Graph Clustering Methods Research Articles

Towards attributed graph clustering using enhanced graph and reconstructed graph structure

Attributed graph clustering, leveraging both structural and attribute information, is crucial in various real-world applications. However, current approaches face challenges stemming from the sparsity of graphs and sensitivity to noise in Graph Convolutional Networks (GCNs). Moreover, GCN-based methods are often designed based on the assumption of homophilic graph and ignore heterophilic graph. To address these, we propose a graph clustering method that consists of four phases: graph enhance, graph reconstruction, graph refine, and dual-guidance supervisor module. An enhanced graph module is defined by an auxiliary graph to consider distant relationships in the topology structure to alleviate the limitations of sparse graphs. The graph reconstruction phase includes the creation and integration of homophily and heterophily graphs to achieve graph-agnostic. In graph refine, the auxiliary graph is iteratively improved to enhance the generalization of the representation. In this phase, a subspace clustering module is applied to convert attribute-based embeddings into relationship-based representations. Finally, the extracted graphs are fed to a dual-guidance supervisor module to obtain the final clustering result. Experimental validation on several benchmark datasets demonstrates the efficiency of our model. Meanwhile, the findings offer significant advancements in attributed graph clustering, promising improved applicability in various domains.

Joint consensus kernel learning and adaptive hypergraph regularization for graph-based clustering

Recent advancements in multiple kernel learning-based graph clustering methods have demonstrated significant promise in effectively learning a consensus kernel matrix from various candidate kernel matrices. This approach enables the creation of a low-dimensional representation in the kernel space of high-dimensional data through self-expressiveness. However, a key challenge remains in capturing the latent geometric properties embedded within different kernel matrices to enhance data representation. In this paper, we propose a novel method called joint consensus kernel learning and adaptive hypergraph regularization for graph-based clustering (JKHR). Our approach integrates an innovative adaptive hypergraph Laplacian regularizer, which is characterized by the fusion of multiple nearest neighbor kernel graphs, into the multiple kernel learning-based graph clustering framework. JKHR jointly and adaptively optimizes both the consensus kernel matrix and the hypergraph Laplacian regularizer to achieve a low-dimensional representation that effectively preserves the intrinsic geometry of the data. Experimental results on both synthetic and real benchmark datasets demonstrate that JKHR outperforms state-of-the-art self-expressiveness-based graph clustering methods as well as traditional clustering techniques.

Model and Methods of Traffic Routing in a Communication Network Using UAVs

Relevance. The development of 5G networks and subsequent generations is accompanied by the development of new services, in particular, virtual, augmented reality services, as well as telepresence, as well as radio access networks. In particular, there is an increase in operating frequencies, which poses additional challenges for organizing a network that can meet the requirements for the quality of traffic service from new services and ensure the availability of communication to users. These problems can be solved by various methods of placing access points, including using UAVs. This approach ensures the efficiency of construction and flexibility of the access network structure, but also requires the use of methods for placing access points in relation to users and other elements of the communication network. Problem statement: development of methods for placing routers in a UAV swarm and selecting traffic routes when organizing an access network, in order to improve the efficiency of the communication network. Purpose of the work: improving the efficiency of building an access network using UAVs through the development of clustering methods and distributing routers in a UAV swarm. Methods. The studies were carried out using the provisions of information theory, mathematical optimization methods, graph theory methods and clustering methods. The numerical results were obtained using the numerical simulation method in Python. Result. The developed model and methods allow for the distribution of network routers (access points) located on UAVs taking into account the quality of service and ensuring the construction of a connected mesh network and its connection with the mobile network, which can be used in both modern and future communication networks. Novelty: a modeling and methodological apparatus has been developed that allows for increasing the efficiency of building wireless access networks using UAVs, in particular, allowing for selecting the placement positions of routers in a UAV swarm and the logical structure of the network. The developed modeling and methodological apparatus solves the problem of traffic routing taking into account the quality of its service. Practical significance: the proposed model and methods can be used to organize service in 5G networks and subsequent generations. In particular, they allow for ensuring the availability of communication and the efficiency of network organization in cases of insufficient coverage, as well as in cases of failure of individual network elements. The ability to unload traffic to a local network allows for improving the quality of traffic service in the operator's network.

