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clustering structure-Induced Robust Multi-View Graph Recovery

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY 2020年第10期30卷 3584-3597页

作者： Wong, Wai Keung Han, Na Fang, Xiaozhao Zhan, Shanhua Wen, Jie Hong Kong Polytech Univ Inst Text & Clothing Hong Kong Peoples R China Hong Kong Polytech Univ Shenzhen Res Inst Hong Kong 518055 Peoples R China Guangdong Univ Technol Sch Comp Sci Guangzhou 510006 Guangdong Peoples R China Guangdong Univ Technol Sch Automat Guangzhou 510006 Guangdong Peoples R China Harbin Inst Technol Shenzhen Grad Sch Biocomp Res Ctr Shenzhen 518055 Guangdong Peoples R China

Graph based classification methods have been widely applied in the fields of computer vision and machine learning. The quality of the graph highly affects the performance of these methods. The same object is commonly represented by different features, i.e., multi-view features, which leads to multiple graphs corresponding to different features in multi-view learning. However, what kind of graph is important for the task is unknown in advance. Moreover, existing multi-view learning methods become weak in dealing with noisy graphs when the data is corrupted by the noise. In this paper, we address this problem by observing that the noise of each graph has specific structure. Then, based on this observation we propose a robust multi-view graph recovery (RMGR) method in which the specific structure is used to clean the multiple input noisy graphs and these cleaned graphs are simultaneously aggregated into a consensus graph by adaptively assigning great weighted coefficients for important graphs. To make the consensus graph suit classification, the clustering structure is introduced to restrain the rank of Laplacian matrix of the consensus graph such that the number of its connected components is equal to that of clustering. In doing so, the graph is adaptively adjusted during optimization to more accurately partition data. The optimization problem is solved by proposed the iterative update algorithm. Extensive experiments on synthetic and several benchmark data sets show the effectiveness of the proposed method.

关键词： Sparse matrices Learning systems Optimization Task analysis Laplace equations clustering algorithms Noise measurement Multi-view learning Laplacian matrix clustering structure alternating optimization

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Joint Learning of Spectral clustering structure and Fuzzy Similarity Matrix of Data

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2019年第1期27卷 31-44页

作者： Bian, Zekang Ishibuchi, Hisao Wang, Shitong Jiangnan Univ Sch Digital Media Wuxi 214122 Peoples R China Jiangnan Univ Jiangsu Prov Key Lab Media Design & Software Tech Wuxi 214122 Peoples R China Southern Univ Sci & Technol Dept Comp Sci & Engn Shenzhen 518055 Peoples R China Osaka Prefecture Univ Dept Comp Sci & Intelligent Sys Osaka 5998531 Japan

When spectral clustering analysis is applied, a similarity matrix of data plays a vital role in both clustering performance and stability of clustering results. In order to enhance the clustering performance and maintain the stability of the clustering results, a new method to jointly learn the similarity matrix and the clustering structure, called the joint learning method (FSCM) of spectral clustering structure and fuzzy similarity matrix of data, is proposed in this paper. In FSCM, the capability of a double-index fuzzy C-means clustering algorithm is used to determine an appropriate fuzzy similarity between any pair of data points. A fuzzy similarity matrix of data is also determined by adaptively assigning fuzzy neighbors of data points so the spectral clustering structure of data can he found and the clustering stability of FSCM can be assured. Experimental results on synthetic and real datasets demonstrate the effectiveness of the proposed method.

关键词： clustering structure fuzzy similarity matrix joint learning neighbors of data points spectral clustering

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Consistent and diverse multi-View subspace clustering with structure constraint

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PATTERN RECOGNITION 2022年 121卷 108196-108196页

作者： Si, Xiaomeng Yin, Qiyue Zhao, Xiaojie Yao, Li Beijing Normal Univ Sch Artificial Intelligence Beijing Peoples R China Chinese Acad Sci Inst Automat Beijing Peoples R China

