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Adaptive multiple kernel clustering using low-rank representation

PATTERN RECOGNITION 2025年 162卷

作者： Dai, Hong-Liang Wang, Lei Sun, Ye-Sen Imran, Muhammad Zaidi, Fatima Sehar Lai, Fei-Tong Lv, Xiao-Ting Lian, Ming-Feng Zhang, Zi-Rong Cao, Sha Li, Xin-Yi Guangzhou Univ Sch Econ & Stat Guangzhou 510006 Peoples R China

multiple kernel clustering (MKC) effectively extracts intrinsic and complementary information from data by integrating diverse kernel functions. The allocation of kernel weights is crucial for MKC performance and is closely related to the relationships among kernel matrices. However, it is very difficult to fully capture the intricate relationships among high-dimensional matrices because previous research mostly relies on predefined metrics to characterize the correlation among kernel matrices. To address this challenge, a novel MKC model called AMKC-LRR is proposed that adaptively learns the interrelations among kernel matrices using low-rank representation and unifies this learning process with the clustering task within an optimization framework. Furthermore, an effective alternate optimization algorithm is designed to solve the resulting problem. Extensive experiments and statistical tests conducted on twelve commonly used benchmark datasets show that our proposed model performs favorably in comparison to state-of-the-art MKC methods. The source code for the proposed model is available at https://***/bala23-w/AMKC-LRR/.

关键词： multiple kernel clustering kernel k-means Low-rank representation

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multiple kernel clustering With Adaptive Multi-Scale Partition Selection

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2024年第11期36卷 6641-6652页

作者： Wang, Jun Li, Zhenglai Tang, Chang Liu, Suyuan Wan, Xinhang Liu, Xinwang Natl Univ Def Technol Sch Comp Changsha 410073 Peoples R China China Univ Geosci Sch Comp Sci Wuhan 430074 Peoples R China

multiple kernel clustering (MKC) enhances clustering performance by deriving a consensus partition or graph from a predefined set of kernels. Despite many advanced MKC methods proposed in recent years, the prevalent approaches involve incorporating all kernels by default to capture diverse information within the data. However, learning from all kernels may not be better than one of a few kernels, particularly since some kernels exhibit a higher proportion of noise than semantic content. Additionally, existing MKC methods, whether based on early-fusion or late-fusion approaches, predominantly rely on pairwise relationships among samples or cluster structures, neglecting potential correlations between these two aspects. To this end, we propose a multiple kernel clustering with an adaptive multi-scale partition selection method (MPS), which exploits multiple-dimensional representations and the pairwise cluster structure for clustering. By the proposed kernel selection framework, potentially harmful kernels are dynamically excluded during the kernel fusion process, and then the multi-scale partitions and similarity graphs derived from the retained kernels are utilized to facilitate the improved consensus partition generation. Finally, extensive experiments are conducted to demonstrate the effectiveness of MPS on eight benchmark datasets.

关键词： kernel Optimization Semantics Noise Linear programming clustering methods Task analysis kernel selection multi-scale embedding learning multiple kernel clustering partition fusion

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multiple kernel clustering with corrupted kernels

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NEUROCOMPUTING 2017年 267卷 447-454页

作者： Li, Teng Dou, Yong Liu, Xinwang Zhao, Yang Lv, Qi Natl Univ Def Technol Natl Lab Parallel & Distributed Proc Changsha 410073 Hunan Peoples R China

multiple kernel clustering (MKC) algorithms usually learn an optimal kernel from a group of pre-specified base kernels to improve the clustering performance. However, we observe that existing MKC algorithms do not well handle the situation that kernels are corrupted with noise and outliers. In this paper, we first propose a novel method to learn an optimal consensus kernel from a group of pre-specified kernel matrices, each of which can be decomposed into the optimal consensus kernel matrix and a sparse error matrix. Further, we propose a scheme to address the problem of considerable corrupted kernels, where each given kernel is adaptively adjusted according to its corresponding error matrix. The inexact augmented Lagrange multiplier scheme is developed for solving the corresponding optimization problem, where the optimal consensus kernel and the localized weight variables are jointly optimized. Extensive experiments well demonstrate the effectiveness and robustness of the proposed algorithm. (C) 2017 Published by Elsevier B.V. All rights reserved.

