structured deep graph clustering network with consistency constraint (CC-DGC) is proposed. The network first constructs an autoencoder to learn and transmit hierarchical attribute information to the graph autoencoder (GAE). Subsequently, the GAE integrates the received hierarchical attribute information with extracted topological information to generate enhanced clustering representations. Moreover, this paper designs a consistency constraint module to promote consistency between the autoencoder and the GAE by optimizing the cluster space distributions they produce. Finally, the feature extraction and clustering classification processes are synchronized and optimized in a self-supervised manner within a unified framework. Extensive experiments illustrate that the proposed CC-DGC demonstrates superiority over the state-of-the-art deep graph clustering methods on five benchmark datasets.

Behavior Based Group Recommendation from Social Media Dataset by Using Deep Learning and Topic Modeling

In this digital era, users frequently share their thoughts, preferences, and ideas through social media, which reflect their Basic Human Values. Basic Human Values (aka values) are the fundamental aspects of human behavior, which define what we consider important, and worth having and pursue them. Existing studies identify the values of individuals from different social network usages such as Facebook and Reddit. However, discovering the similarity (or diversity) of value priorities among the members in a group is important since we can reveal many interesting insights such as finding a set of target customers, identifying the chain of misdeed groups, searching for similar acquaintances in workplaces, etc. In this paper, a graph dataset is compiled using the strongest correlation among the features and then we apply a graph clustering technique to identify a suitable hedonist group (i.e., one dimension of values) for users’ recommendations. Then, we also propose a behavior based (i.e., value ) group recommendation technique by analyzing users’ contextual and psychological attributes. Finally, we validate those group members in real life by introducing two hypotheses. In particular, we analyze the tweets of a total of 1140 users collected from Twitter. We obtain a substantial intra-cluster correlation coefficient (ICC) and silhouette clustering coefficient (SCC) scores of 65% and 76%, respectively, among the members in our discovered group.

Attributed graph subspace clustering with residual compensation guided by adaptive dual manifold regularization

As an important technology for recommendation system, attributed graph clustering has received extensive attention recently. Attributed graph clustering methods based on graph neural networks are the mainstream methods . However, their assumption that the attributes of adjacent nodes are similar is often not satisfied in the real world, which influences the clustering performance. To this end, this paper proposes an attributed graph subspace clustering algorithm with residual compensation guided by adaptive dual manifold regularization (ADMRGC). On the basis of the low rank representation subspace clustering (LRR) model, ADMRGC introduces attributed manifold regularization, topological manifold regularization and residual compensation, which make ADMRGC possible to utilize attributed similarity and topological similarity at the same time, thus solving the problem that traditional subspace clustering only considers attributed information. In addition, ADMRGC balances the contribution of node attributes and topology by adaptively weighting the dual manifold regularization, and uses the residual representation matrix to describe the difference between node attributed similarity and topological neighbor relationship. Therefore, ADMRGC can avoid the limitation of graph neural network models assuming that the attributes of adjacent nodes are similar. Experimental results on 7 public graph datasets show that ADMRGC can achieve the best clustering performance on both high-homophily and low-homophily datasets. Especially, for datasets with low homophily, ADMRGC as a shallow model can also achieve better clustering performance than state-of-the-art deep neural network models.

A low-rank ODE for spectral clustering stability

Spectral clustering is a well-known technique which identifies k clusters in an undirected graph, with n vertices and weight matrix W∈Rn×n, by exploiting its graph Laplacian L(W). In particular, the k clusters can be identified by the knowledge of the eigenvectors associated with the k−1 smallest non zero eigenvalues of L(W), say λ2,…,λk (recall that λ1=0). Identifying k is an essential task of a clustering algorithm, since if λk+1 is close to λk the reliability of the method is reduced. The k-th spectral gap λk+1−λk is often considered as a stability indicator. This difference can be seen as an unstructured distance between L(W) and an arbitrary symmetric matrix L⋆ with vanishing k-th spectral gap. A more appropriate structured distance to ambiguity such that L⋆ represents the Laplacian of a graph has been proposed in Andreotti et al. (2021) [2]. This is defined as the minimal distance between L(W) and Laplacians of graphs with the same vertices and edges, but with weights that are perturbed such that the k-th spectral gap vanishes. In this article we consider a slightly different approach, still based on the reformulation of the problem into the minimization of a suitable functional in the eigenvalues. After determining the gradient system associated with this functional, we introduce a low-rank projected system, suggested by the underlying low-rank structure of the extremizers of the problem. The integration of this low-rank system, requires both a moderate computational effort and a memory requirement, as it is shown in some illustrative numerical examples.

