Multi-view clustering algorithm based on bipartite graph and consensus graph learning

doi:10.11772/j.issn.1001-9081.2024111593

Journal of Computer Applications ›› 2025, Vol. 45 ›› Issue (11): 3583-3592.DOI: 10.11772/j.issn.1001-9081.2024111593

• Data science and technology • Previous Articles

Multi-view clustering algorithm based on bipartite graph and consensus graph learning

Shunyong LI¹^,², Kun LIU¹, Lina CAO¹, Xingwang ZHAO³^,⁴()

^1.School of Mathematics and Statistics，Shanxi University，Taiyuan Shanxi 030006，China
^2.Key Laboratory of Complex Systems and Data Science of Ministry of Education （Shanxi University），Taiyuan Shanxi 030006，China
^3.School of Computer and Information Technology，Shanxi University，Taiyuan Shanxi 030006，China
^4.Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education （Shanxi University），Taiyuan Shanxi 030006，China

Received:2024-11-11 Revised:2025-01-26 Accepted:2025-02-08 Online:2025-02-21 Published:2025-11-10
Contact: Xingwang ZHAO
About author:LI Shunyong， born in 1975， Ph. D.， professor. His research interests include statistical machine learning， data mining.
LIU Kun， born in 2001， M. S. candidate. Her research interests include statistical machine learning.
CAO Lina， born in 2002， M. S. candidate. Her research interests include statistical machine learning.
Supported by:
National Natural Science Foundation of China(82274360);Fundamental Research Program of Shanxi Province(202303021221054);Research Project of Shanxi Returned Overseas Students(2024-002)

基于二部图和一致图学习的多视图聚类算法

李顺勇¹^,², 刘坤¹, 曹利娜¹, 赵兴旺³^,⁴()

^1.山西大学数学与统计学院，太原 030006
^2.复杂系统与数据科学教育部重点实验室（山西大学），太原 030006
^3.山西大学计算机与信息技术学院，太原 030006
^4.计算智能与中文信息处理教育部重点实验室（山西大学），太原 030006

通讯作者: 赵兴旺
作者简介:李顺勇（1975—），男，山西大同人，教授，博士，CCF专业会员，主要研究方向：统计机器学习、数据挖掘
刘坤（2001—），女，山西吕梁人，硕士研究生，CCF会员，主要研究方向：统计机器学习
曹利娜（2002—），女，山西吕梁人，硕士研究生，CCF会员，主要研究方向：统计机器学习
基金资助:
国家自然科学基金资助项目(82274360);山西省基础研究计划项目(202303021221054);山西省基础研究计划项目(202403021211086);山西省回国留学人员科研项目(2024-002)

Abstract

Abstract:

Most existing multi-view clustering algorithms suffer from issues such as incomplete fusion mechanisms， insufficient exploration of multi-view collaborative relationships， and weak robustness. These limitations result in low consistency in clustering results and unstable performance under noise and redundant information. To address these issues， a Multi-View Clustering algorithm based on Bipartite Graph and Consensus graph learning （BGC-MVC） was developed to enhance clustering consistency and complementarity by integrating information from multiple views. Specifically， BGC-MVC constructed a bipartite graph to capture neighborhood relationships across different views， and then learned a consensus graph to strengthen inter-view similarity. It integrated embeddings of the original multi-view data into a unified framework that combined graph learning with clustering process， thereby improving the overall clustering performance. Experimental results demonstrate that BGC-MVC achieves significant improvements in accuracy， F-score， Normalized Mutual Information （NMI） and purity under convergence conditions. Notably， on the MSRC_v1 dataset， BGC-MVC outperforms Large-scale Multi-View Subspace Clustering （LMVSC） by increasing the F-score by 19.48 percentage points and exhibits enhanced robustness and accuracy.

Key words: multi-view clustering, bipartite graph, consensus graph, graph fusion, embedding learning

摘要：

目前大多数多视图聚类算法存在融合机制不够完善、对多视图协同关系挖掘不足以及鲁棒性较弱等问题，导致聚类结果一致性偏低，且在噪声和冗余信息下的性能不够稳健。针对上述问题，提出一种基于二部图和一致图学习的多视图聚类算法（BGC-MVC），旨在通过融合各视图信息来提升聚类的一致性和互补性。该算法通过构造二部图以捕获不同视图之间的邻域关系，并通过学习一致性图强化视图间的相似性。它将原始多视图数据的嵌入整合进一个统一的框架中，结合了图学习与聚类过程，从而能提高聚类的整体效果。实验结果表明，BGC-MVC在满足收敛性条件下的准确度、F-score、归一化互信息（NMI）和纯度均有明显的提升。其中，在MSRC_v1数据集上的F-score比LMVSC（Large-scale Multi-View Subspace Clustering）算法提高了19.48个百分点，并且表现出更强的鲁棒性与准确度。

关键词: 多视图聚类, 二部图, 一致图, 图融合, 嵌入学习

CLC Number:

TP391

Shunyong LI, Kun LIU, Lina CAO, Xingwang ZHAO. Multi-view clustering algorithm based on bipartite graph and consensus graph learning[J]. Journal of Computer Applications, 2025, 45(11): 3583-3592.

