Semi-supervised Multi-view Clustering based on NMF with Fusion Regularization
Abstract
1 Introduction
2 Related Work
2.1 Unsupervised Multi-view Clustering
2.2 Semi-Supervised Multi-View Clustering
3 Semi-Supervised Multi-View Clustering with Fusion Regularization
4 Optimization Procedure
4.1 Optimization Algorithm of FRSMNMF_N1
4.1.1 Fixing Hc, updating Wv and Hv.
4.1.2 Fixing W and Hv, updating Hc.
![](https://dl.acm.org/cms/10.1145/3653022/asset/5493796b-e820-4994-a569-ebd8442347a7/assets/images/medium/tkdd-2022-10-0416-algo1.jpg)
4.2 Optimization Algorithm of FRSMNMF_N2
![](https://dl.acm.org/cms/10.1145/3653022/asset/f9bf74ea-43ae-4ba9-866f-260f0d2b4a05/assets/images/medium/tkdd-2022-10-0416-algo2.jpg)
4.3 Computational Complexity Analysis of FRSMNMF_N1 and FRSMNMF_N2
5 Experiments
5.1 Evaluation Metrics
5.2 Datasets
dataset | Size | Views | Features | Classes |
---|---|---|---|---|
Yale | 165 | 3 | 2048/256/1024 | 15 |
ORL | 400 | 3 | 2048/256/1024 | 40 |
FEI | 700 | 3 | 2048/256/1024 | 50 |
3sources | 169 | 3 | 3560/3631/3068 | 6 |
Texas | 187 | 2 | 187/1703 | 5 |
Carotid | 1378 | 2 | 17/17 | 2 |
5.3 Comparative Algorithms
5.4 Convergence Analysis
![](https://dl.acm.org/cms/10.1145/3653022/asset/f18c2eb3-4438-41d6-ac8a-dbf4f7239581/assets/images/medium/tkdd-2022-10-0416-f01.jpg)
5.5 Parameter Analysis and Comparisons
5.5.1 Parameter Analysis.
FRSMNMF_N1 | FRSMNMF_N2 | |||||
---|---|---|---|---|---|---|
10 \(\%\) | 20 \(\%\) | 30 \(\%\) | 10 \(\%\) | 20 \(\%\) | 30 \(\%\) | |
Yale | (0, \(-\) 1) | (5, 4) | (5, 4) | (2, 1) | (2, 0) | (2, 1) |
ORL | (0, \(-\) 1) | (0, \(-\) 1) | (0, \(-\) 1) | (3, 2) | (5, 5) | (5, 4) |
FEI | (5, 4) | (5, 3) | (5, 4) | (5, 4) | (5, 3) | (5, 4) |
3sources | (0, \(-\) 1) | (0, \(-\) 1) | (0, \(-\) 1) | (0, \(-\) 2) | (0, \(-\) 2) | (0, \(-\) 1) |
Texas | (5, 5) | (1, \(-\) 1) | (0, \(-\) 1) | (5, 5) | (5, 5) | (1, \(-\) 1) |
Carotid | (5, 5) | (5, 5) | (5, 5) | (5, 5) | (5, 5) | (5, 5) |
![](https://dl.acm.org/cms/10.1145/3653022/asset/883dafc9-78b8-4676-beb2-dd300cf50468/assets/images/medium/tkdd-2022-10-0416-f02.jpg)
![](https://dl.acm.org/cms/10.1145/3653022/asset/abab326d-d764-4df4-9217-61af4994e08a/assets/images/medium/tkdd-2022-10-0416-f03.jpg)
