Local clustering aims to find a compact cluster near the given starting instances. This work focuses on graph local clustering, which has broad applications beyond graphs because of the internal connectivities within various modalities. While most existing studies on local graph clustering adopt the discrete graph setting (i.e., unweighted graphs without self-loops), real-world graphs can be more complex. In this paper, we extend the non-approximating Andersen-Chung-Lang ("ACL") algorithm beyond discrete graphs and generalize its quadratic optimality to a wider range of graphs, including weighted, directed, and self-looped graphs and hypergraphs. Specifically, leveraging PageRank, we propose two algorithms: GeneralACL for graphs and HyperACL for hypergraphs. We theoretically prove that, under two mild conditions, both algorithms can identify a quadratically optimal local cluster in terms of conductance with at least 1/2 probability. On the property of hypergraphs, we address a fundamental gap in the literature by defining conductance for hypergraphs from the perspective of hypergraph random walks. Additionally, we provide experiments to validate our theoretical findings.
Intelligent streetlight systems divide the streetlight network into multiple sectors, activating only the streetlights in the corresponding sectors when traffic elements pass by, rather than all streetlights, effectively reducing energy waste. This strategy requires streetlights to understand their neighbor relationships to illuminate only the streetlights in their respective sectors. However, manually configuring the neighbor relationships for a large number of streetlights in complex large-scale road streetlight networks is cumbersome and prone to errors. Due to the crisscrossing nature of roads, it is also difficult to determine the neighbor relationships using GPS or communication positioning. In response to these issues, this article proposes a systematic approach to model the streetlight network as a social network and construct a neighbor relationship probabilistic graph using IoT event records of streetlights detecting traffic elements. Based on this, a multi-objective genetic algorithm based probabilistic graph clustering method is designed to discover the neighbor relationships of streetlights. Considering the characteristic that pedestrians and vehicles usually move at a constant speed on a section of a road, speed consistency is introduced as an optimization objective, which, together with traditional similarity measures, forms a multi-objective function, enhancing the accuracy of neighbor relationship discovery. Extensive experiments on simulation datasets were conducted, comparing the proposed algorithm with other probabilistic graph clustering algorithms. The results demonstrate that the proposed algorithm can more accurately identify the neighbor relationships of streetlights compared to other algorithms, effectively achieving adaptive streetlight control for traffic elements.
We present a method for graph clustering that is analogous with gradient ascent methods previously proposed for clustering points in space. We show that, when applied to a random geometric graph with data iid from some density with Morse regularity, the method is asymptotically consistent. Here, consistency is understood with respect to a density-level clustering defined by the partition of the support of the density induced by the basins of attraction of the density modes.
Clustering complex data in the form of attributed graphs has attracted increasing attention, where appropriate graph representation is a critical prerequisite for accurate cluster analysis. However, the Graph Convolutional Network will homogenize the representation of graph nodes due to the well-known over-smoothing effect. This limits the network architecture to a shallow one, losing the ability to capture the critical global distribution information for clustering. Therefore, we propose a generalized graph auto-encoder network, which introduces quaternion operations to the encoders to achieve efficient structured feature representation learning without incurring deeper network and larger-scale parameters. The generalization of our method lies in the following two aspects: 1) connecting the quaternion operation naturally suitable for four feature components with graph data of arbitrary attribute dimensions, and 2) introducing a generalized graph clustering objective as a loss term to obtain clustering-friendly representations without requiring a pre-specified number of clusters $k$. It turns out that the representations of nodes learned by the proposed Graph Clustering based on Generalized Quaternion representation learning (GCGQ) are more discriminative, containing global distribution information, and are more general, suiting downstream clustering under different $k$s. Extensive experiments including significance tests, ablation studies, and qualitative results, illustrate the superiority of GCGQ. The source code is temporarily opened at \url{https://anonymous.4open.science/r/ICLR-25-No7181-codes}.
Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering methods often face practical challenges related to data isolation. Moreover, the absence of collaborative methods for graph clustering limits their effectiveness. In this paper, we propose a collaborative graph clustering framework for attributed graphs, supporting attributed graph clustering over vertically partitioned data with different participants holding distinct features of the same data. Our method leverages a novel technique that reduces the sample space, improving the efficiency of the attributed graph clustering method. Furthermore, we compare our method to its centralized counterpart under a proximity condition, demonstrating that the successful local results of each participant contribute to the overall success of the collaboration. We fully implement our approach and evaluate its utility and efficiency by conducting experiments on four public datasets. The results demonstrate that our method achieves comparable accuracy levels to centralized attributed graph clustering methods. Our collaborative graph clustering framework provides an efficient and effective solution for graph clustering challenges related to data isolation.
Optimal transport (OT) is a general framework for finding a minimum-cost transport plan, or coupling, between probability distributions, and has many applications in machine learning. A key challenge in applying OT to massive datasets is the quadratic scaling of the coupling matrix with the size of the dataset. [Forrow et al. 2019] introduced a factored coupling for the k-Wasserstein barycenter problem, which [Scetbon et al. 2021] adapted to solve the primal low-rank OT problem. We derive an alternative parameterization of the low-rank problem based on the $\textit{latent coupling}$ (LC) factorization previously introduced by [Lin et al. 2021] generalizing [Forrow et al. 2019]. The LC factorization has multiple advantages for low-rank OT including decoupling the problem into three OT problems and greater flexibility and interpretability. We leverage these advantages to derive a new algorithm $\textit{Factor Relaxation with Latent Coupling}$ (FRLC), which uses $\textit{coordinate}$ mirror descent to compute the LC factorization. FRLC handles multiple OT objectives (Wasserstein, Gromov-Wasserstein, Fused Gromov-Wasserstein), and marginal constraints (balanced, unbalanced, and semi-relaxed) with linear space complexity. We provide theoretical results on FRLC, and demonstrate superior performance on diverse applications -- including graph clustering and spatial transcriptomics -- while demonstrating its interpretability.
We introduce the ParClusterers Benchmark Suite (PCBS) -- a collection of highly scalable parallel graph clustering algorithms and benchmarking tools that streamline comparing different graph clustering algorithms and implementations. The benchmark includes clustering algorithms that target a wide range of modern clustering use cases, including community detection, classification, and dense subgraph mining. The benchmark toolkit makes it easy to run and evaluate multiple instances of different clustering algorithms, which can be useful for fine-tuning the performance of clustering on a given task, and for comparing different clustering algorithms based on different metrics of interest, including clustering quality and running time. Using PCBS, we evaluate a broad collection of real-world graph clustering datasets. Somewhat surprisingly, we find that the best quality results are obtained by algorithms that not included in many popular graph clustering toolkits. The PCBS provides a standardized way to evaluate and judge the quality-performance tradeoffs of the active research area of scalable graph clustering algorithms. We believe it will help enable fair, accurate, and nuanced evaluation of graph clustering algorithms in the future.
This paper presents a multiscale graph construction method using both graph and signal features. Multiscale graph is a hierarchical representation of the graph, where a node at each level indicates a cluster in a finer resolution. To obtain the hierarchical clusters, existing methods often use graph clustering; however, they may ignore signal variations. As a result, these methods could fail to detect the clusters having similar features on nodes. In this paper, we consider graph and node-wise features simultaneously for multiscale clustering of a graph. With given clusters of the graph, the clusters are merged hierarchically in three steps: 1) Feature vectors in the clusters are extracted. 2) Similarities among cluster features are calculated using optimal transport. 3) A variable $k$-nearest neighbor graph (V$k$NNG) is constructed and graph spectral clustering is applied to the V$k$NNG to obtain clusters at a coarser scale. Additionally, the multiscale graph in this paper has \textit{non-local} characteristics: Nodes with similar features are merged even if they are spatially separated. In experiments on multiscale image and point cloud segmentation, we demonstrate the effectiveness of the proposed method.