Fast adaptively balanced min-cut clustering

Min-cut clustering is a typical graph clustering method, which has been extensively applied for pattern recognition, data analysis and image processing. However, min-cut has trivial solutions, which leads to skewed clustering performance. Spectral clustering (SC) alleviates this by relaxing indicator matrix into continuous embedding and then discretizes the embedding. However, there are two primary challenges in SC, which are high computational complexity and two-stage process. To resolve these issues, a fast adaptively balanced min-cut clustering model (FBMC) is proposed, which directly solves the discrete indicator matrix without any post-processing. We utilize the bipartite graph to accelerate the construction of affinity graph and process of optimization. Besides, the balance factors are added in the model, which could alleviate skewed clustering results. Two specific methods are proposed, in which one adds a balance factor to all clusters while the other assigns balance factors to each cluster separately, referred to as FBMC1 and FBMC2. What is more, a one-step optimization is proposed to solve FBMC1 and FBMC2, the complexity of which is linear of time. Finally, comprehensive experiments results highlight the superior performance of our proposed method.

Auto-weighted multi-view clustering via hierarchical bipartite graph

The expensive time consumption and hyper-parameters are two main drawbacks of most existing multi-view graph clustering methods. Especially in large-scale data clustering, these two defects are more serious. Aiming at these two problems, we propose a novel auto-weighted multi-view clustering method based on the hierarchical bipartite graph to effectively address these two limitations. Similar to the idea of an anchor graph, firstly, the bisecting k-means method is used instead of traditional method to generate a hierarchical anchor points set. And then, the hierarchical bipartite graph can be constructed between the original points and the anchor points of last layer. Since we only consider the anchor points on the last layer rather than using a larger number of anchors to obtain the bipartite graph, our proposed method will greatly reduce the time consumption. Moreover, the automatic learning strategy was adopted to select the appropriate weights for each view in our proposed approach, which remove the weight-related hyper-parameters and effectively avoid the vexing problem of hyper-parameters in multi-view graph clustering. Finally, experiments were carried out on synthetic data and different sizes benchmark data respectively to verify the validity of our method.

Multi-order graph clustering with adaptive node-level weight learning

Current graph clustering methods emphasize individual node and edge connections, while ignoring higher-order organization at the level of motif. Recently, higher-order graph clustering approaches have been designed by motif-based hypergraphs. However, these approaches often suffer from hypergraph fragmentation issue seriously, which degrades the clustering performance greatly. Moreover, real-world graphs usually contain diverse motifs, with nodes participating in multiple motifs. A key challenge is how to achieve precise clustering results by integrating information from multiple motifs at the node level. In this paper, we propose a multi-order graph clustering model (MOGC) to integrate multiple higher-order structures and edge connections at node level. MOGC employs an adaptive weight learning mechanism to automatically adjust the contributions of different motifs for each node. This not only tackles hypergraph fragmentation issue but enhances clustering accuracy. MOGC is efficiently solved by an alternating minimization algorithm. Experiments on seven real-world datasets illustrate the effectiveness of MOGC.