5.5.2 Comparisons.
Datasets | Yale | ORL | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
10 \(\%\) | 20 \(\%\) | 30 \(\%\) | 10 \(\%\) | 20 \(\%\) | 30 \(\%\) | |||||||
AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | |
AMVNMF [43] | 49.97 | \(\lt\) 0.001 | 55.80 | \(\lt\) 0.001 | 62.95 | \(\lt\) 0.001 | 63.65 | \(\lt\) 0.001 | 68.02 | \(\lt\) 0.001 | 72.57 | \(\lt\) 0.001 |
MVCNMF [5] | 50.93 | \(\lt\) 0.001 | 57.93 | \(\lt\) 0.001 | 63.56 | \(\lt\) 0.001 | 66.17 | \(\lt\) 0.001 | 70.07 | \(\lt\) 0.001 | 74.22 | \(\lt\) 0.001 |
MVOCNMF [6] | 51.14 | \(\lt\) 0.001 | 58.03 | \(\lt\) 0.001 | 64.98 | \(\lt\) 0.001 | 66.40 | \(\lt\) 0.001 | 70.75 | \(\lt\) 0.001 | 75.30 | \(\lt\) 0.001 |
GPSNMF [28] | 57.73 | \(\lt\) 0.001 | 67.50 | \(\lt\) 0.001 | 74.06 | \(\lt\) 0.001 | 68.82 | \(\lt\) 0.001 | 81.24 | \(\lt\) 0.001 | 84.09 | \(\lt\) 0.001 |
FRSMNMF_N2 | 62.25 | 0.777 | 70.79 | 0.484 | 78.00 | 0.903 | 72.05 | \(\lt\) 0.001 | 82.65 | \(\lt\) 0.001 | 87.98 | 0.015 |
FRSMNMF_N1 | 62.01 | – | 71.41 | – | 78.07 | – | 76.40 | – | 85.48 | – | 89.24 | – |
NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | |
AMVNMF [43] | 53.11 | \(\lt\) 0.001 | 59.62 | \(\lt\) 0.001 | 66.42 | \(\lt\) 0.001 | 79.27 | \(\lt\) 0.001 | 82.23 | \(\lt\) 0.001 | 84.81 | \(\lt\) 0.001 |
MVCNMF [5] | 54.60 | \(\lt\) 0.001 | 61.62 | \(\lt\) 0.001 | 67.19 | \(\lt\) 0.001 | 81.07 | \(\lt\) 0.001 | 83.69 | \(\lt\) 0.001 | 86.01 | \(\lt\) 0.001 |
MVOCNMF [6] | 54.59 | \(\lt\) 0.001 | 61.51 | \(\lt\) 0.001 | 68.13 | \(\lt\) 0.001 | 81.13 | \(\lt\) 0.001 | 84.02 | \(\lt\) 0.001 | 86.64 | \(\lt\) 0.001 |
GPSNMF [28] | 59.27 | \(\lt\) 0.001 | 66.00 | \(\lt\) 0.001 | 72.05 | \(\lt\) 0.001 | 83.35 | \(\lt\) 0.001 | 90.04 | \(\lt\) 0.001 | 91.46 | \(\lt\) 0.001 |
FRSMNMF_N2 | 61.11 | 0.001 | 68.03 | 0.298 | 75.15 | 0.980 | 83.97 | \(\lt\) 0.001 | 89.77 | \(\lt\) 0.001 | 92.33 | 0.020 |
FRSMNMF_N1 | 63.14 | – | 68.77 | – | 75.16 | – | 86.63 | – | 90.96 | – | 93.05 | – |
Datasets | FEI | 3sources | ||||||||||
10 \(\%\) | 20 \(\%\) | 30 \(\%\) | 10 \(\%\) | 20 \(\%\) | 30 \(\%\) | |||||||
AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | |
AMVNMF [43] | 56.65 | \(\lt\) 0.001 | 60.06 | \(\lt\) 0.001 | 66.36 | \(\lt\) 0.001 | 59.27 | \(\lt\) 0.001 | 65.83 | \(\lt\) 0.001 | 70.79 | \(\lt\) 0.001 |