Multi-view subspace clustering algorithms have recently been developed to process multi-view dataset clustering by accurately depicting the essential characteristics of multi-view data. Most existing methods focus on conduct self-representation property using a consistent representation and a set of specific representations with well-designed regularization to learn the common and specific knowledge among different views. However, specific representations only contain the unique information of each individual view, which limits their ability to fully excavate the diversity of multi-view data to enhance the complementarity among different views. Moreover, when conducting multi-view subspace clustering, the learned subspace self-representation and clustering are sequential and independent, which lacks consideration of the interaction between representation learning and the final clustering calculation. In this paper, a novel method termed consistent and diverse multi-view subspace clustering with structure constraint (CDMSC2) is proposed to overcome the above-described deficiencies. (1) An exclusivity constraint term is employed to enhance the diversity of specific representations among different views for modeling consistency and diversity in a unified framework. (2) A clustering structure constraint is imposed on the subspace self-representation by factorizing the learned subspace self-representation into the cluster centroids and the cluster assignments with the goal of obtaining a clustering-oriented subspace self-representation. In addition, we carefully designed an efficient optimization algorithm to solve the objective function through relaxation and alternating minimization. Extensive experiments on five benchmark datasets in terms of six evaluation metrics demonstrate that our method outperforms the state-of-the-art methods. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Subspace self-representation Multi-view clustering Consistency Diversity clustering structure

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Clusterability test for categorical data

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KNOWLEDGE AND INFORMATION SYSTEMS 2025年第5期67卷 4113-4138页

作者： Hu, Lianyu Dong, Junjie Jiang, Mudi Liu, Yan He, Zengyou Dalian Univ Technol Sch Software Dalian 116620 Peoples R China Dalian Univ Sch Software Engn Dalian 116622 Peoples R China Key Lab Ubiquitous Network & Serv Software Liaonin Dalian 116620 Peoples R China

The objective of clusterability evaluation is to check whether a clustering structure exists within the data set. As a crucial yet often-overlooked issue in cluster analysis, it is essential to conduct such a test before applying any clustering algorithm. If a data set is unclusterable, any subsequent clustering analysis would not yield valid results. Despite its importance, the majority of existing studies focus on numerical data, leaving the clusterability evaluation issue for categorical data as an open problem. Here, we present TestCat, a testing-based approach to assess the clusterability of categorical data in terms of an analytical p-value. The key idea underlying TestCat is that clusterable categorical data possess many strongly associated attribute pairs and hence the sum of Chi-squared statistics of all attribute pairs is employed as the test statistic for p-value calculation. We apply our method to a set of benchmark categorical data sets, showing that TestCat outperforms those solutions based on existing clusterability evaluation methods for numeric data. To the best of our knowledge, our work provides the first way to effectively recognize the clusterability of categorical data in a statistically sound manner.

关键词： Clusterability Categorical data clustering structure Statistical hypothesis test

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Graph-Regularized Consensus Learning and Diversity Representation for unsupervised multi-view feature selection

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KNOWLEDGE-BASED SYSTEMS 2025年 311卷

作者： Xu, Shengke Xie, Xijiong Cao, Zhiwen Ningbo Univ Sch Informat Sci & Engn Ningbo 315211 Peoples R China Key Lab Mobile Network Applicat Technol Zhejiang P Ningbo 315211 Peoples R China

In the existing data dimensionality reduction methods, unsupervised multi-view feature selection has been widely adopted for its effectiveness. However, most of the current methods lack sufficient integration of consensus and complementarity principles. On the one hand, some methods focus solely on the consensus representation of multiple views and neglect the inter-view complementarity and the uniqueness of each view. On the other hand, some methods obtain intrinsic representation matrices for each view and combine them crudely to form the final result, which fails to exploit complementary information among views. Inspired by these two aspects, this paper proposes the Graph-Regularized Consensus Learning and Diversity Representation (GCDUFS) for unsupervised multi-view feature selection. The algorithm leverages graph regularization to constrain the consensus matrix, better capturing common manifold information. It also utilizes kernel functions to measure the dependency of the data in the Hilbert space, effectively capturing the diverse information across all views. Additionally, symmetric non-negative matrix factorization (SNMF) is employed for clustering analysis. The above-mentioned methods are smoothly integrated into a unified model framework, and the GCDUFS algorithm is optimized using the alternating direction method of multipliers (ADMM) minimization strategy. Through the analysis of nine multi-view datasets, we conducted comprehensive clustering experiments and verified that our proposed method outperforms several state-of-the-art competitors in terms of performance.