ADPSCAN: Structural Graph Clustering with Adaptive Density Peak Selection and Noise Re-Clustering

Structural graph clustering is a data analysis technique that groups nodes within a graph based on their connectivity and structural similarity. The Structural graph clustering SCAN algorithm, a density-based clustering method, effectively identifies core points and their neighbors within areas of high density to form well-defined clusters. However, the clustering quality of SCAN heavily depends on the input parameters, ϵ and μ, making the clustering results highly sensitive to parameter selection. Different parameter settings can lead to significant differences in clustering results, potentially compromising the accuracy of the clusters. To address this issue, a novel structural graph clustering algorithm based on the adaptive selection of density peaks is proposed in this paper. Unlike traditional methods, our algorithm does not rely on external parameters and eliminates the need for manual selection of density peaks or cluster centers by users. Density peaks are adaptively identified using the generalized extreme value distribution, with consideration of the structural similarities and interdependencies among nodes, and clusters are expanded by incorporating neighboring nodes, enhancing the robustness of the clustering process. Additionally, a distance-based structural similarity method is proposed to re-cluster noise nodes to the correct clusters. Extensive experiments on real and synthetic graph datasets validate the effectiveness of our algorithm. The experiment results show that the ADPSCAN has a superior performance compared with several state-of-the-art (SOTA) graph clustering methods.

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.

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.

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.

New approach for learning structured graph with Laplacian rank constraint

Many existing graph-clustering methods get results in a two-stage manner, including constructing a graph from data and partitioning it. It always leads to sub-optimal performances. To address the drawbacks, imposing rank constraint on the graph’s Laplacian matrix is an effective way. It can learn a structured graph that connected components are exactly equal to the cluster numbers. According to separate connected components, it directly obtains clustering assignments. However, previous works heuristically solve it during the optimization without any theory guarantee. To handle this issue, we propose a novel solver to optimize this problem with theoretical advantages, enabling the structured bipartite graphs to directly indicate clustering results. Initially, we discover that pairwise and bipartite graphs exhibit the same connected components after undergoing a specific operation. Then, we derive an efficient algorithm to optimize two different clustering models with rank constraints based on this property. Moreover, our proposed method exhibits linear computational complexity to the data scale. Extensive empirical results on both synthetic and real benchmark data demonstrate that the proposed method outperforms existing methods.

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.

Dual Information Enhanced Multiview Attributed Graph Clustering.

Multiview attributed graph clustering is an important approach to partition multiview data based on the attribute characteristics and adjacent matrices from different views. Some attempts have been made in using graph neural network (GNN), which have achieved promising clustering performance. Despite this, few of them pay attention to the inherent specific information embedded in multiple views. Meanwhile, they are incapable of recovering the latent high-level representation from the low-level ones, greatly limiting the downstream clustering performance. To fill these gaps, a novel dual information enhanced multiview attributed graph clustering (DIAGC) method is proposed in this article. Specifically, the proposed method introduces the specific information reconstruction (SIR) module to disentangle the explorations of the consensus and specific information from multiple views, which enables graph convolutional network (GCN) to capture the more essential low-level representations. Besides, the contrastive learning (CL) module maximizes the agreement between the latent high-level representation and low-level ones and enables the high-level representation to satisfy the desired clustering structure with the help of the self-supervised clustering (SC) module. Extensive experiments on several real-world benchmarks demonstrate the effectiveness of the proposed DIAGC method compared with the state-of-the-art baselines.

A Clustering Method for Single-Cell RNA-Seq Data Based on Automatic Weighting Penalty and Low-Rank Representation.

Advances in high-throughput single-cell RNA sequencing (scRNA-seq) technology have provided more comprehensive biological information on cell expression. Clustering analysis is a critical step in scRNA-seq research and provides clear knowledge of the cell identity. Unfortunately, the characteristics of scRNA-seq data and the limitations of existing technologies make clustering encounter a considerable challenge. Meanwhile, some existing methods treat different features equally and ignore differences in feature contributions, which leads to a loss of information. To overcome limitations, we introduce a weighted distance constraint into the construction of the similarity graph and combine the similarity constraint. We propose the Joint Automatic Weighting Similarity Graph and Low-rank Representation (JAGLRR) clustering method. Evaluating the contributions of each feature and assigning various weight values can increase the significance of valuable features while decreasing the interference of redundant features. The similarity constraint allows the model to generate a more symmetric affinity matrix. Benefitting from that affinity matrix, JAGLRR recovers the original linear relationship of the data more accurately and obtains more discriminative information. The results on simulated datasets and 8 real datasets show that JAGLRR outperforms 11 existing comparison methods in clustering experiments, with higher clustering accuracy and stability.