MVCNMF [5] | 59.19 | \(\lt\) 0.001 | 63.58 | \(\lt\) 0.001 | 69.60 | \(\lt\) 0.001 | 61.65 | \(\lt\) 0.001 | 69.83 | \(\lt\) 0.001 | 72.72 | \(\lt\) 0.001 |
MVOCNMF [6] | 59.88 | \(\lt\) 0.001 | 63.47 | \(\lt\) 0.001 | 69.68 | \(\lt\) 0.001 | 57.44 | \(\lt\) 0.001 | 72.30 | \(\lt\) 0.001 | 81.12 | \(\lt\) 0.001 |
GPSNMF [28] | 81.45 | \(\lt\) 0.001 | 84.56 | \(\lt\) 0.001 | 88.84 | \(\lt\) 0.001 | 80.79 | \(\lt\) 0.001 | 88.30 | \(\lt\) 0.001 | 91.05 | \(\lt\) 0.001 |
FRSMNMF_N2 | 83.67 | 0.506 | 87.03 | 0.428 | 91.78 | 0.796 | 87.91 | 0.020 | 92.06 | 0.083 | 93.45 | \(\lt\) 0.001 |
FRSMNMF_N1 | 83.88 | – | 86.79 | – | 91.83 | – | 89.91 | – | 93.30 | – | 95.24 | – |
NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | |
AMVNMF [43] | 76.13 | \(\lt\) 0.001 | 78.16 | \(\lt\) 0.001 | 82.36 | \(\lt\) 0.001 | 55.62 | \(\lt\) 0.001 | 61.02 | \(\lt\) 0.001 | 65.74 | \(\lt\) 0.001 |
MVCNMF [5] | 77.43 | \(\lt\) 0.001 | 80.33 | \(\lt\) 0.001 | 84.35 | \(\lt\) 0.001 | 60.00 | \(\lt\) 0.001 | 66.76 | \(\lt\) 0.001 | 66.67 | \(\lt\) 0.001 |
MVOCNMF [6] | 77.79 | \(\lt\) 0.001 | 80.16 | \(\lt\) 0.001 | 84.37 | \(\lt\) 0.001 | 51.77 | \(\lt\) 0.001 | 59.36 | \(\lt\) 0.001 | 68.13 | \(\lt\) 0.001 |
GPSNMF [28] | 90.04 | 0.009 | 91.51 | 0.111 | 93.60 | \(\lt\) 0.001 | 67.39 | \(\lt\) 0.001 | 75.00 | \(\lt\) 0.001 | 78.56 | \(\lt\) 0.001 |
FRSMNMF_N2 | 90.53 | 0.739 | 91.93 | 0.659 | 95.04 | 0.895 | 74.57 | \(\lt\) 0.001 | 82.21 | 0.029 | 84.04 | \(\lt\) 0.001 |
FRSMNMF_N1 | 90.88 | – | 91.84 | – | 95.06 | – | 79.39 | – | 84.70 | – | 88.06 | – |
Datasets | Texas | Carotid | ||||||||||
10 \(\%\) | 20 \(\%\) | 30 \(\%\) | 10 \(\%\) | 20 \(\%\) | 30 \(\%\) | |||||||
AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | |
AMVNMF [43] | 45.55 | \(\lt\) 0.001 | 49.66 | \(\lt\) 0.001 | 55.73 | \(\lt\) 0.001 | 53.47 | \(\lt\) 0.001 | 56.61 | \(\lt\) 0.001 | 54.53 | \(\lt\) 0.001 |
MVCNMF [5] | 64.61 | \(\lt\) 0.001 | 67.80 | \(\lt\) 0.001 | 70.77 | \(\lt\) 0.001 | 56.47 | \(\lt\) 0.001 | 60.49 | \(\lt\) 0.001 | 61.65 | \(\lt\) 0.001 |
MVOCNMF [6] | 66.32 | \(\lt\) 0.001 | 67.91 | \(\lt\) 0.001 | 69.80 | \(\lt\) 0.001 | 56.43 | \(\lt\) 0.001 | 60.01 | \(\lt\) 0.001 | 65.45 | \(\lt\) 0.001 |
GPSNMF [28] | 64.57 | \(\lt\) 0.001 | 70.12 | \(\lt\) 0.001 | 75.25 | 0.032 | 70.23 | 0.062 | 75.56 | 0.086 | 78.88 | 0.194 |