Fast Clustering by Directly Solving Bipartite Graph Clustering Problem.

Spectral clustering (SC) has been widely used in many applications and shows excellent performance. Its high computational cost limits its applications; many strategies including the anchor technique can partly alleviate the high computational cost problem. However, early methods ignore the fact that SC usually involves two stages: relaxation and postprocessing, i.e., it relaxes the discrete constraints to continuous constraints, and then conducts the postprocessing to get the discrete solution, which is time-consuming and deviates from directly solving the primal problem. In this article, we first adopt the bipartite graph strategy to reduce the time complexity of SC, and then an improved coordinate descent (CD) method is proposed to solve the primal problem directly without singular value decomposition (SVD) and postprocessing, i.e., directly solving the primal problem not approximately solving. Experiments on various real-world benchmark datasets show that the proposed method can get better solutions faster with better clustering performance than traditional optimization methods. Furthermore, it can jump out of local minima of traditional methods and continue to obtain better local solutions. Moreover, compared with other clustering methods, it also shows its superiority.

AGCM: A multi-stage attack correlation and scenario reconstruction method based on graph aggregation

With an increase in the complexity and scale of networks, cybersecurity faces increasingly severe challenges. For instance, an attacker can combine individual attacks into complex multi-stage attacks to infiltrate targets. Traditional intrusion detection systems (IDS) generate large number of alerts during an attack, including attack clues along with many false positives. Furthermore, due to the complexity and changefulness of attacks, security analysts spend considerable time and effort on discovering attack paths. Existing methods rely on attack knowledgebases or predefined correlation rules but can only identify known attacks. To address these limitations, this paper presents an attack correlation and scenario reconstruction method. We transform the abnormal flows corresponding to the alerts into abnormal states relationship graph (ASR-graph) and automatically correlate attacks through graph aggregation and clustering. We also implemented an attack path search algorithm to mine attack paths and trace the attack process. This method does not rely on prior knowledge; thus, it can well adapt to the changed attack plan, making it effective in correlating unknown attacks and identifying attack paths. Evaluation results show that the proposed method has higher accuracy and effectiveness than existing methods.

A Tree Segmentation Algorithm for Airborne Light Detection and Ranging Data Based on Graph Theory and Clustering

A Tree Segmentation Algorithm for Airborne Light Detection and Ranging Data Based on Graph Theory and Clustering

SymNOM-GED: Symmetric neighbor outlier mining in gene expression datasets

The accurate detection of outliers in gene expression datasets plays a crucial role in the unraveling of intricate biological processes. This research introduces "SymNOM-GED," an innovative algorithm for outlier mining in gene expression datasets, with a focus on Esophageal Squamous Cell Carcinoma (ESCC). SymNOM-GED leverages symmetric neighbor to effectively identify outliers by considering local and global gene expression patterns. Extensive experiments demonstrate that SymNOM-GED outperforms existing algorithms in terms of accuracy, robustness, and scalability. The algorithm's performance is validated using clustering coefficient, graph density, and modularity, confirming its superiority. SymNOM-GED's precise and reliable outlier detection capabilities contribute significantly to bioinformatics research, offering insights into gene expression patterns in diverse biological contexts.

Clustering and Cliques in Preferential Attachment Random Graphs with Edge Insertion

Clustering and Cliques in Preferential Attachment Random Graphs with Edge Insertion

Multi-scale graph clustering network

Deep graph clustering, a fundamental yet formidable task in data analysis, aims to partition samples belonging to the same category into their respective clusters. Recently, significant advancements in graph self-supervised learning have been made through generative and contrastive learning methods. However, existing methods focus on directly aggregating neighboring node information during the feature extraction stage, thereby neglecting the crucial long-range correlations between nodes. Consequently, non-neighbor node information within the same category remains unexplored, leading to subpar performance in the clustering task. To address this issue, we propose a generative method named Multi-scale Graph Clustering Network (MGCN) to learn comprehensive and rich graph representations for deep graph clustering in the feature encoding stage. Specifically, we design a Multi-hop Adaptive Convolutional Module (MACM) integrated into MGCN, which effectively aggregates high-order neighbor node features in each layer of the network. Additionally, we develop an autoencoder to assist MACM in enhancing attribute information, which prevents the node's own features from being overshadowed in the multi-scale feature learning process. Experimental results demonstrate that our proposed MGCN method achieves significantly better clustering performance than existing methods on multiple public datasets.