A large-scale graph clustering method for cell conditions spatio-temporal localization in aluminum electrolysis

Sensor nodes (industrial nodes) clustering is an efficacious method for gaining local working conditions real-timely in the production process. The existing deep graph neural networks-based industrial nodes clustering studies construct static graphs to describe the potential spatial correlation among industrial nodes, but the temporal correlation among industrial nodes is ignored, resulting in inferior real-time performance. Meanwhile, these deep learning models fail to obtain good clustering results due to the large-scale and noise-containing characteristics of industrial nodes. In this paper, a large-scale graph clustering method (LsGCM) is proposed for cell conditions spatio-temporal localization in aluminum electrolysis to address the above issues. Specifically, a spatio-temporal graph construction method based on industrial process mechanism knowledge and local working condition boundary types statistical feature fusion is proposed for capturing effective spatio-temporal correlations between industrial nodes. Then, hysteresis knowledge of industrial production system is used to guide the nodes merging, thereby avoiding the incorrect merging of time-asynchronous nodes when performing the spatio-temporal region detection of local working conditions. Finally, combined with the actual spatio-temporal location information of industrial nodes, a novel spatio-temporal information expansion method (StIEM) of the sub-spatio-temporal graph describing local working condition is proposed for obtaining spatio-temporal feature information of the neighborhood, which is beneficial to improve the performance of industrial node clustering. Validation studies on a numerical simulation example and multiple real aluminum electrolysis industrial datasets certificate the effectiveness and superiority of the proposed method. In particular, compared with existing graph clustering methods, our method improves the clustering accuracy by 7.79%.

Enforced Block Diagonal Graph Learning for Multikernel Clustering

The existing multikernel graph clustering (MKGC) methods have emerged with notable success on nonlinear clustering tasks since the graph learning can effectively capture graph structure similarity between sample pair. Ideally, a high-quality graph should enjoy the good block diagonal property, i.e. the intercluster similarities correspond to zeros, while intracluster similarities represent nonzeros. Meanwhile, the number of diagonal blocks for a graph equals to the number of clusters on the dataset. However, most of the existing MKGC methods design a corpulent three-parts graph leaning process that poses challenges for hyperparameter tuning, time cost, and clustering performance. To overcome these challenging issues, we propose an enforced block diagonal graph learning for multikernel clustering (EBDGL-MKC) method, where we pursue a high-quality block diagonal graph via well-designed one-part graph leaning scheme rather than three parts. Inspired by symmetric matrix factorization (SMF), we first design a one-part block diagonal graph learning scheme to learn multiple block diagonal graphs, by exploring an explicit theoretical connection between the clustering partition of kernel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula> -means and the excellent block diagonal graph. Then, these block diagonal graphs are stacked into a low-rank tensor for exploiting the high-order structure information hidden in the nonlinear data. After that, an effective alternate algorithm with convergence proof is performed on extensive experiments to demonstrate the superiority of EBDGL compared with the state-of-the-art multikernel clustering (MKC) methods.

Deep Self-Supervised Attributed Graph Clustering for Social Network Analysis

Deep graph clustering is an unsupervised learning task that divides nodes in a graph into disjoint regions with the help of graph auto-encoders. Currently, such methods have several problems, as follows. (1) The deep graph clustering method does not effectively utilize the generated pseudo-labels, resulting in sub-optimal model training results. (2) Each cluster has a different confidence level, which affects the reliability of the pseudo-label. To address these problems, we propose a Deep Self-supervised Attribute Graph Clustering model (DSAGC) to fully leverage the information of the data itself. We divide the proposed model into two parts: an upstream model and a downstream model. In the upstream model, we use the pseudo-label information generated by spectral clustering to form a new high-confidence distribution with which to optimize the model for a higher performance. We also propose a new reliable sample selection mechanism to obtain more reliable samples for downstream tasks. In the downstream model, we only use the reliable samples and the pseudo-label for the semi-supervised classification task without the true label. We compare the proposed method with 17 related methods on four publicly available citation network datasets, and the proposed method generally outperforms most existing methods in three performance metrics. By conducting a large number of ablative experiments, we validate the effectiveness of the proposed method.