FRSMNMF_N2 | 69.29 | 0.224 | 72.23 | 0.002 | 73.54 | \(\lt\) 0.001 | 71.04 | 0.870 | 75.91 | 0.687 | 79.19 | 1.000 |
FRSMNMF_N1 | 69.96 | – | 73.96 | – | 77.20 | – | 71.11 | – | 76.03 | – | 79.19 | – |
NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | |
AMVNMF [43] | 20.31 | \(\lt\) 0.001 | 23.37 | \(\lt\) 0.001 | 28.57 | \(\lt\) 0.001 | 0.93 | \(\lt\) 0.001 | 3.41 | \(\lt\) 0.001 | 2.11 | \(\lt\) 0.001 |
MVCNMF [5] | 32.27 | \(\lt\) 0.001 | 36.23 | \(\lt\) 0.001 | 41.71 | \(\lt\) 0.001 | 1.98 | \(\lt\) 0.001 | 4.88 | \(\lt\) 0.001 | 8.65 | \(\lt\) 0.001 |
MVOCNMF [6] | 32.49 | \(\lt\) 0.001 | 36.14 | \(\lt\) 0.001 | 40.78 | \(\lt\) 0.001 | 1.90 | \(\lt\) 0.001 | 4.51 | \(\lt\) 0.001 | 7.06 | \(\lt\) 0.001 |
GPSNMF [28] | 26.44 | 0.098 | 39.96 | 0.185 | 53.80 | \(\lt\) 0.001 | 12.50 | 0.125 | 20.29 | 0.333 | 26.00 | 0.501 |
FRSMNMF_N2 | 28.87 | 0.731 | 37.01 | \(\lt\) 0.001 | 47.10 | 0.525 | 13.41 | 0.945 | 20.49 | 0.656 | 26.31 | 1.000 |
FRSMNMF_N1 | 29.16 | – | 41.52 | – | 46.42 | – | 13.45 | – | 20.70 | – | 26.31 | – |
Datasets | Yale | ORL | FEI | 3sources | Texas | Carotid | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | |
VCGNMF [4] | 54.24 | \(\lt\) 0.001 | 71.33 | \(\lt\) 0.001 | 69.54 | \(\lt\) 0.001 | 59.17 | \(\lt\) 0.001 | 62.51 | \(\lt\) 0.001 | 61.51 | \(\lt\) 0.001 |
VAGNMF [4] | 50.00 | \(\lt\) 0.001 | 69.13 | \(\lt\) 0.001 | 68.83 | \(\lt\) 0.001 | 62.66 | \(\lt\) 0.001 | 54.28 | \(\lt\) 0.001 | 57.17 | \(\lt\) 0.001 |
LP-DiNMF [42] | 50.85 | \(\lt\) 0.001 | 70.43 | \(\lt\) 0.001 | 69.54 | \(\lt\) 0.001 | 62.78 | \(\lt\) 0.001 | 55.35 | \(\lt\) 0.001 | 57.03 | \(\lt\) 0.001 |
rNNMF [10] | 50.42 | \(\lt\) 0.001 | 65.58 | \(\lt\) 0.001 | 55.26 | \(\lt\) 0.001 | 62.07 | \(\lt\) 0.001 | 60.37 | \(\lt\) 0.001 | 57.89 | \(\lt\) 0.001 |
UDNMF [52] | 47.88 | \(\lt\) 0.001 | 67.95 | \(\lt\) 0.001 | 74.71 | \(\lt\) 0.001 | 62.78 | \(\lt\) 0.001 | 54.71 | \(\lt\) 0.001 | 60.86 | \(\lt\) 0.001 |
MPMNMF \(\_\) 1 [46] | 50.85 | \(\lt\) 0.001 | 70.40 | \(\lt\) 0.001 | 69.04 | \(\lt\) 0.001 | 72.13 | \(\lt\) 0.001 | 65.72 | \(\lt\) 0.001 | 57.20 | \(\lt\) 0.001 |
MPMNMF \(\_\) 2 [46] | 50.12 | \(\lt\) 0.001 | 69.20 | \(\lt\) 0.001 | 68.76 | \(\lt\) 0.001 | 65.27 | \(\lt\) 0.001 | 61.71 | \(\lt\) 0.001 | 56.99 | \(\lt\) 0.001 |