李顺勇, 刘坤, 曹利娜, 赵兴旺. 基于二部图和一致图学习的多视图聚类算法[J]. 《计算机应用》唯一官方网站, 2025, 45(11): 3583-3592.

Figures/Tables 13

Tab. 1 Symbols and definitions

符号	含义	符号	含义	符号	含义
n	样本数	$A v ∈ R d v × t$	第v个视图的锚点矩阵	$F v ∈ R n × c$	嵌入矩阵
v	第v个视图	$Z v ∈ R t × n$	二部图矩阵	$F * ∈ R n × c$	谱嵌入矩阵
m	视图数	$S v ∈ R d v × n$	第v个视图的相似度矩阵	$F ∈ R n × c$	聚类指示矩阵
$d v$	第v个视图的特征维数	$G ∈ R d v × n$	一致图矩阵	$α v$	第v个视图的权重
$X v ∈ R d v × n$	第v个视图的数据矩阵

Tab. 1 Symbols and definitions

符号	含义	符号	含义	符号	含义
n	样本数	$A v ∈ R d v × t$	第v个视图的锚点矩阵	$F v ∈ R n × c$	嵌入矩阵
v	第v个视图	$Z v ∈ R t × n$	二部图矩阵	$F * ∈ R n × c$	谱嵌入矩阵
m	视图数	$S v ∈ R d v × n$	第v个视图的相似度矩阵	$F ∈ R n × c$	聚类指示矩阵
$d v$	第v个视图的特征维数	$G ∈ R d v × n$	一致图矩阵	$α v$	第v个视图的权重
$X v ∈ R d v × n$	第v个视图的数据矩阵

Fig. 1 Flowchart of BGC-MVC algorithm

Tab. 2 Description of multi-view datasets

数据集	样本数	视图数	聚类数	第v个视图的特征维数d_v
数据集	样本数	视图数	聚类数	d₁	d₂	d₃	d₄	d₅	d₆
3sources	169	3	6	3 560	3 631	3 068	—	—	—
BBCsport	116	4	5	1 991	2 063	2 113	2 156	—	—
Cal7	1 474	6	7	48	40	254	1 984	512	926
MSRC_v1	210	6	7	1 302	48	512	100	256	210
Handwritten	2 000	6	10	240	76	216	47	64	6

Tab. 3 Accuracies of different clustering algorithms on datasets

算法	3sources	BBCsport	Cal7	MSRC_v1	Handwritten
K-means	0.496 1	0.277 2	0.372 6	0.591 1	0.503 8
SC	0.414 2	0.422 4	0.440 3	0.542 9	0.548 5
EOMSC-CA	0.572 8	0.500 1	0.835 1	0.671 4	0.834 0
EMKMC	0.656 8	0.666 2	0.516 0	0.633 7	0.572 7
LMVSC	0.499 4	0.506 0	0.726 6	0.720 4	0.896 5
DUBGL	0.825 4	0.889 0	0.703 2	0.727 1	0.887 5
GMC	0.692 3	0.560 3	0.692 0	0.747 6	0.882 0
COMVSC	0.686 4	0.698 3	0.813 4	0.771 4	0.945 0
IBFDMVC	0.796 0	0.805 6	0.736 8	0.895 0	0.896 5
SIB-MSC	0.774 7	0.715 6	0.714 5	0.724 5	0.805 7
BGC-MVC	0.826 3	0.704 8	0.735 9	0.757 1	0.904 8

Tab. 4 F-scores of different clustering algorithms on datasets

算法	3sources	BBCsport	Cal7	MSRC_v1	Handwritten
K-means	0.455 6	0.456 9	0.465 4	0.695 2	0.632 0
SC	0.486 6	0.390 9	0.427 8	0.456 8	0.680 8
EOMSC-CA	0.596 2	0.577 6	0.796 7	0.547 5	0.873 8
EMKMC	0.716 0	0.701 7	0.813 0	0.709 5	0.712 5
DUBGL	0.810 7	0.835 3	0.804 8	0.756 8	0.795 8
LMVSC	0.520 7	0.603 4	0.694 7	0.714 3	0.854 0
GMC	0.604 7	0.443 9	0.721 7	0.696 8	0.865 3
COMVSC	0.678 8	0.532 2	0.772 8	0.677 6	0.893 4
IBFDMVC	0.805 4	0.753 4	0.785 4	0.895 3	0.883 4
SIB-MSC	0.754 2	0.783 5	0.735 4	0.845 7	0.836 9
BGC-MVC	0.833 8	0.793 5	0.823 3	0.909 1	0.919 4