关键词： Unsupervised multi-view feature selection Graph-Regularized Consensus Learning Independent diversity Subspace learning clustering structure

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Robust feature enhanced deep kernel support vector machine via low rank representation and clustering

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 271卷

作者： Li, Hongtao Jiang, Lulu Ganaa, Ernest Domanaanmwi Li, Peiwang Shen, Xiang-Jun Nanjing Univ Sci & Technol Sch Elect & Opt Engn Nanjing 210094 Peoples R China Jiangsu Univ Sch Comp Sci & Commun Engn Zhenjiang Peoples R China Hilla Limann Tech Univ Wa Ghana Jiangsu Yangjing Petrochem Grp Co Ltd Yangjing Peoples R China Nanjing Univ Posts & Telecommun Nanjing 222000 Jiangsu Peoples R China

Traditional support vector machines (SVM) obtain classifiers by maximizing margins of data samples in original data features, which leads to poor robustness and weak generalization ability in noisy scenarios. We address this problem by proposing a robust feature-enhanced deep kernel support vector machine classification method. In our proposed method, we learn the low-rank subspaces of data samples and feed this intrinsic low rank representation into the SVM model. Through this, our SVM model has good robustness in noisy data. By finding a low-dimensional classifier associated with our low-rank data representation, we improve the classification generalization of our proposed method. Furthermore, considering a data sample shares similar semantics among its neighbors, the clustering structure is introduced in the proposed method to further enhance the final feature representation by its neighbors. Incorporating the above ideas into the deep neural tangent kernel (NTK) framework, we propose our deep feature-enhanced SVM model. Experimental evaluations on many image classification datasets, such as MNIST, USPS, COIL10 and Batch demonstrate our proposed algorithm outperforms the other state-of-the-art SVM methods, such as CMLS, MSVM, L-TI-RI-SVM, SDCRKL-GP, and CNN-SVM in image classification.

关键词： Robustness Feature enhancement Low-rank representation clustering structure

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Cluster-preserving sampling algorithm for large-scale graphs

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Science China(Information Sciences) 2023年第1期66卷 60-76页

作者： Jianpeng ZHANG Hongchang CHEN Dingjiu YU Yulong PEI Yingjun DENG National Digital Switching System E&T Research Center Information Engineering University Network Systems Department of the Strategic Support Force School of Computer Science and Technology Eindhoven University of Technology Center for Applied Mathematics Tianjin University

Graph sampling is a very effective method to deal with scalability issues when analyzing largescale graphs. Lots of sampling algorithms have been proposed, and sampling qualities have been quantified using explicit properties(e.g., degree distribution) of the sample. However, the existing sampling techniques are inadequate for the current sampling task: sampling the clustering structure, which is a crucial property of the current networks. In this paper, using different expansion strategies, two novel top-leader sampling methods(i.e., TLS-e and TLS-i) are proposed to obtain representative samples, and they are capable of effectively preserving the clustering structure. The rationale behind them is to select top-leader nodes of most clusters into the sample and then heuristically incorporate peripheral nodes into the sample using specific expansion strategies. Extensive experiments are conducted to investigate how well sampling techniques preserve the clustering structure of graphs. Our empirical results show that the proposed sampling algorithms can preserve the population's clustering structure well and provide feasible solutions to sample the clustering structure from large-scale graphs.