MVCDMF [60] | 53.52 | \(\lt\) 0.001 | 69.28 | \(\lt\) 0.001 | 68.84 | \(\lt\) 0.001 | 77.28 | \(\lt\) 0.001 | 56.74 | \(\lt\) 0.001 | 57.49 | \(\lt\) 0.001 |
MvDGNMF [26] | 50.79 | \(\lt\) 0.001 | 70.45 | \(\lt\) 0.001 | 74.17 | \(\lt\) 0.001 | 71.66 | \(\lt\) 0.001 | 58.13 | \(\lt\) 0.001 | 56.79 | \(\lt\) 0.001 |
FRSMNMF_N2 | 62.25 | 0.777 | 72.05 | \(\lt\) 0.001 | 83.67 | 0.254 | 87.91 | \(\lt\) 0.001 | 69.29 | 0.050 | 71.04 | 0.333 |
FRSMNMF_N1 | 62.01 | – | 76.40 | – | 83.88 | – | 89.91 | – | 69.96 | – | 71.11 | – |
NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | |
VCGNMF [4] | 57.55 | \(\lt\) 0.001 | 84.68 | \(\lt\) 0.001 | 85.40 | \(\lt\) 0.001 | 58.68 | \(\lt\) 0.001 | 28.70 | \(\lt\) 0.001 | 3.97 | \(\lt\) 0.001 |
VAGNMF [4] | 52.74 | \(\lt\) 0.001 | 83.67 | \(\lt\) 0.001 | 84.48 | \(\lt\) 0.001 | 56.50 | \(\lt\) 0.001 | 21.48 | \(\lt\) 0.001 | 2.36 | \(\lt\) 0.001 |
LP-DiNMF [42] | 53.81 | \(\lt\) 0.001 | 84.65 | \(\lt\) 0.001 | 84.50 | \(\lt\) 0.001 | 56.37 | \(\lt\) 0.001 | 24.49 | \(\lt\) 0.001 | 2.34 | \(\lt\) 0.001 |
rNNMF [10] | 52.56 | \(\lt\) 0.001 | 80.91 | \(\lt\) 0.001 | 74.13 | \(\lt\) 0.001 | 57.83 | \(\lt\) 0.001 | 27.89 | \(\lt\) 0.001 | 2.31 | \(\lt\) 0.001 |
UDNMF [52] | 50.69 | \(\lt\) 0.001 | 82.22 | \(\lt\) 0.001 | 87.17 | \(\lt\) 0.001 | 58.41 | \(\lt\) 0.001 | 22.93 | \(\lt\) 0.001 | 4.44 | \(\lt\) 0.001 |
MPMNMF \(\_\) 1 [46] | 54.39 | \(\lt\) 0.001 | 84.21 | \(\lt\) 0.001 | 85.09 | \(\lt\) 0.001 | 65.71 | \(\lt\) 0.001 | 31.48 | \(\lt\) 0.001 | 2.38 | \(\lt\) 0.001 |
MPMNMF \(\_\) 2 [46] | 52.54 | \(\lt\) 0.001 | 84.46 | \(\lt\) 0.001 | 85.08 | \(\lt\) 0.001 | 58.61 | \(\lt\) 0.001 | 26.46 | \(\lt\) 0.001 | 2.59 | \(\lt\) 0.001 |
MVCDMF [60] | 56.05 | \(\lt\) 0.001 | 84.27 | \(\lt\) 0.001 | 84.54 | \(\lt\) 0.001 | 71.59 | \(\lt\) 0.001 | 25.12 | \(\lt\) 0.001 | 2.16 | \(\lt\) 0.001 |
MvDGNMF [26] | 53.44 | \(\lt\) 0.001 | 84.53 | \(\lt\) 0.001 | 87.15 | \(\lt\) 0.001 | 61.67 | \(\lt\) 0.001 | 28.39 | \(\lt\) 0.001 | 2.11 | \(\lt\) 0.001 |
FRSMNMF_N2 | 61.11 | 0.001 | 83.97 | \(\lt\) 0.001 | 90.53 | 0.372 | 74.57 | \(\lt\) 0.001 | 28.87 | 0.026 | 13.41 | 0.691 |
FRSMNMF_N1 | 63.14 | – | 86.63 | – | 90.88 | – | 79.39 | – | 29.16 | – | 13.45 | – |
![](https://dl.acm.org/cms/10.1145/3653022/asset/79c11fc2-59f3-424b-a1ec-fc45e4781fc5/assets/images/medium/tkdd-2022-10-0416-f04.jpg)