Multi-view clustering is an important machine learning task for multi-media data, encompassing various domains such as images, videos, and texts. Moreover, with the growing abundance of graph data, the significance of multi-view graph clustering (MVGC) has become evident. Most existing methods focus on graph neural networks (GNNs) to extract information from both graph structure and feature data to learn distinguishable node representations. However, traditional GNNs are designed with the assumption of homophilous graphs, making them unsuitable for widely prevalent heterophilous graphs. Several techniques have been introduced to enhance GNNs for heterophilous graphs. While these methods partially mitigate the heterophilous graph issue, they often neglect the advantages of traditional GNNs, such as their simplicity, interpretability, and efficiency. In this paper, we propose a novel multi-view graph clustering method based on dual-optimized adaptive graph reconstruction, named DOAGC. It mainly aims to reconstruct the graph structure adapted to traditional GNNs to deal with heterophilous graph issues while maintaining the advantages of traditional GNNs. Specifically, we first develop an adaptive graph reconstruction mechanism that accounts for node correlation and original structural information. To further optimize the reconstruction graph, we design a dual optimization strategy and demonstrate the feasibility of our optimization strategy through mutual information theory. Numerous experiments demonstrate that DOAGC effectively mitigates the heterophilous graph problem.
Graph clustering is an essential aspect of network analysis that involves grouping nodes into separate clusters. Recent developments in deep learning have resulted in graph clustering, which has proven effective in many applications. Nonetheless, these methods often encounter difficulties when dealing with real-world graphs, particularly in the presence of noisy edges. Additionally, many denoising graph clustering methods tend to suffer from lower performance, training instability, and challenges in scaling to large datasets compared to non-denoised models. To tackle these issues, we introduce a new framework called the Robust Deep Graph Clustering Framework via Dual Soft Assignment (RDSA). RDSA consists of three key components: (i) a node embedding module that effectively integrates the graph's topological features and node attributes; (ii) a structure-based soft assignment module that improves graph modularity by utilizing an affinity matrix for node assignments; and (iii) a node-based soft assignment module that identifies community landmarks and refines node assignments to enhance the model's robustness. We assess RDSA on various real-world datasets, demonstrating its superior performance relative to existing state-of-the-art methods. Our findings indicate that RDSA provides robust clustering across different graph types, excelling in clustering effectiveness and robustness, including adaptability to noise, stability, and scalability.
Network analysis is increasingly important across various fields, including the fragrance industry, where perfumes are represented as nodes and shared user preferences as edges in perfume networks. Community detection can uncover clusters of similar perfumes, providing insights into consumer preferences, enhancing recommendation systems, and informing targeted marketing strategies. This study aims to apply community detection techniques to group perfumes favored by users into relevant clusters for better recommendations. We constructed a bipartite network from user reviews on the Persian retail platform "Atrafshan," with nodes representing users and perfumes, and edges formed by positive comments. This network was transformed into a Perfume Co-Preference Network, connecting perfumes liked by the same users. By applying community detection algorithms, we identified clusters based on shared preferences, enhancing our understanding of user sentiment in the fragrance market. To improve sentiment analysis, we integrated emojis and a user voting system for greater accuracy. Emojis, aligned with their Persian counterparts, captured the emotional tone of reviews, while user ratings for scent, longevity, and sillage refined sentiment classification. Edge weights were adjusted by combining adjacency values with user ratings in a 60:40 ratio, reflecting both connection strength and user preferences. These enhancements led to improved modularity of detected communities, resulting in more accurate perfume groupings. This research pioneers the use of community detection in perfume networks, offering new insights into consumer preferences. Our advancements in sentiment analysis and edge weight refinement provide actionable insights for optimizing product recommendations and marketing strategies in the fragrance industry.
