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Low model-dependent sensor placement method for water distribution networks using adaptive attributed graph clustering

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JOURNAL OF WATER PROCESS ENGINEERING 2025年 71卷

作者： Sun, Qingshuai Zhang, Yingjie Li, Ming Liu, Hualiang Lu, Biliang Li, Shujie Hunan Univ Coll Comp Sci & Elect Engn Changsha 410082 Peoples R China Hunan Univ Sci & Technol Sch Informat & Elect Engn Xiangtan 411201 Peoples R China Res Ctr Hunan Water Metrol Informat Engn Technol Changde 415000 Peoples R China

The installation of sensors is a crucial preliminary step in developing a smart water platform. Effective sensor placement can enhance real-time monitoring capabilities, thereby improving water production, distribution, and pipeline maintenance. However, sensor placement is often constrained by cost considerations and by the complexity and variability of water distribution network topologies, which pose significant challenges for location selection. This paper proposes a low model-dependent method for sensor placement by formulating the problem as a node classification task within a graph and utilizing attributed graph clustering to adaptively identify optimal placement locations across different networks. The proposed method incorporates topological characteristics and water usage patterns, reducing reliance on hydraulic models and improving the efficiency of sensor placement. Through this method, user nodes are classified based on a predefined number of sensors, and the center of each category is identified as the optimal location for sensor installation. The effectiveness of the proposed method is evaluated on six benchmark networks of different sizes and types. Comparative analyses with existing methods demonstrate that the proposed sensor placement method is highly adaptable to various water distribution networks, significantly improving leak identification performance and expediting the node selection process.

关键词： Water distribution network Sensor placement Leak identification attributed graph clustering graph convolution

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Homophily Induced Contrastive attributed graph clustering

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IEEE Transactions on Circuits and Systems for Video Technology 2025年

作者： Chen, Man-Sheng Lai, Pei-Yuan Liao, De-Zhang Wang, Chang-Dong Lai, Jian-Huang Sun Yat-sen University School of Computer Science and Engineering Guangzhou China Guangxi Zhuang Autonomous Region Information Center Guangxi Key Laboratory of Digital Infrastructure Nanning China Guangdong Key Laboratory of Big Data Analysis and Processing Guangzhou China Key Laboratory of Machine Intelligence and Advanced Computing Ministry of Education China South China Technology Commercialization Center Guangzhou China Guangdong Key Laboratory of Information Security Technology Guangzhou China

attributed graph clustering, aiming to discover the underlying graph structure and partition the graph nodes into several disjoint categories, is a basic task in graph data analysis. Although recent efforts over graph contrastive clustering have achieved decent performances, most of them get accustomed to construct the positive neighbor set by the generated pseudo clustering information, directly ignoring the ready-made neighbor nodes and the underlying semantics of edges in a graph. How to well deal with the graph neighbor-specific information to facilitate the performance of graph contrastive clustering is still a challenging problem. Therefore, in this work, we propose a novel Homophily Induced Contrastive attributed graph clustering (HomoCAGC) method, where the power of homophily is exploited in facilitating the performance of contrastive attributed graph clustering, while the pseudo homophily in a graph is also explored and distinguished. Especially, the node feature as reliable information guidance is used to compute the underlying feature-oriented pair-wise node similarity, based on which the positive node pairs in contrastive regularizer are adjusted for better node representation characterization. According to the refined node representations, a triplet self-supervised clustering objective is well-designed to ensure the output embedding is cluster-oriented, and suitable for the downstream clustering task. Extensive experiments on seven benchmarks are conducted to demonstrate the effectiveness of HomoCAGC. © 1991-2012 IEEE.