Information-enhanced deep graph clustering network

Graph clustering is a significant task in complex network research. Deep graph clustering aims to uncover the potential community structure in graph data using the powerful feature extraction capability of deep learning, garnering much attention in recent decades. However, existing graph clustering methods fall short in fully utilizing available information, particularly in effectively fusing structural and attribute information, as well as utilizing coarse-grained data. Consequently, learned node representations remain limited, leading to suboptimal clustering results. To address these challenges, we propose Information-Enhanced Deep Graph Clustering Network (IEDGCN) for unsupervised attribute graphs. IEDGCN introduces key components to enhance information utilization and improve clustering performance. Firstly, we design a new higher-order neighborhood-weighted attribute matrix, effectively integrating higher-order neighborhood information with attributes. Secondly, a graph generation model guides the learning of the structural feature space more effectively. Additionally, IEDGCN captures more coarse-grained information by utilizing community and higher-order neighborhood features to refine clustering results. Finally, the proposed method is uniformly guided through a jointly supervised strategy for representation learning and cluster assignment. Experimental results on different benchmark datasets demonstrate the effectiveness of IEDGCN compared to state-of-the-art methods, emphasizing the importance of information enhancement for graph clustering.

Deep graph clustering by integrating community structure with neighborhood information

Deep graph clustering approaches employ deep graph neural networks to encode node embeddings and subsequently partition nodes based on these representations. Recent one-step methods have demonstrated progress; however, they often encounter issues during the representation learning phase. A primary challenge is that the encoding networks fail to capture the high-order structural information of the graph for effective clustering. We believe that combining the two distributions comprehensively characterizes the real node distribution in terms of neighborhood proximity and community aggregation to achieve better clustering. Additionally, the prevalent representation learning paradigms based on adjacency matrix reconstruction are computationally intensive and increase optimization challenges. This paper presents a novel deep graph clustering model, termed Deep Integration of Community structure and Neighborhood information (DICN). The model incorporates a graph self-attention mechanism to aggregate neighborhood-level node information, and utilizes a probabilistic generative model for edge community detection to captain community-level node information. These two-level embeddings are employed to compute explicit node membership distributions for the clustering loss. This ensures that the clustering objective effectively integrates both low-order and high-order node characteristics. The comprehensive learning process of DICN optimizes not only the node embeddings but also the clustering results by integrating the two-level losses from representation learning and the clustering loss with a weak guidance loss for clustering. Experiments on some benchmark datasets illustrate that DICN model has superior performance over existing state-of-the-art methods.

A faster deep graph clustering network based on dynamic graph weight update mechanism

A faster deep graph clustering network based on dynamic graph weight update mechanism

Explainable graph clustering via expanders in the massively parallel computation model

Explainable clustering provides human-understandable reasons for decisions in black-box learning models. In a previous work, a decision tree built on the set of dimensions was used to define ranges of values for k-means clusters. For explainable graph clustering, we use expander graphs instead of dense subgraphs since powering an expander graph is guaranteed to result in a clique after at most a logarithmic number of steps.Consider a set of multi-dimensional points labeled with k labels. We introduce the heat map sorting problem as reordering the rows and columns of an input matrix (each point is a column and each row is a dimension) such that the labels of the entries of the matrix form connected components (clusters). A cluster is preserved if it remains connected, i.e., if it is not split into several clusters and no two clusters are merged. In the massively parallel computation model (MPC), each machine has a sublinear memory and the total memory of the machines is linear.We prove the problem is NP-hard. We give a fixed-parameter algorithm in MPC and an approximation algorithm based on expander decomposition. We empirically compare our algorithm with explainable k-means on several graphs of email and computer networks.

A Spectral Clustering Algorithm for Non-Linear Graph Embedding in Information Networks

With the development of network technology, information networks have become one of the most important means for people to understand society. As the scale of information networks expands, the construction of network graphs and high-dimensional feature representation will become major factors affecting the performance of spectral clustering algorithms. To address this issue, in this paper, we propose a spectral clustering algorithm based on similarity graphs and non-linear deep embedding, named SEG_SC. This algorithm introduces a new spectral clustering model that explores the underlying structure of graphs through sparse similarity graphs and deep graph representation learning, thereby enhancing graph clustering performance. Experimental analysis with multiple types of real datasets shows that the performance of this model surpasses several advanced benchmark algorithms and performs well in clustering on medium- to large-scale information networks.