Fair graph clustering is crucial for ensuring equitable representation and treatment of diverse communities in network analysis. Traditional methods often ignore disparities among social, economic, and demographic groups, perpetuating biased outcomes and reinforcing inequalities. This study introduces fair graph clustering within the framework of the disparate impact doctrine, treating it as a joint optimization problem integrating clustering quality and fairness constraints. Given the NP-hard nature of this problem, we employ a semidefinite relaxation approach to approximate the underlying optimization problem. For up to medium-sized graphs, we utilize a singular value decomposition-based algorithm, while for larger graphs, we propose a novel algorithm based on the alternative direction method of multipliers. Unlike existing methods, our formulation allows for tuning the trade-off between clustering quality and fairness. Experimental results on graphs generated from the standard stochastic block model demonstrate the superiority of our approach in achieving an optimal accuracy-fairness trade-off compared to state-of-the-art methods.
Temporal graph clustering is a complex task that involves discovering meaningful structures in dynamic graphs where relationships and entities change over time. Existing methods typically require centralized data collection, which poses significant privacy and communication challenges. In this work, we introduce a novel Federated Temporal Graph Clustering (FTGC) framework that enables decentralized training of graph neural networks (GNNs) across multiple clients, ensuring data privacy throughout the process. Our approach incorporates a temporal aggregation mechanism to effectively capture the evolution of graph structures over time and a federated optimization strategy to collaboratively learn high-quality clustering representations. By preserving data privacy and reducing communication overhead, our framework achieves competitive performance on temporal graph datasets, making it a promising solution for privacy-sensitive, real-world applications involving dynamic data.
With the increasing prevalence of graph-structured data, multi-view graph clustering has been widely used in various downstream applications. Existing approaches primarily rely on a unified message passing mechanism, which significantly enhances clustering performance. Nevertheless, this mechanism limits its applicability to heterophilous situations, as it is fundamentally predicated on the assumption of homophily, i.e., the connected nodes often belong to the same class. In reality, this assumption does not always hold; a moderately or even mildly homophilous graph is more common than a fully homophilous one due to inevitable heterophilous information in the graph. To address this issue, in this paper, we propose a novel SiMilarity-enhanced Homophily for Multi-view Heterophilous Graph Clustering (SMHGC) approach. By analyzing the relationship between similarity and graph homophily, we propose to enhance the homophily by introducing three similarity terms, i.e., neighbor pattern similarity, node feature similarity, and multi-view global similarity, in a label-free manner. Then, a consensus-based inter- and intra-view fusion paradigm is proposed to fuse the improved homophilous graph from different views and utilize them for clustering. The state-of-the-art experimental results on both multi-view heterophilous and homophilous datasets collectively demonstrate the strong capacity of similarity for unsupervised multi-view heterophilous graph learning. Additionally, the consistent performance across semi-synthetic datasets with varying levels of homophily serves as further evidence of SMHGC's resilience to heterophily.
Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting interpretability and practical visualization. In this work, we introduce Topological Evolution Rate (TopER), a novel, low-dimensional embedding approach grounded in topological data analysis. TopER simplifies a key topological approach, Persistent Homology, by calculating the evolution rate of graph substructures, resulting in intuitive and interpretable visualizations of graph data. This approach not only enhances the exploration of graph datasets but also delivers competitive performance in graph clustering and classification tasks. Our TopER-based models achieve or surpass state-of-the-art results across molecular, biological, and social network datasets in tasks such as classification, clustering, and visualization.
Cross-camera data association is one of the cornerstones of the multi-camera computer vision field. Although often integrated into detection and tracking tasks through architecture design and loss definition, it is also recognized as an independent challenge. The ultimate goal is to connect appearances of one item from all cameras, wherever it is visible. Therefore, one possible perspective on this task involves supervised clustering of the affinity graph, where nodes are instances captured by all cameras. They are represented by appropriate visual features and positional attributes. We leverage the advantages of GNN (Graph Neural Network) architecture to examine nodes' relations and generate representative edge embeddings. These embeddings are then classified to determine the existence or non-existence of connections in node pairs. Therefore, the core of this approach is graph connectivity prediction. Experimental validation was conducted on multicamera pedestrian datasets across diverse environments such as the laboratory, basketball court, and terrace. Our proposed method, named SGC-CCA, outperformed the state-of-the-art method named GNN-CCA across all clustering metrics, offering an end-to-end clustering solution without the need for graph post-processing. The code is available at https://github.com/djordjened92/cca-gnnclust.