5.5.3 Studying the Effects of Individual Views.
Datasets | Yale | ORL | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
view1 | view2 | view3 | view1 | view2 | view3 | |||||||
AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | |
MVCNMF [5] | 60.95 | \(\lt\) 0.001 | 64.70 | \(\lt\) 0.001 | 56.56 | \(\lt\) 0.001 | 74.13 | \(\lt\) 0.001 | 74.54 | \(\lt\) 0.001 | 74.14 | \(\lt\) 0.001 |
MVOCNMF [6] | 63.91 | \(\lt\) 0.001 | 63.97 | \(\lt\) 0.001 | 64.07 | \(\lt\) 0.001 | 75.06 | \(\lt\) 0.001 | 75.37 | \(\lt\) 0.001 | 74.42 | \(\lt\) 0.001 |
FRSMNMF_N2 | 77.84 | 0.954 | 77.96 | 0.954 | 76.71 | 0.954 | 88.01 | 0.133 | 88.41 | 0.133 | 87.35 | 0.133 |
FRSMNMF_N1 | 77.98 | – | 77.93 | – | 76.67 | – | 89.16 | – | 89.61 | – | 88.17 | – |
NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | |
MVCNMF [5] | 64.68 | \(\lt\) 0.001 | 68.03 | \(\lt\) 0.001 | 61.01 | \(\lt\) 0.001 | 85.99 | \(\lt\) 0.001 | 86.22 | \(\lt\) 0.001 | 86.02 | \(\lt\) 0.001 |
MVOCNMF [6] | 67.64 | \(\lt\) 0.001 | 67.64 | \(\lt\) 0.001 | 67.63 | \(\lt\) 0.001 | 86.65 | \(\lt\) 0.001 | 86.70 | \(\lt\) 0.001 | 86.28 | \(\lt\) 0.001 |
FRSMNMF_N2 | 74.69 | 0.952 | 74.93 | 0.952 | 73.88 | 0.952 | 92.24 | 0.084 | 92.55 | 0.084 | 91.77 | 0.084 |
FRSMNMF_N1 | 74.76 | – | 74.92 | – | 73.85 | – | 92.92 | – | 93.32 | – | 92.34 | – |
Datasets | 3sources | Carotid | – | |||||||||
view1 | view2 | view3 | view1 | view2 | – | |||||||
AC | p-value | AC | p-value | AC | p-value | AC | p-value | AC | p-value | – | – | |
MVCNMF [5] | 71.65 | \(\lt\) 0.001 | 69.54 | \(\lt\) 0.001 | 68.89 | \(\lt\) 0.001 | 63.78 | \(\lt\) 0.001 | 64.73 | \(\lt\) 0.001 | – | – |
MVOCNMF [6] | 81.75 | \(\lt\) 0.001 | 81.72 | \(\lt\) 0.001 | 81.74 | \(\lt\) 0.001 | 65.22 | \(\lt\) 0.001 | 65.22 | \(\lt\) 0.001 | – | – |
FRSMNMF_N2 | 93.01 | 0.004 | 92.86 | 0.004 | 93.30 | 0.004 | 76.58 | 1.000 | 72.96 | 1.000 | – | – |
FRSMNMF_N1 | 95.18 | – | 94.58 | – | 94.87 | – | 76.58 | – | 72.96 | – | – | – |
NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | NMI | p-value | – | – | |
MVCNMF [5] | 67.38 | \(\lt\) 0.001 | 65.82 | \(\lt\) 0.001 | 64.77 | \(\lt\) 0.001 | 12.01 | \(\lt\) 0.001 | 10.71 | \(\lt\) 0.001 | – | – |
MVOCNMF [6] | 69.13 | \(\lt\) 0.001 | 69.07 | \(\lt\) 0.001 | 69.09 | \(\lt\) 0.001 | 6.82 | \(\lt\) 0.001 | 6.82 | \(\lt\) 0.001 | – | – |
FRSMNMF_N2 | 82.64 | \(\lt\) 0.001 | 82.54 | \(\lt\) 0.001 | 83.82 | \(\lt\) 0.001 | 21.81 | 1.000 | 15.96 | 1.000 | – | – |
