融合高阶信息和局部结构的鲁棒多视图聚类

doi:10.13229/j.cnki.jdxbgxb.20250377

摘要/Abstract

摘要：

现有的基于张量的多视图聚类算法虽然取得较好的聚类结果，但存在一定的局限性：①忽略了数据各视图特有的局部几何结构，难以处理非线性结构的数据；②易受大规模高强度噪声的影响；③基于奇异值分解的张量核范数对奇异值采用统一收缩策略，无法反映奇异值之间的差异。为此，本文提出融合高阶信息和局部结构的鲁棒多视图聚类算法。该算法通过融合加权张量Schatten-p范数和超拉普拉斯正则化，捕获数据高阶信息的同时保留各视图特有的局部结构，解决非线性数据的聚类问题。同时采用l_1，2范数增强簇结构，并利用柯西伪范数约束噪声项，减少噪声数据对聚类结果的影响。与10个聚类算法在8个公开的多视图数据集上进行实验比较，结果表明本文方法的性能大多数情况下优于对比算法。

关键词: 多视图聚类, 高阶信息和局部结构, 超拉普拉斯正则化, 加权张量Schatten-p范数, 柯西伪范数

Abstract:

Although existing tensor-based multi-view clustering algorithms have achieved good clustering results， they have certain limitations：① These methods often ignore the unique local geometric structure of each view， making it difficult to cluster data with nonlinear structures； ② They are highly susceptible to large-scale and high-intensity noise； ③ The tensor nuclear norm， typically based on singular value decomposition， applies a uniform shrinkage strategy to singular values， failing to account for the intrinsic differences between them. To solve these problems， a robust multi-view clustering algorithm based on integrating high-order information and local structure is proposed. The algorithm integrates the weighted tensor Schatten-p norm and hyper-Laplacian regularization to capture high-order information while retaining the unique local geometric structure of each view， solving the clustering problem for nonlinear data. At the same time， l_1，2 norm is used to enhance the cluster structure， and Cauchy pseudo-norm is used to constrain the noise matrix to reduce the impact of noisy data on the clustering results. Experimental results with 10 comparison algorithms on 8 publicly available multi-view datasets show that the performance of the proposed algorithm is better than the comparison algorithm in most cases.

Key words: multi-view clustering, high-order information and local structure, hyper-laplacian regularization, the weighted tensor schatten-p norm, cauchy pseudo-norm

中图分类号:

TP311

陈梅,郭爱霞,王洁,王欢. 融合高阶信息和局部结构的鲁棒多视图聚类[J]. 吉林大学学报(工学版), 2026, 56(10): 2662-2674.

Mei CHEN,Ai-xia GUO,Jie WANG,Huan WANG. Robust multi-view clustering integrating high-order information and local structure[J]. Journal of Jilin University(Engineering and Technology Edition), 2026, 56(10): 2662-2674.

图/表 16

表1

符号及含义"

符号	含义
$z, Z, Z ?$	向量，矩阵，张量
$I$	单位矩阵
$Z v ∈ R d v × n$	第v个视图的特征矩阵
$d v$	第v个视图的特征维度
$n$	数据个数
$m$	视图个数
$Z ∈ R n × n × m$	表示张量旋转体
$Z ? ∈ R n × m × n$	表示张量
$Z ? #$	张量核范数
$Z i, :, :$	$Z$ 的第i个水平切面
$Z :, j, :$	$Z$ 的第j个侧切面
$Z :, :, k; Z k$	$Z$ 的第k个正切面

表1

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图1

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表11

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图5

参考文献 27

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数据集	视图数	簇数	数据量	特征维度
BBC	4	5	685	4659/4633/4665/4684
BBCSport	2	5	544	3183/3203
ORL	3	40	400	4096/3304/6750
NGs	3	5	500	2000/2000/2000
HW	6	10	2 000	216/76/64/6/240/47
MSRCV1	6	7	210	1302/48/512/100/256/210
YaleA	3	5	165	9/512/50
WebKB	2	2	1 051	1840/3000

数据集	Accuracy	NMI	F?score	ARI
SC（best）	0.696 4	0.483 0	0.541 4	0.400 8
GBS	0.693 4	0.485 2	0.633 3	0.478 9
LSLMC	0.849 6	0.680 7	0.783 1	0.717 2
UGLTL	0.824 8	0.705 2	0.712 5	0.633 4
WTNNM	0.924 1	0.784 3	0.866 5	0.825 5
LSGMC	0.941 6	0.824 7	0.899 8	0.869 4
TBGL	0.903 6	0.821 8	0.855 9	0.812 1
MSCVC	0.988 3	0.956 6	0.946 5	0.969 3
FLMSC	0.896 4	0.750 2	0.824 1	0.770 3
ALPC	0.746 0	0.562 5	0.645 3	0.631 3
ours	0.995 6	0.984 1	0.992 3	0.989 9

数据集	Accuracy	NMI	F?score	ARI
SC（best）	0.8364	0.6880	0.7825	0.7130
GBS	0.8070	0.7226	0.7943	0.7218
LSLMC	0.9449	0.8544	0.8863	0.8511
UGLTL	0.6563	0.5902	0.6073	0.4970
WTNNM	0.9735	0.9168	0.9488	0.9331
LSGMC	0.8879	0.7921	0.7748	0.7057
TBGL	0.8511	0.7011	0.7640	0.6736
MSCVC	0.9945	0.9812	0.9866	0.9824
FLMSC	0.7555	0.5455	0.6271	0.5069
ALPC	0.9430	0.8391	0.8837	0.8909
ours	1.0000	1.0000	1.0000	1.0000

数据集	Accuracy	NMI	F-score	ARI
SC（best）	0.819 3	0.902 3	0.751 9	0.746 0
GBS	0.652 5	0.814 2	0.396 5	0.375 4
LSLMC	0.820 5	0.910 6	0.760 9	0.755 1
UGLTL	0.942 5	0.920 1	0.982 7	0.957 5
WTNNM	0.967 5	0.990 6	0.967 1	0.966 3
LSGMC	0.795 0	0.919 6	0.740 0	0.733 1
TBGL	0.907 5	0.851 2	0.870 5	0.852 8
MSCVC	0.965 0	0.990 6	0.966 3	0.965 5
FLMSC	0.772 5	0.880 8	0.695 7	0.688 4
ALPC	0.692 5	0.840 5	0.586 0	0.630 6
ours	1.000 0	1.000 0	1.000 0	1.000 0

数据集	Accuracy	NMI	F?score	ARI
SC（best）	0.634 0	0.514 4	0.590 6	0.474 6
GBS	0.982 0	0.939 2	0.964 3	0.955 4
LSLMC	0.960 0	0.872 9	0.921 7	0.902 3
UGLTL	0.944 0	0.848 7	0.891 8	0.865 0
WTNNM	0.990 0	0.965 2	0.980 0	0.975 1
LSGMC	0.948 0	0.853 4	0.899 8	0.874 9
TBGL	0.782 0	0.636 1	0.624 5	0.535 3
MSCVC	0.990 0	0.965 2	0.980 1	0.975 1
FLMSC	0.892 0	0.791 0	0.815 5	0.768 1
ALPC	0.874 0	0.719 5	0.772 2	0.776 8
ours	1.000 0	1.000 0	1.000 0	1.000 0