Tab. 5 NMI values of different clustering algorithms on datasets

算法	3sources	BBCsport	Cal7	MSRC_v1	Handwritten
K-means	0.535 6	0.433 6	0.471 0	0.650 5	0.610 8
SC	0.441 4	0.289 5	0.486 8	0.485 3	0.706 7
EOMSC-CA	0.519 4	0.474 7	0.521 9	0.560 8	0.776 7
EMKMC	0.673 7	0.743 8	0.544 0	0.685 1	0.618 3
LMVSC	0.575 4	0.544 3	0.519 3	0.759 6	0.844 3
DUBGL	0.757 3	0.806 9	0.609 2	0.767 3	0.800 1
GMC	0.621 6	0.477 1	0.659 5	0.750 9	0.804 1
COMVSC	0.530 1	0.534 6	0.531 1	0.704 0	0.892 5
IBFDMVC	0.746 5	0.714 6	0.765 2	0.816 0	0.832 3
SIB-MSC	0.775 4	0.725 7	0.704 6	0.726 7	0.805 3
BGC-MVC	0.729 3	0.753 2	0.698 2	0.836 3	0.872 5

Tab. 6 Purity values of different clustering algorithms on datasets

算法	3sources	BBCsport	Cal7	MSRC_v1	Handwritten
K-means	0.427 9	0.453 4	0.363 4	0.525 4	0.525 7
SC	0.458 6	0.425 4	0.326 7	0.552 7	0.646 5
EOMSC-CA	0.595 2	0.683 4	0.577 3	0.706 2	0.793 5
EMKMC	0.576 7	0.676 2	0.676 3	0.726 5	0.836 5
LMVSC	0.638 7	0.726 5	0.794 7	0.784 5	0.896 5
DUBGL	0.775 8	0.806 7	0.845 4	0.884 6	0.845 6
GMC	0.616 3	0.796 1	0.834 3	0.914 5	0.805 3
COMVSC	0.714 6	0.806 5	0.836 7	0.825 6	0.823 7
IBFDMVC	0.735 6	0.754 3	0.794 6	0.900 0	0.895 6
SIB-MSC	0.757 8	0.796 3	0.774 3	0.885 7	0.796 7
BGC-MVC	0.795 6	0.829 6	0.805 2	0.895 1	0.905 4

Tab. 7 Comparison of p values on cancer datasets

算法	Breast	Colon	GBM	Melanoma
EOMSC-CA	0.467 7	0.362 3	0.014 3	0.007 3
EMKMC	0.563 2	0.627 6	0.283 6	0.025 2
DUBGL	0.015 4	0.254 2	0.193 5	0.179 3
LMVSC	0.025 6	0.042 5	0.028 3	0.284 2
GMC	0.014 5	0.266 7	0.156 8	0.000 4
COMVSC	0.239 5	0.025 2	0.456 4	0.134 6
IBFDMVC	0.005 2	0.000 5	0.052 4	0.085 2
SIB-MSC	0.009 4	0.232 7	0.000 3	0.253 4
BGC-MVC	0.004 2	0.000 3	0.000 3	0.000 2

Fig. 2 Sensitivity analysis of clustering performance to number of anchor points

Fig. 3 Parameter sensitivity analysis

Fig. 4 Time complexity analysis

Tab. 8 Ablation experimental results

数据集	算法	准确度	F-score
3sources	BGC-MVC	0.826 3	0.833 8
	de-Ⅰ	0.506 3	0.703 5
	de-Ⅱ	0.546 3	0.627 9
	de-Ⅲ	0.606 3	0.636 7
BBCsport	BGC-MVC	0.704 8	0.793 5
	de-Ⅰ	0.638 7	0.597 3
	de-Ⅱ	0.625 4	0.724 7
	de-Ⅲ	0.517 7	0.663 5
Cal7	BGC-MVC	0.735 9	0.823 3
	de-Ⅰ	0.494 6	0.792 1
	de-Ⅱ	0.513 4	0.652 6
	de-Ⅲ	0.613 4	0.684 8
MSRC_v1	BGC-MVC	0.757 1	0.909 1
	de-Ⅰ	0.782 6	0.434 5
	de-Ⅱ	0.623 4	0.723 4
	de-Ⅲ	0.525 4	0.834 5
Handwritten	BGC-MVC	0.904 8	0.919 4
	de-Ⅰ	0.802 5	0.834 2
	de-Ⅱ	0.820 9	0.502 3
	de-Ⅲ	0.638 3	0.591 3

Fig. 5 Convergence curves

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Multi-view clustering algorithm based on bipartite graph and consensus graph learning

基于二部图和一致图学习的多视图聚类算法

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