关键词： kernel method clustering multiple kernel clustering Corrupted kernels

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multiple kernel clustering with structure-preserving and block diagonal property

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MULTIMEDIA TOOLS AND APPLICATIONS 2024年第3期83卷 6425-6445页

作者： Chen, Cuiling Li, Zhi Guangxi Normal Univ Sch Comp Sci & Engn 15 Yucai Rd Guilin 541004 Guangxi Peoples R China

It is well known that graph-based multiple kernel clustering (GMKC) methods improve the clustering performance by integrating multiple kernel learning and graph-based clustering. However, existing GMKC methods either do not consider the global and local structure of data in kernel space simultaneously, or ignore block diagonal property of the affinity matrix, thus impairing the final clustering performance greatly. To address this issue, in this paper we propose a novel method named multiple kernel clustering with structure-preserving and block diagonal property (SBDMKC) by combining GMKC and block diagonal regularizer. Typically, the local structure-preserving regularization term is an accurate measurement for the similarity between data in kernel space, rather than original space. Furthermore, the affinity matrix is encouraged to be block diagonal by a soft regularizer, which helps to achieve good data clustering. In addition, a simple kernel weight strategy is given, which can automatically weight each base kernel to find an optimal consensus kernel. Experimental results on the ten benchmark data sets show that our method outperforms the nine state-of-the-art clustering methods.

关键词： multiple kernel clustering Block diagonal representation Structure preserving

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multiple kernel clustering Based on Self-Weighted Local kernel Alignment

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Computers, Materials & Continua 2019年第7期61卷 409-421页

作者： Chuanli Wang En Zhu Xinwang Liu Jiaohua Qin Jianping Yin Kaikai Zhao College of Computer National University of Defense TechnologyChangsha410073China College of Computer and Information Engineering Central South University of Forestry and TechnologyChangsha410004China College of Computer Dongguan University of TechnologyDongguan523000China School of Informatics Computingand EngineeringIndiana UniversityIndiana47408USA

multiple kernel clustering based on local kernel alignment has achieved outstanding clustering performance by applying local kernel alignment on each ***,we observe that most of existing works usually assume that each local kernel alignment has the equal contribution to clustering performance,while local kernel alignment on different sample actually has different contribution to clustering *** this assumption could have a negative effective on clustering *** solve this issue,we design a multiple kernel clustering algorithm based on self-weighted local kernel alignment,which can learn a proper weight to clustering performance for each local kernel ***,we introduce a new optimization variable-weight-to denote the contribution of each local kernel alignment to clustering performance,and then,weight,kernel combination coefficients and cluster membership are alternately optimized under kernel alignment *** addition,we develop a three-step alternate iterative optimization algorithm to address the resultant optimization *** experiments on five benchmark data sets have been put into effect to evaluate the clustering performance of the proposed *** experimental results distinctly demonstrate that the proposed algorithm outperforms the typical multiple kernel clustering algorithms,which illustrates the effectiveness of the proposed algorithm.

关键词： multiple kernel clustering kernel alignment local kernel alignment self-weighted

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multiple kernel clustering with pure graph learning scheme

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NEUROCOMPUTING 2021年 424卷 215-225页

作者： Li, Xingfeng Ren, Zhenwen Lei, Haoyun Huang, Yuqing Sun, Quansen Southwest Univ Sci & Technol Sch Informat Engn Mianyang 621010 Sichuan Peoples R China Southwest Univ Sci & Technol Sch Natl Def Sci & Technol Mianyang 621010 Sichuan Peoples R China Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing 210094 Peoples R China