关键词： graph sampling clustering structure top-leader nodes expansion strategies large-scale graphs

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Cluster-preserving sampling from fully-dynamic streaming graphs

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INFORMATION SCIENCES 2019年 482卷 279-300页

作者： Zhang, Jianpeng Zhu, Kaijie Pei, Yulong Fletcher, George Pechenizkiy, Mykola Eindhoven Univ Technol NL-5600 MB Eindhoven Netherlands Natl Digital Switching Syst Engn & Technol R&D Ct Zhengzhou 450002 Henan Peoples R China

Current sampling techniques on graphs (i.e., network-structured data) mainly study static graphs and suppose that the whole graph is available at all times. However, a surge of graphs are becoming too large-scale and/or fully-dynamic (i.e., nodes and edges are added or deleted arbitrarily) to be handled with small memory footprint. Moreover, the intrinsic property (i.e., clustering structure) has been ignored and is not preserved well when the sampling performs. To solve these issues, we propose a Cluster-preserving Partially Induced Edge Sampling (CPIES) algorithm that dynamically keep up-to-date samples in an online fashion and preserve the inherent clustering structure in streaming graphs. The experiments on various synthetic and real-world graphs demonstrated that the proposed CPIES algorithm is capable of preserving the inherent clustering structure while sampling from the fully-dynamic streaming graphs, and performs better than other competing algorithms in cluster-related properties. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Graph sampling Fully-dynamic streaming graph clustering structure Reservoir sampling Isolated nodes

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Unsupervised and Semisupervised Projection With Graph Optimization

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021年第4期32卷 1547-1559页

作者： Nie, Feiping Dong, Xia Li, Xuelong Northwestern Polytech Univ Sch Comp Sci Xian 710072 Peoples R China Northwestern Polytech Univ Ctr Opt IMagery Anal & Learning OPTIMAL Xian 710072 Peoples R China

Graph-based technique is widely used in projection, clustering, and classification tasks. In this article, we propose a novel and solid framework, named unsupervised projection with graph optimization (UPGO), for both dimensionality reduction and clustering. Different from the existing algorithms which treat graph construction and projection learning as two separate steps, UPGO unifies graph construction and projection learning into a general framework. It learns the graph similarity matrix adaptively based on the relationships among the low-dimensional representations. A constraint is introduced to the Laplacian matrix to learn a structured graph which contains the clustering structure, from which the clustering results can be obtained directly without requiring any postprocessing. The structured graph achieves the ideal neighbors assignment, based on which an optimal low-dimensional subspace can be learned. Moreover, we generalize UPGO to tackle the semisupervised case, namely semisupervised projection with graph optimization (SPGO), a framework for both dimensionality reduction and classification. An efficient algorithm is derived to optimize the proposed frameworks. We provide theoretical analysis about convergence analysis, computational complexity, and parameter determination. Experimental results on real-world data sets show the effectiveness of the proposed frameworks compared with the state-of-the-art algorithms. Results also confirm the generality of the proposed frameworks.

关键词： Dimensionality reduction Optimization clustering algorithms Laplace equations Linear programming Task analysis Manifolds Classification clustering structure dimensionality reduction graph-based semisupervised learning unsupervised learning

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Soft adaptive loss based Laplacian eigenmaps

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APPLIED INTELLIGENCE 2022年第1期52卷 321-338页

作者： Chen, Baihua Gao, Yunlong Wu, Shunxiang Pan, Jinyan Liu, Jinghua Fan, Yuling Xiamen Univ Dept Automat Xiamen 361102 Peoples R China Jimei Univ Sch Informat Engn Xiamen 361021 Peoples R China

The Laplacian eigenmaps (LE) is one of the most commonly used nonlinear dimensionality reduction methods and aims to find a low-dimensional representation to preserve the topological relationship between sample points in the original data. However, the l(2)-norm based loss function makes LE unable to preserve the relationship in many cases. Additionally, the topological relationship does not represent the real intrinsic structure of data. For example, the overemphasis of the topological relationship by LE easily breaks the manifold structure into multiple local areas in the embedding space, which makes the spectral clustering analysis of multi-manifold data more difficult to carry out. To solve this problem, we propose the soft adaptive loss based LE (SALE). With the soft adaptive loss, SALE can adaptively emphasize the topological relationship between sample points and the clustering structure of data. The model is tested and validated on UCI, face and gene expression data sets, and compared with some state-of-the-art models. The experimental results show that the method is robust to noise.

关键词： Adaptive loss Laplacian eigenmaps Nonlinear dimensionality reduction Topological relationship clustering structure

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