关键词： attributed graph clustering contrastive learning graph homophily self-supervised clustering

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attributed graph clustering with multi-task embedding learning

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NEURAL NETWORKS 2022年 152卷 224-233页

作者： Zhang, Xiaotong Liu, Han Zhang, Xianchao Liu, Xinyue Dalian Univ Technol Sch Software Dalian Peoples R China Key Lab Ubiquitous Network & Serv Software Liaonin Dalian Peoples R China

attributed graph clustering is challenging as it needs to effectively combine both graph structure and node feature information to accomplish node clustering. Recent studies mostly adopt graph neural networks to learn node embeddings, then apply traditional clustering methods to obtain clusters. However, their node embeddings are not specifically designed for clustering. Moreover, most of their loss functions only rely on either structure or feature information, making both kinds of information not fully retained in node embeddings. In this paper, we propose a multi-task embedding learning method (MTEL) for attributed graph clustering, which constructs two prediction tasks in terms of structure and feature based adjacency matrices respectively. To make the node embeddings helpful for the downstream clustering, in each task, we predict the minimum hop number between each pair of nodes in the adjacency matrix, so that the correlation degrees among nodes can be encoded into node embeddings. To improve the performance of the prediction task, we regularize the model parameters in these two tasks via l(2,1) norm, through which the model parameters can be jointly learned. Experiments on real attributed graphs show that MTEL is superior for attributed graph clustering over state-of-the-art methods. (C) 2022 Elsevier Ltd. All rights reserved.

关键词： attributed graph clustering Multi-task learning Network embedding

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Effective multi-view representation learning for single-view attributed graph clustering

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Knowledge-Based Systems 2025年 322卷

作者： Liu, Heng Zhao, Weizhi Bao, Zhou Ye, Mingquan Shan, Caifeng School of Computer Science and Technology Anhui University of Technology Anhui Maanshan 243032 China School of Medical Information Wannan Medical College Anhui Wuhu 241002 China Institute of Artificial Intelligence Heifei Comprehensive National Science Center Hefei 230088 China School of Intelligence Science and Technology Nanjing University Nanjing 210023 China College of Electrical Engineering and Automation Shandong University of Science and Technology Shandong Qingdao 266590 China

Recent advances in graph convolutional networks (GCNs) have increasingly used graph attention mechanisms for generating embedded feature representations for graph clustering. However, regardless of whether multi-view or single-view clustering is used, owing to the sensitivity of graph attention mechanisms to structural noise, the obtained embedded feature representations often lack robustness. Furthermore, with single-view data, existing multi-view clustering methods lose their collaborative potential when relying on a single-view graph structure, making it challenging to generate effective multi-view representations. To address these issues, this study proposes a novel single-view attributed graph clustering model - S2M, which learns effective multi-view feature embeddings. We propose a flexible and controllable data enhancement method for single-view data that constructs a multi-view graph while reducing the impact of structural noise. Subsequently, we introduce a novel approach that leverages node predictions to guide multi-view feature fusion, enabling the learning of clustering-oriented representations and deriving target distribution from high-confidence nodes. In addition, we improve clustering robustness through cross-coding, leveraging the consistency and collaboration of embeddings across multiple view branches. Extensive experiments on benchmark datasets confirm that the proposed method delivers superior clustering performance, surpassing state-of-the-art approaches. This code is available at https://***/hengliusky/S2M_clustering. © 2025

关键词： attributed graph clustering Embedded representations GCN Multi-view graph Single-view data

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Towards attributed graph clustering using enhanced graph and reconstructed graph structure

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ARTIFICIAL INTELLIGENCE REVIEW 2024年第11期57卷 1-31页

作者： Yang, Xuejin Xie, Cong Zhou, Kemin Song, Shaoyun Yang, Junsheng Li, Bin Wuhan Polytech Univ Coll Mech Engn Wuhan 430048 Hubei Peoples R China

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.

关键词： attributed graph clustering graph convolutional networks Enhanced graph Reconstructing structure Subspace clustering Dual-guidance supervisor

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CAMAS: A cluster-aware multiagent system for attributed graph clustering

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INFORMATION FUSION 2017年 37卷 10-21页

作者： Bu, Zhan Gao, Guangliang Li, Hui-Jia Cao, Jie Nanjing Univ Finance & Econ Jiangsu Prov Key Lab E Business Nanjing Jiangsu Peoples R China Nanjing Univ Sci & Technol Coll Comp Sci & Engn Nanjing Jiangsu Peoples R China Cent Univ Finance & Econ Sch Management Sci & Engn Beijing Peoples R China

