Journal of Jilin University(Engineering and Technology Edition) ›› 2026, Vol. 56 ›› Issue (10): 2662-2674.doi: 10.13229/j.cnki.jdxbgxb.20250377

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Robust multi-view clustering integrating high-order information and local structure

Mei CHEN(),Ai-xia GUO,Jie WANG,Huan WANG   

  1. School of Electronic and Information Engineering，Lanzhou Jiaotong University，Lanzhou 730070，China
  • Received:2025-04-28 Online:2026-10-01 Published:2026-10-09

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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， l1，2 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

CLC Number: 

  • TP311

Table 1

Notations and their descriptions"

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

Table 2

Statistics of the datasets"

数据集视图数簇数数据量特征维度
BBC456854659/4633/4665/4684
BBCSport255443183/3203
ORL3404004096/3304/6750
NGs355002000/2000/2000
HW6102 000216/76/64/6/240/47
MSRCV1672101302/48/512/100/256/210
YaleA351659/512/50
WebKB221 0511840/3000

Table 3

Clustering results on BBC dataset"

数据集AccuracyNMIF?scoreARI
SC（best）0.696 40.483 00.541 40.400 8
GBS0.693 40.485 20.633 30.478 9
LSLMC0.849 60.680 70.783 10.717 2
UGLTL0.824 80.705 20.712 50.633 4
WTNNM0.924 10.784 30.866 50.825 5
LSGMC0.941 60.824 70.899 80.869 4
TBGL0.903 60.821 80.855 90.812 1
MSCVC0.988 30.956 60.946 50.969 3
FLMSC0.896 40.750 20.824 10.770 3
ALPC0.746 00.562 50.645 30.631 3
ours0.995 60.984 10.992 30.989 9

Table 4

Clustering results on BBCSport dataset"

数据集AccuracyNMIF?scoreARI
SC（best）0.83640.68800.78250.7130
GBS0.80700.72260.79430.7218
LSLMC0.94490.85440.88630.8511
UGLTL0.65630.59020.60730.4970
WTNNM0.97350.91680.94880.9331
LSGMC0.88790.79210.77480.7057
TBGL0.85110.70110.76400.6736
MSCVC0.99450.98120.98660.9824
FLMSC0.75550.54550.62710.5069
ALPC0.94300.83910.88370.8909
ours1.00001.00001.00001.0000

Table 5

Clustering results on ORL dataset"

数据集AccuracyNMIF-scoreARI
SC（best）0.819 30.902 30.751 90.746 0
GBS0.652 50.814 20.396 50.375 4
LSLMC0.820 50.910 60.760 90.755 1
UGLTL0.942 50.920 10.982 70.957 5
WTNNM0.967 50.990 60.967 10.966 3
LSGMC0.795 00.919 60.740 00.733 1
TBGL0.907 50.851 20.870 50.852 8
MSCVC0.965 00.990 60.966 30.965 5
FLMSC0.772 50.880 80.695 70.688 4
ALPC0.692 50.840 50.586 00.630 6
ours1.000 01.000 01.000 01.000 0

Table 6

Clustering results on NGs dataset"

数据集AccuracyNMIF?scoreARI
SC（best）0.634 00.514 40.590 60.474 6
GBS0.982 00.939 20.964 30.955 4
LSLMC0.960 00.872 90.921 70.902 3
UGLTL0.944 00.848 70.891 80.865 0
WTNNM0.990 00.965 20.980 00.975 1
LSGMC0.948 00.853 40.899 80.874 9
TBGL0.782 00.636 10.624 50.535 3
MSCVC0.990 00.965 20.980 10.975 1
FLMSC0.892 00.791 00.815 50.768 1
ALPC0.874 00.719 50.772 20.776 8
ours1.000 01.000 01.000 01.000 0

Table 7

Clustering results on HW dataset"

数据集AccuracyNMIF?scoreARI
SC（best）0.819 50.837 60.798 80.775 3
GBS0.881 00.892 30.865 40.849 9
LSLMC0.968 50.931 10.938 20.931 4
UGLTL0.992 50.981 60.991 00.998 9
WTNNM0.995 00.987 20.990 00.988 9
LSGMC0.977 00.945 60.954 50.949 4
TBGL0.944 50.893 40.870 60.840 8
MSCVC0.981 50.958 50.963 40.959 3
FLMSC0.889 50.801 40.797 90.775 5
ALPC0.643 00.602 10.521 60.541 5
ours0.992 50.981 60.985 10.983 4

Table 8

Clustering results on MSRCV1 dataset"

数据集AccuracyNMIF?scoreARI
SC（best）0.761 90.658 00.624 80.563 3
GBS0.895 20.816 40.799 70.766 8
LSLMC0.795 20.695 00.664 90.610 0
UGLTL0.981 00.960 40.962 20.956 2
WTNNM0.990 50.990 50.980 50.977 3
LSGMC0.938 10.870 70.879 50.860 0
TBGL0.976 20.949 20.952 30.944 6
MSCVC0.976 20.946 10.952 10.944 4
FLMSC0.971 40.938 70.943 60.934 5
ALPC0.881 90.775 80.763 70.775 7
ours0.990 50.978 30.980 50.977 3

Table 9

Clustering results on YaleA dataset"

数据集AccuracyNMIF?scoreARI
SC（best）0.866 70.903 10.806 40.793 5
GBS0.612 10.655 10.383 00.329 3
LSLMC0.854 50.883 10.786 00.771 8
UGLTL0.897 00.930 20.867 40.858 5
WTNNM0.987 90.987 50.975 80.974 2
LSGMC0.860 60.886 70.796 70.783 3
TBGL0.866 70.858 20.679 50.655 4
MSCVC0.884 80.947 00.881 10.873 0
FLMSC0.915 20.900 90.837 50.826 9
ALPC0.848 50.884 40.793 60.810 9
ours0.993 90.992 30.987 30.986 5

Table 10

Clustering results on WebKB dataset"

数据集AccuracyNMIF?scoreARI
SC（best）0.833 50.161 70.821 70.256 2
GBS0.776 40.001 00.786 70.010 2
LSLMC0.829 70.131 40.813 70.267 4
UGLTL0.634 60.010 40.615 40.041 9
WTNNM0.779 30.002 80.791 80.004 9
LSGMC0.687 00.016 90.661 80.071 6
TBGL0.785 90.013 80.795 70.024 3
MSCVC0.966 70.749 70.949 70.860 1
FLMSC0.635 50.355 00.639 20.398 1
ALPC0.778 30.002 60.790 90.853 2
ours0.978 10.813 50.966 90.906 2

Fig.1

t-SNE visualization on NGs dataset"

Fig.2

Robustness experiments with different Gaussian noise"

Fig.3

Verify the effectiveness with different datasets"

Table 11

Clustering results of different views on ORL dataset"

视图AccuracyNMIF-scoreARI
v10.537 50.712 50.377 00.360 9
v20.705 20.838 30.608 90.599 5
v30.607 50.791 30.517 40.505 5
v1+v20.775 00.878 20.671 20.663 0
v1+v30.742 50.872 00.667 90.659 7
v2+v30.737 50.860 70.639 00.630 0
v1+v2+v31.000 01.000 01.000 01.000 0

Fig.4

Parameter sensitivity analysis"

Fig.5

Convergence analysis on BBC and YaleA datasets"

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