FRSMNMF_N1 | 87.99 | – | 86.11 | – | 87.46 | – | 21.81 | – | 15.96 | – | – | – |
5.5.4 Ablation Study.
Yale | ORL | ||||
---|---|---|---|---|---|
Norm | Method | AC | NMI | AC | NMI |
None | FRSMNMF | 61.55 \(\pm\) 3.02 | 60.97 \(\pm\) 2.17 | 69.69 \(\pm\) 2.03 | 82.35 \(\pm\) 1.40 |
\(||{\bf W}_{\cdot j}^v||_2=1\) | FRSMNMF_N1 | 62.01 \(\pm\) 2.31 | 63.14 \(\pm\) 1.62 | 76.40 \(\pm\) 1.39 | 86.63 \(\pm\) 0.71 |
FRSMNMF_N1 w \(|\) o GR | 58.43 \(\pm\) 2.40 | 59.74 \(\pm\) 1.91 | 71.24 \(\pm\) 1.50 | 82.97 \(\pm\) 0.73 | |
FRSMNMF_N1 w \(|\) o FR | 49.78 \(\pm\) 0.91 | 53.23 \(\pm\) 0.54 | 67.97 \(\pm\) 0.71 | 82.96 \(\pm\) 0.29 | |
\(||{\bf W}_{\cdot j}^v||_1=1\) | FRSMNMF_N2 | 62.25 \(\pm\) 3.01 | 61.11 \(\pm\) 2.00 | 72.05 \(\pm\) 1.51 | 83.97 \(\pm\) 0.76 |
FRSMNMF_N2 w \(|\) o GR | 44.48 \(\pm\) 1.14 | 48.05 \(\pm\) 0.71 | 62.56 \(\pm\) 0.79 | 78.60 \(\pm\) 0.40 | |
FRSMNMF_N2 w \(|\) o FR | 51.47 \(\pm\) 0.99 | 54.97 \(\pm\) 0.86 | 68.64 \(\pm\) 0.71 | 83.51 \(\pm\) 0.28 | |
3sources | Carotid | ||||
Norm | Method | AC | NMI | AC | NMI |
None | FRSMNMF | 84.35 \(\pm\) 3.90 | 67.82 \(\pm\) 5.68 | 69.07 \(\pm\) 1.48 | 10.91 \(\pm\) 1.74 |
\(||{\bf W}_{\cdot j}^v||_2=1\) | FRSMNMF_N1 | 89.91 \(\pm\) 2.49 | 79.39 \(\pm\) 3.41 | 71.11 \(\pm\) 1.49 | 13.45 \(\pm\) 1.96 |
FRSMNMF_N1 w \(|\) o GR | 85.04 \(\pm\) 4.17 | 73.76 \(\pm\) 3.63 | 61.11 \(\pm\) 1.09 | 4.14 \(\pm\) 0.58 | |
FRSMNMF_N1 w \(|\) o FR | 60.55 \(\pm\) 2.53 | 56.42 \(\pm\) 1.86 | 55.76 \(\pm\) 0.12 | 2.54 \(\pm\) 0.07 | |
\(||{\bf W}_{\cdot j}^v||_1=1\) | FRSMNMF_N2 | 87.91 \(\pm\) 2.71 | 74.57 \(\pm\) 3.95 | 71.04 \(\pm\) 1.46 | 13.41 \(\pm\) 1.90 |
FRSMNMF_N2 w \(|\) o GR | 53.68 \(\pm\) 1.76 | 50.50 \(\pm\) 1.60 | 58.48 \(\pm\) 0.29 | 3.32 \(\pm\) 0.17 | |
FRSMNMF_N2 w \(|\) o FR | 59.10 \(\pm\) 0.64 | 55.08 \(\pm\) 0.85 | 57.17 \(\pm\) 0.81 | 2.60 \(\pm\) 0.41 |
5.5.5 Performance on Noise Datasets.
Yale | ||||||
Noise | 10 \(\%\) | 20 \(\%\) | 30 \(\%\) | |||
Method | AC | NMI | AC | NMI | AC | NMI |
MVCNMF [5] | 56.45 \(\pm\) 1.69 | 60.18 \(\pm\) 1.68 | 53.32 \(\pm\) 1.71 | 57.85 \(\pm\) 1.34 | 49.01 \(\pm\) 1.46 | 53.40 \(\pm\) 1.17 |
MVOCNMF [6] | 56.61 \(\pm\) 1.66 | 60.44 \(\pm\) 1.37 | 53.82 \(\pm\) 1.68 | 58.22 \(\pm\) 1.53 | 50.02 \(\pm\) 1.57 | 54.22 \(\pm\) 1.31 |
FRSMNMF_N2 | 57.59 \(\pm\) 2.54 | 56.16 \(\pm\) 1.79 | 54.60 \(\pm\) 2.78 | 52.14 \(\pm\) 2.23 | 52.37 \(\pm\) 2.62 | 50.03 \(\pm\) 2.40 |