attributed graphs describe nodes via attribute vectors and also relationships between different nodes via edges. To partition nodes into clusters with tighter correlations, an effective way is applying clustering techniques on attributed graphs based on various criteria such as node connectivity and/or attribute similarity. Even though clusters typically form around nodes with tight edges and similar attributes, existing methods have only focused on one of these two data modalities. In this paper, we comprehend each node as an autonomous agent and develop an accurate and scalable multiagent system for extracting overlapping clusters in attributed graphs. First, a kernel function with a tunable bandwidth factor delta is introduced to measure the influence of each agent, and those agents, with highest local influence can be viewed as the "leader" agents. Then, a novel local expansion strategy is proposed, which can be applied by each leader agent to absorb the most relevant followers in the graph. Finally, we design the cluster-aware multiagent system (CAMAS), in which agents communicate with each other freely under an efficient communication mechanism. Using the proposed multiagent system, we are able to uncover the optimal overlapping cluster configuration, i.e. nodes within one cluster are not only connected closely with each other but also with similar attributes. Our method is highly efficient, and the computational time is shown that nearly linearly dependent on the number of edges when delta is an element of [0.5, 1). Finally, applications of the proposed method on a variety of synthetic benchmark graphs and real-life attributed graphs are demonstrated to verify the systematic performance. (C) 2017 Elsevier B.V. All rights reserved.

关键词： attributed graph clustering Cluster-aware Multiagent system Leader identification Cluster extraction

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GBAGC: A General Bayesian Framework for attributed graph clustering

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ACM TRANSACTIONS ON KNOWLEDGE DISCOVERY FROM DATA 2014年第1期9卷 1–43页

作者： Xu, Zhiqiang Ke, Yiping Wang, Yi Cheng, Hong Cheng, James Nanyang Technol Univ Sch Comp Engn Singapore 639798 Singapore Inst High Performance Comp Singapore 138632 Singapore Chinese Univ Hong Kong Dept Syst Engn & Engn Management Shatin Hong Kong Peoples R China Chinese Univ Hong Kong Dept Comp Sci & Engn Shatin Hong Kong Peoples R China

graph clustering, also known as community detection, is a long-standing problem in data mining. In recent years, with the proliferation of rich attribute information available for objects in real-world graphs, how to leverage not only structural but also attribute information for clustering attributed graphs becomes a new challenge. Most existing works took a distance-based approach. They proposed various distance measures to fuse structural and attribute information and then applied standard techniques for graph clustering based on these distance measures. In this article, we take an alternative view and propose a novel Bayesian framework for attributed graph clustering. Our framework provides a general and principled solution to modeling both the structural and the attribute aspects of a graph. It avoids the artificial design of a distance measure in existing methods and, furthermore, can seamlessly handle graphs with different types of edges and vertex attributes. We develop an efficient variational method for graph clustering under this framework and derive two concrete algorithms for clustering unweighted and weighted attributed graphs. Experimental results on large real-world datasets show that our algorithms significantly outperform the state-of-the-art distance-based method, in terms of both effectiveness and efficiency.

关键词： attributed graph clustering model-based clustering Bayesian method

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Smoothness Sensor: Adaptive Smoothness-Transition graph Convolutions for attributed graph clustering

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IEEE TRANSACTIONS ON CYBERNETICS 2022年第12期52卷 12771-12784页

作者： Ji, Chaojie Chen, Hongwei Wang, Ruxin Cai, Yunpeng Wu, Hongyan Chinese Acad Sci Joint Engn Res Ctr Hlth Big Data Intelligent Anal Shenzhen Inst Adv Technol Shenzhen 518055 Peoples R China Chinese Acad Sci Shenzhen Inst Adv Technol Shenzhen 518055 Peoples R China Univ Chinese Acad Sci Beijing 100049 Peoples R China

clustering techniques attempt to group objects with similar properties into a cluster. clustering the nodes of an attributed graph, in which each node is associated with a set of feature attributes, has attracted significant attention. graph convolutional networks (GCNs) represent an effective approach for integrating the two complementary factors of node attributes and structural information for attributed graph clustering. Smoothness is an indicator for assessing the degree of similarity of feature representations among nearby nodes in a graph. Oversmoothing in GCNs, caused by unnecessarily high orders of graph convolution, produces indistinguishable representations of nodes, such that the nodes in a graph tend to be grouped into fewer clusters, and pose a challenge due to the resulting performance drop. In this study, we propose a smoothness sensor for attributed graph clustering based on adaptive smoothness-transition graph convolutions, which senses the smoothness of a graph and adaptively terminates the current convolution once the smoothness is saturated to prevent oversmoothing. Furthermore, as an alternative to graph-level smoothness, a novel fine-grained nodewise-level assessment of smoothness is proposed, in which smoothness is computed in accordance with the neighborhood conditions of a given node at a certain order of graph convolution. In addition, a self-supervision criterion is designed considering both the tightness within clusters and the separation between clusters to guide the entire neural network training process. The experiments show that the proposed methods significantly outperform 13 other state-of-the-art baselines in terms of different metrics across five benchmark datasets. In addition, an extensive study reveals the reasons for their effectiveness and efficiency.