Fast Clustering With Anchor Guidance.

Clustering aims to partition a set of objects into different groups through the internal nature of these objects. Most existing methods face intractable hyper-parameter problems triggered by various regularization terms, which degenerates the applicability of models. Moreover, traditional graph clustering methods always encounter the expensive time overhead. To this end, we propose a Fast Clustering model with Anchor Guidance (FCAG). The proposed model not only avoids trivial solutions without extra regularization terms, but is also suitable to deal with large-scale problems by utilizing the prior knowledge of the bipartite graph. Moreover, the proposed FCAG can cope with out-of-sample extension problems. Three optimization methods Projected Gradient Descent (PGD) method, Iteratively Re-Weighted (IRW) algorithm and Coordinate Descent (CD) algorithm are proposed to solve FCAG. Extensive experiments verify the superiority of the optimization method CD. Besides, compared with other bipartite graph models, FCAG has the better performance with the less time cost. In addition, we prove through theory and experiment that when the learning rate of PGD tends to infinite, PGD is equivalent to IRW.

Product Space Clustering with Graph Learning for Diversifying Industrial Production

During economic crises, diversifying industrial production emerges as a critical strategy to address societal challenges. The Product Space, a graph representing industrial knowledge proximity, acts as a valuable tool for recommending diversified product offerings. These recommendations rely on the edges of the graph to identify suitable products. They can be improved by grouping similar products together, which results in more precise suggestions. Unlike the topology, the textual data in nodes of the Product Space graph are typically unutilized in graph clustering methods. In this context, we propose a novel approach for economic graph learning that incorporates learning node data alongside network topology. By applying this method to the Product Space dataset, we demonstrate how recommendations have been improved by presenting real-life applications. Our research employing a graph neural network demonstrates superior performance compared to methods like Louvain and I-Louvain. Our contribution introduces a node data-based deep graph clustering graph neural network that significantly advances the macroeconomic literature and addresses the imperative of diversifying industrial production. We discuss both the advantages and limitations of deep graph learning models in economics, laying the groundwork for future research.

Attribute-Missing Graph Clustering Network

Deep clustering with attribute-missing graphs, where only a subset of nodes possesses complete attributes while those of others are missing, is an important yet challenging topic in various practical applications. It has become a prevalent learning paradigm in existing studies to perform data imputation first and subsequently conduct clustering using the imputed information. However, these ``two-stage" methods disconnect the clustering and imputation processes, preventing the model from effectively learning clustering-friendly graph embedding. Furthermore, they are not tailored for clustering tasks, leading to inferior clustering results. To solve these issues, we propose a novel Attribute-Missing Graph Clustering (AMGC) method to alternately promote clustering and imputation in a unified framework, where we iteratively produce the clustering-enhanced nearest neighbor information to conduct the data imputation process and utilize the imputed information to implicitly refine the clustering distribution through model optimization. Specifically, in the imputation step, we take the learned clustering information as imputation prompts to help each attribute-missing sample gather highly correlated features within its clusters for data completion, such that the intra-class compactness can be improved. Moreover, to support reliable clustering, we maximize inter-class separability by conducting cost-efficient dual non-contrastive learning over the imputed latent features, which in turn promotes greater graph encoding capability for clustering sub-network. Extensive experiments on five datasets have verified the superiority of AMGC against competitors.