Existing graph-based multiple kernel clustering (GMKC) methods usually adopt a hybridization scheme, termed HGMKC for short, which binds multiple kernel learning (MKL) and graph-based clustering (GBC) together, the former aims to construct a consensus kernel and the latter is used to learn an affinity graph based on the consensus kernel. Obviously, HGMKC performs graph learning and spectral clustering separately. Additionally, the performance of this hybridization is largely determined by MKL, which is empirically contrary to the fact that graph learning is the key of graph-based methods, rather than kernel learning. In this paper, we propose a pure GMKC method, dubbed PGMKC, which contains two parts, including candidate kernel graphs learning (CKGL) and kernel graph fusion (KGF). Specially, CKGL concentrates on constructing multiple candidate kernel graphs in Hilbert kernel space relying on kernel self-expressiveness;KGF leverages a flexibly auto-weighted graph fusion strategy and a connectivity regularizer to yield a consensus kernel graph directly. Compared to HGMKC, PGMKC avoids paying too much attention to consensus kernel construction, thus can focus more on affinity graph learning. Moreover, an efficient and effective optimization algorithm is developed to solve the proposed model. Experimental results on ten benchmark datasets demonstrate that the proposed PGMKC performs better than the state-of-the-art HGMKC competitors. (c) 2020 Elsevier B.V. All rights reserved.

关键词： Unsupervised learning Subspace clustering kernel method multiple kernel clustering Affinity graph

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multiple kernel clustering with Dual Noise Minimization 22

Multiple Kernel Clustering with Dual Noise Minimization

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30th ACM International Conference on Multimedia (MM)

作者： Zhang, Junpu Li, Liang Wang, Siwei Liu, Jiyuan Liu, Yue Liu, Xinwang Zhu, En Natl Univ Def Technol Changsha Peoples R China

ISBN: (纸本)9781450392037

clustering is a representative unsupervised method widely applied in multi-modal and multi-view scenarios. multiple kernel clustering (MKC) aims to group data by integrating complementary information from base kernels. As a representative, late fusion MKC first decomposes the kernels into orthogonal partition matrices, then learns a consensus one from them, achieving promising performance recently. However, these methods fail to consider the noise inside the partition matrix, preventing further improvement of clustering performance. We discover that the noise can be disassembled into separable dual parts, i.e. N-noise and C-noise (Null space noise and Column space noise). In this paper, we rigorously define dual noise and propose a novel parameter-free MKC algorithm by minimizing them. To solve the resultant optimization problem, we design an efficient two-step iterative strategy. To our best knowledge, it is the first time to investigate dual noise within the partition in the kernel space. We observe that dual noise will pollute the block diagonal structures and incur the degeneration of clustering performance, and C-noise exhibits stronger destruction than N-noise. Owing to our efficient mechanism to minimize dual noise, the proposed algorithm surpasses the recent methods by large margins.

关键词： Multi-view clustering multiple kernel clustering noise minimization

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Optimal Neighborhood multiple kernel clustering With Adaptive Local kernels

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2022年第6期34卷 2872-2885页

作者： Liu, Jiyuan Liu, Xinwang Xiong, Jian Liao, Qing Zhou, Sihang Wang, Siwei Yang, Yuexiang Natl Univ Def Technol Coll Comp Changsha 410073 Hunan Peoples R China Southwestern Univ Finance & Econ Sch Business Adm Chengdu 611130 Sichuan Peoples R China Harbin Inst Technol Shenzhen Dept Comp Sci & Technol Shenzhen 518055 Guangdong Peoples R China

multiple kernel clustering (MKC) algorithm aims to group data into different categories by optimally integrating information from a group of pre-specified kernels. Though demonstrating superiorities in various applications, we observe that existing MKC algorithms usually do not sufficiently consider the local density around individual data samples and excessively limit the representation capacity of the learned optimal kernel, leading to unsatisfying performance. In this paper, we propose an algorithm, called optimal neighborhood MKC with adaptive local kernels (ON-ALK), to address the two issues. In specific, we construct adaptive local kernels to sufficiently consider the local density around individual data samples, where different numbers of neighbors are discriminatingly selected on each sample. Further, the proposed ON-ALK algorithm boosts the representation of the learned optimal kernel via relaxing it into the neighborhood area of weighted combination of the pre-specified kernels. To solve the resultant optimization problem, a three-step iterative algorithm is designed and theoretically proven to be convergent. After that, we also study the generalization bound of the proposed algorithm. Extensive experiments have been conducted to evaluate the clustering performance. As indicated, the algorithm significantly outperforms state-of-the-art methods in recent literatures on six challenging benchmark datasets, verifying its advantages and effectiveness.