Hypergraphs tackle the limitations of traditional graphs by introducing {\em hyperedges}. While graph edges connect only two nodes, hyperedges connect an arbitrary number of nodes along their edges. Also, the underlying message-passing mechanisms in Hypergraph Neural Networks (HGNNs) are in the form of vertex-hyperedge-vertex, which let HGNNs capture and utilize richer and more complex structural information than traditional Graph Neural Networks (GNNs). More recently, the idea of overlapping subgraphs has emerged. These subgraphs can capture more information about subgroups of vertices without limiting one vertex belonging to just one group, allowing vertices to belong to multiple groups or subgraphs. In addition, one of the most important problems in graph clustering is to find densest overlapping subgraphs (DOS). In this paper, we propose a solution to the DOS problem via Agglomerative Greedy Enumeration (DOSAGE) algorithm as a novel approach to enhance the process of generating the densest overlapping subgraphs and, hence, a robust construction of the hypergraphs. Experiments on standard benchmarks show that the DOSAGE algorithm significantly outperforms the HGNNs and six other methods on the node classification task.
Recent advances in unsupervised deep graph clustering have been significantly promoted by contrastive learning. Despite the strides, most graph contrastive learning models face challenges: 1) graph augmentation is used to improve learning diversity, but commonly used random augmentation methods may destroy inherent semantics and cause noise; 2) the fixed positive and negative sample selection strategy is limited to deal with complex real data, thereby impeding the model's capability to capture fine-grained patterns and relationships. To reduce these problems, we propose the Clustering-guided Curriculum Graph contrastive Learning (CCGL) framework. CCGL uses clustering entropy as the guidance of the following graph augmentation and contrastive learning. Specifically, according to the clustering entropy, the intra-class edges and important features are emphasized in augmentation. Then, a multi-task curriculum learning scheme is proposed, which employs the clustering guidance to shift the focus from the discrimination task to the clustering task. In this way, the sample selection strategy of contrastive learning can be adjusted adaptively from early to late stage, which enhances the model's flexibility for complex data structure. Experimental results demonstrate that CCGL has achieved excellent performance compared to state-of-the-art competitors.
Graph clustering is a crucial task in network analysis with widespread applications, focusing on partitioning nodes into distinct groups with stronger intra-group connections than inter-group ones. Recently, contrastive learning has achieved significant progress in graph clustering. However, most methods suffer from the following issues: 1) an over-reliance on meticulously designed data augmentation strategies, which can undermine the potential of contrastive learning. 2) overlooking cluster-oriented structural information, particularly the higher-order cluster(community) structure information, which could unveil the mesoscopic cluster structure information of the network. In this study, Structure-enhanced Contrastive Learning (SECL) is introduced to addresses these issues by leveraging inherent network structures. SECL utilizes a cross-view contrastive learning mechanism to enhance node embeddings without elaborate data augmentations, a structural contrastive learning module for ensuring structural consistency, and a modularity maximization strategy for harnessing clustering-oriented information. This comprehensive approach results in robust node representations that greatly enhance clustering performance. Extensive experiments on six datasets confirm SECL's superiority over current state-of-the-art methods, indicating a substantial improvement in the domain of graph clustering.
Graph clustering is a fundamental and challenging learning task, which is conventionally approached by grouping similar vertices based on edge structure and feature similarity.In contrast to previous methods, in this paper, we investigate how multi-view feature propagation can influence cluster discovery in graph data.To this end, we present Graph Clustering With Cross-View Feature Propagation (GCCFP), a novel method that leverages multi-view feature propagation to enhance cluster identification in graph data.GCCFP employs a unified objective function that utilizes graph topology and multi-view vertex features to determine vertex cluster membership, regularized by a module that supports key latent feature propagation. We derive an iterative algorithm to optimize this function, prove model convergence within a finite number of iterations, and analyze its computational complexity. Our experiments on various real-world graphs demonstrate the superior clustering performance of GCCFP compared to well-established methods, manifesting its effectiveness across different scenarios.