FRSMNMF_N1 | 65.59 \(\pm\) 1.86 | 64.85 \(\pm\) 1.97 | 61.71 \(\pm\) 1.94 | 61.15 \(\pm\) 1.89 | 59.38 \(\pm\) 2.55 | 58.39 \(\pm\) 2.03 |
ORL | ||||||
Noise | 10 \(\%\) | 20 \(\%\) | 30 \(\%\) | |||
Method | AC | NMI | AC | NMI | AC | NMI |
MVCNMF [5] | 67.06 \(\pm\) 1.11 | 81.10 \(\pm\) 0.51 | 64.21 \(\pm\) 1.09 | 78.64 \(\pm\) 0.69 | 58.94 \(\pm\) 1.16 | 74.74 \(\pm\) 0.49 |
MVOCNMF [6] | 66.92 \(\pm\) 0.76 | 80.92 \(\pm\) 0.45 | 64.12 \(\pm\) 1.00 | 78.64 \(\pm\) 0.53 | 58.90 \(\pm\) 0.92 | 74.92 \(\pm\) 0.41 |
FRSMNMF_N2 | 78.42 \(\pm\) 1.69 | 85.35 \(\pm\) 1.12 | 75.70 \(\pm\) 1.92 | 83.24 \(\pm\) 1.12 | 71.82 \(\pm\) 1.51 | 80.01 \(\pm\) 1.14 |
FRSMNMF_N1 | 82.26 \(\pm\) 1.45 | 88.68 \(\pm\) 0.84 | 80.09 \(\pm\) 1.20 | 86.91 \(\pm\) 0.82 | 75.43 \(\pm\) 1.24 | 83.69 \(\pm\) 0.78 |
FEI | ||||||
Noise | 10 \(\%\) | 20 \(\%\) | 30 \(\%\) | |||
Method | AC | NMI | AC | NMI | AC | NMI |
MVCNMF [5] | 60.09 \(\pm\) 0.85 | 77.25 \(\pm\) 0.51 | 54.76 \(\pm\) 1.20 | 73.23 \(\pm\) 0.62 | 51.48 \(\pm\) 0.87 | 70.29 \(\pm\) 0.54 |
MVOCNMF [6] | 59.85 \(\pm\) 0.90 | 77.04 \(\pm\) 0.60 | 54.63 \(\pm\) 1.08 | 73.27 \(\pm\) 0.51 | 51.08 \(\pm\) 0.86 | 70.22 \(\pm\) 0.57 |
FRSMNMF_N2 | 83.68 \(\pm\) 1.05 | 90.18 \(\pm\) 0.70 | 79.54 \(\pm\) 1.36 | 87.16 \(\pm\) 0.76 | 76.93 \(\pm\) 1.21 | 84.74 \(\pm\) 0.75 |
FRSMNMF_N1 | 83.79 \(\pm\) 1.13 | 90.21 \(\pm\) 0.72 | 79.72 \(\pm\) 1.59 | 87.20 \(\pm\) 0.81 | 76.87 \(\pm\) 1.11 | 84.70 \(\pm\) 0.67 |
Carotid | ||||||
Noise | 10 \(\%\) | 20 \(\%\) | 30 \(\%\) | |||
Method | AC | NMI | AC | NMI | AC | NMI |
MVCNMF [5] | 59.88 \(\pm\) 1.65 | 4.54 \(\pm\) 1.06 | 59.07 \(\pm\) 1.12 | 3.89 \(\pm\) 0.78 | 58.62 \(\pm\) 0.81 | 5.06 \(\pm\) 0.65 |
MVOCNMF [6] | 59.69 \(\pm\) 1.54 | 4.39 \(\pm\) 0.96 | 58.82 \(\pm\) 1.12 | 3.71 \(\pm\) 0.74 | 59.54 \(\pm\) 0.56 | 4.18 \(\pm\) 0.31 |
FRSMNMF_N2 | 74.56 \(\pm\) 1.02 | 18.28 \(\pm\) 1.47 | 73.88 \(\pm\) 1.36 | 17.26 \(\pm\) 1.90 | 72.74 \(\pm\) 1.97 | 15.70 \(\pm\) 2.71 |
FRSMNMF_N1 | 74.54 \(\pm\) 0.88 | 18.23 \(\pm\) 1.28 | 73.95 \(\pm\) 0.96 | 17.34 \(\pm\) 1.39 | 73.23 \(\pm\) 1.29 | 16.33 \(\pm\) 1.86 |
5.5.6 Feature Visualization.
![](https://dl.acm.org/cms/10.1145/3653022/asset/ab3fda8f-919c-4061-99e7-1efda5d13461/assets/images/medium/tkdd-2022-10-0416-f05.jpg)
![](https://dl.acm.org/cms/10.1145/3653022/asset/d61d39a3-c41e-4962-8862-b0bd4bdc2dee/assets/images/medium/tkdd-2022-10-0416-f06.jpg)
6 Conclusion
Acknowledgments
Footnotes
References
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