关键词： multiple kernel clustering kernel alignment kernel k-mean

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A Fast and Effective multiple kernel clustering Method on Incomplete Data

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Computers, Materials & Continua 2021年第4期67卷 267-284页

作者： Lingyun Xiang Guohan Zhao Qian Li Gwang-Jun Kim Osama Alfarraj Amr Tolba Changsha Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on Transportation School of Computer and Communication EngineeringChangsha University of Science and TechnologyChangsha410114China Hunan Key Laboratory of Smart Roadway and Cooperative Vehicle-Infrastructure Systems Changsha University of Science and TechnologyChangsha410114China Faculty of Engineering and Information Technology Global Big Data Technologies CentreUniversity of Technology SydneyUltimoNSW2007Australia Department of Computer Engineering Chonnam National UniversityGwangju61186Korea Computer Science Department Community CollegeKing Saud UniversityRiyadh11437Saudi Arabia Department of Mathematics and Computer Science Faculty of ScienceMenoua UniversityShebin-El-kom32511Egyp

multiple kernel clustering is an unsupervised data analysis method that has been used in various scenarios where data is easy to be collected but hard to be ***,multiple kernel clustering for incomplete data is a critical yet challenging *** the existing absent multiple kernel clustering methods have achieved remarkable performance on this task,they may fail when data has a high value-missing rate,and they may easily fall into a local *** address these problems,in this paper,we propose an absent multiple kernel clustering(AMKC)method on incomplete *** AMKC method rst clusters the initialized incomplete ***,it constructs a new multiple-kernel-based data space,referred to as K-space,from multiple sources to learn kernel combination ***,it seamlessly integrates an incomplete-kernel-imputation objective,a multiple-kernel-learning objective,and a kernel-clustering objective in order to achieve absent multiple kernel *** three stages in this process are carried out simultaneously until the convergence condition is *** on six datasets with various characteristics demonstrate that the kernel imputation and clustering performance of the proposed method is signicantly better than state-of-the-art ***,the proposed method gains fast convergence speed.

关键词： multiple kernel clustering absent-kernel imputation incomplete data kernel k-means clustering

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On the Consistency and Large-Scale Extension of multiple kernel clustering

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2024年第10期46卷 6935-6947页

作者： Liang, Weixuan Tang, Chang Liu, Xinwang Liu, Yong Liu, Jiyuan Zhu, En He, Kunlun Natl Univ Def Technol Coll Comp Changsha 410073 Hunan Peoples R China China Univ Geosci Sch Comp Sci Wuhan 430079 Hubei Peoples R China Renmin Univ China Gaoling Sch Artificial Intelligence Beijing 100872 Peoples R China Natl Univ Def Technol Coll Syst Engn Changsha 410073 Hunan Peoples R China Chinese Peoples Liberat Army Gen Hosp Med Big Data Res Ctr Beijing 100010 Peoples R China

Existing multiple kernel clustering (MKC) algorithms have two ubiquitous problems. From the theoretical perspective, most MKC algorithms lack sufficient theoretical analysis, especially the consistency of learned parameters, such as the kernel weights. From the practical perspective, the high complexity makes MKC unable to handle large-scale datasets. This paper tries to address the above two issues. We first make a consistency analysis of an influential MKC method named Simple multiple kernel k -Means (SimpleMKKM). Specifically, suppose that gamma<^>(n) are the kernel weights learned by SimpleMKKM from the training samples. We also define the expected version of SimpleMKKM and denote its solution as gamma(& lowast;). We establish an upper bound of parallel to gamma<^>(n)-gamma(& lowast;)parallel to(infinity) in the order of O(1/root n) , where n is the sample number. Based on this result, we also derive its excess clustering risk calculated by a standard clustering loss function. For the large-scale extension, we replace the eigen decomposition of SimpleMKKM with singular value decomposition (SVD). Consequently, the complexity can be decreased to O(n) such that SimpleMKKM can be implemented on large-scale datasets. We then deduce several theoretical results to verify the approximation ability of the proposed SVD-based method. The results of comprehensive experiments demonstrate the superiority of the proposed method.

关键词： kernel clustering algorithms Training Matrix decomposition Upper bound Standards Eigenvalues and eigenfunctions multiple kernel clustering consistency large-scale extension

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