关键词： Convolution Matrix decomposition Deep learning Laplace equations Smoothing methods Eigenvalues and eigenfunctions Unsupervised learning Adaptive graph convolutions attributed graph clustering graph neural networks smoothness of graph signals

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Deep linear graph attention model for attributed graph clustering

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KNOWLEDGE-BASED SYSTEMS 2022年 246卷

作者： Liao, Huifa Hu, Jie Li, Tianrui Du, Shengdong Peng, Bo Southwest Jiaotong Univ Sch Comp & Artificial Intelligence Chengdu 611756 Peoples R China

attributed graph clustering is an important task for grouping the nodes in a graph. In recent years, the algorithms based on graph convolutional networks (GCN) have achieved promising performance. However, almost all existing methods ignore that the nonlinearity between two consecutive GCN layers is unnecessary for improving the performance of attributed graph clustering, and may even harm the efficiency of the model. In this paper, we propose a novel deep linear graph attention model for attributed graph clustering (DLGAMC), which consists of an attention-based aggregation module and a similarity preserve module. Specifically, we simply exploit cosine similarity to construct the attention for aggregation, which does not need to learn extra attention parameters. It is worth noting that the attention we designed not only explicitly considers the similarity of attribute information, but also implicitly takes into account the local graph structure. To select the proper order of aggregation, we propose an adaptive strategy to evaluate the smoothness of node representations, where intra-cluster distance and inter-cluster distance are the key indicators in this process. To learn node representations for clustering, we design a similarity preserve module to preserve local similarity and global dissimilarity of the smooth features obtained by multiple aggregations, which is different from the ideas in reconstruction-based methods. Finally, k-means is performed on the learned representations to obtain the cluster partition. Experiments on several datasets show that our algorithm achieves great performance in attributed graph clustering tasks. (c) 2022 Elsevier B.V. All rights reserved.

关键词： attributed graph clustering Linear model Attention-based fusion graph neural network graph representation learning

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Efficient nonparametric and asymptotic Bayesian model selection methods for attributed graph clustering

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KNOWLEDGE AND INFORMATION SYSTEMS 2017年第1期53卷 239-268页

作者： Xu, Zhiqiang Cheng, James Xiao, Xiaokui Fujimaki, Ryohei Muraoka, Yusuke King Abdullah Univ Sci & Technol KAUST Comp Elect & Math Sci & Engn Div Thuwal Saudi Arabia Chinese Univ Hong Kong Dept Comp Sci & Engn Shatin Hong Kong Peoples R China Nanyang Technol Univ Sch Comp Engn Singapore Singapore NEC Labs Amer 10080 North Wolfe Rd SW 350 Cupertino CA 95014 USA NEC Labs Japan Nakahara Ku 1753 Shimonumabe Kawasaki Kanagawa 2118666 Japan

attributed graph clustering, also known as community detection on attributed graphs, attracts much interests recently due to the ubiquity of attributed graphs in real life. Many existing algorithms have been proposed for this problem, which are either distance based or model based. However, model selection in attributed graph clustering has not been well addressed, that is, most existing algorithms assume the cluster number to be known a priori. In this paper, we propose two efficient approaches for attributed graph clustering with automatic model selection. The first approach is a popular Bayesian nonparametric method, while the second approach is an asymptotic method based on a recently proposed model selection criterion, factorized information criterion. Experimental results on both synthetic and real datasets demonstrate that our approaches for attributed graph clustering with automatic model selection significantly outperform the state-of-the-art algorithm.

关键词： attributed graph clustering Model selection Dirichlet process Factorized information criterion

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