Robust Semi-supervised Fuzzy Clustering Algorithm based on Pairwise Constraints

Document Type : Research Paper

Authors

1 Xi'an Polytechnic University

2 Northwest University, Xi’an Polytechnic University

3 Department of Mathematics, Graduate University of Advanced Technology, Kerman, Iran

Abstract

Semi-supervised clustering, utilizing the supervision information to guide the clustering process, could improve the clustering effect of the models. Most of existing semi-supervised clustering models only consider pairwise constraints or pointwise constraints. In this paper, the semi-supervised method is applied to the fuzzy clustering algorithm, and a robust semi-supervised fuzzy clustering algorithm is proposed. Firstly, fully considering prior knowledge, our models integrate pointwise constraints and pairwise constraints into a unified framework to improve the clustering performance of the fuzzy clustering algorithm. Secondly, in order to alleviate the impact of outliers, the robust performance of the models is considered by introducing an adaptive loss function into the models. Thirdly, our models can capture the global structures and the local manifold structures of data sets. Finally, a simple and efficient algorithm is proposed to solve the models, which ensures that the obtained solution is sparse and satisfies the constraint conditions in our models. Compared with five representative methods, experimental results on public datasets, such as text dataset (dbworld), voice dataset (Isolet), image datasets (YALE, Umist), chemical dataset (wine) and biological datasets (colon, TOX-171), show the effectiveness of the proposed models.

Keywords

Main Subjects

References

[1] J. C. Bezdek, A convergence theorem for the fuzzy ISODATA clustering algorithms, IEEE Transactions on Pattern
Analysis and Machine Intelligence, 2(1) (1980), 1-8. https://doi.org/10.1109/TPAMI.1980.4766964
[2] J. C. Bezdek, Pattern recognition with fuzzy objective function algorithms, Springer Science and Business Media,
1981. https://doi.org/10.1007/978-1-4757-0450-1
[3] D. P. Branco, F. D. A. de Carvalho, Medoid based semi-supervised fuzzy clustering algorithms for multi-view relational
data, Fuzzy Sets and Systems, 469(15) (2023), 108630. https://doi.org/10.1016/j.fss.2023.108630
[4] X. Chang, F. Nie, Y. Yang, H. Huang, A convex formulation for semi-supervised multi-label feature selection,
Proceedings of the AAAI Conference on Artificial Intelligence, 28(1) (2014), 1171-1177. https://doi.org/10.
5555/2893873.2894055
[5] R. Chen, Y. Tang, W. Zhang, W. Feng, Deep multi-view semi-supervised clustering with sample pairwise constraints,
Neurocomputing, 500(21) (2022), 832-845. https://doi.org/10.1016/j.neucom.2022.05.091
[6] C. Ding, A new robust function that smoothly interpolates between ℓ1 and ℓ2 error functions, Univerisity of Texas
at Arlington Tech Report, (2013), 1621-1630.
[7] H. Dong, Y. Li, Z. Zhou, Learning from semi-supervised weak-label data, Proceedings of the AAAI Conference on
Artificial Intelligence, 32(1) (2018). https://doi.org/10.5555/3504035.3504392
[8] H. Gan, Z. Yang, R. Zhou, Adaptive safety-aware semi-supervised clustering, Expert Systems with Applications,
212 (2023), 118751. https://doi.org/10.1016/j.eswa.2022.118751
[9] G. Gonz´alez-Almagro, J. L. Su´arez, P. S´anchez-Bermejo, J. R. Cano, S. Garc´ıa, Semi-supervised clustering with two
types of background knowledge: Fusing pairwise constraints and monotonicity constraints, Information Fusion, 102
(2024). https://doi.org/10.1016/j.inffus.2023.102064
[10] Y. Guo, A. Sengur, NCM: Neutrosophic c-means clustering algorithm, Pattern Recognition, 48(8) (2015), 2710-
2724. https://doi.org/10.1016/j.patcog.2015.02.018
[11] A. Isazadeh, M. Ghorbani, Fuzzy c-means and its generalization by ℓp-norm space, WSEAS Transactions Mathematics,
2(1) (2003), 168-170.
[12] Y. Jia, G. Lu, H. Liu, J. Hou, Semi-supervised subspace clustering via tensor low-rank representation, IEEE
Transactions on Circuits and Systems for Video Technology, 33(7) (2023), 3455-3461. https://doi.org/10.1109/
TCSVT.2023.3234556
[13] W. Li, S. Wang, X. Guo, E. Zhu, Deep graph clustering with multi-level subspace fusion, Pattern Recognition, 134
(2023), 109077. https://doi.org/10.1016/j.patcog.2022.109077
[14] L. Li, J. Zhang, S. Wang, X. Liu, K. Li, K. Li, Multi-view bipartite graph clustering with coupled noisy feature
filter, Indian Journal of Pure and Applied Mathematics, 35(12) (2023), 12842-12854. https://doi.org/10.1109/
TKDE.2023.3268215
[15] X. Li, Y. Zhang, R. Zhang, Semi-supervised feature selection via generalized uncorrelated constraint and manifold
embedding, IEEE Transactions on Neural Networks and Learning Systems, 33(9) (2022), 5070-5079. https://doi.
org/10.1109/TNNLS.2021.3069038
[16] S. K. Majhi, S. Bhatachharya, R. Pradhan, S. Biswal, Fuzzy clustering using salp swarm algorithm for automobile
insurance fraud detection, Indian Journal of Pure and Applied Mathematics, 36(3) (2019), 2333-2344. https:
//doi.org/10.3233/JIFS-169944
[17] J. Mei, H. Lv, J. Cao, W. Gong, Pairwise constrained fuzzy clustering: Relation, comparison and parallelization, International Journal of Fuzzy Systems, 21(6) (2019), 1938-1949. https://doi.org/10.1007/s40815-019-00683-1
[18] F. Nie, H. Huang, X. Cai, C. Ding, Efficient and robust feature selection via joint ℓ2,1-norms minimization,
Advances in Neural Information Processing Systems, 23 (2010), 1813-1821. https://doi.org/10.5555/2997046.
2997098
[19] F. Nie, H. Wang, H. Huang, C. Ding, Unsupervised and semi-supervised learning via ℓ1-norm graph, International
Conference on Computer Vision, 32(11) (2011), 2268-2273. https://doi.org/10.1109/ICCV.2011.6126506
[20] F. Nie, H. Wang, H. Huang, C. Ding, Adaptive loss minimization for semi-supervised elastic embedding, Twenty-
Third International Joint Conference on Artificial Intelligence, (2013), 1565-1571. https://doi.org/10.5555/
2540128.2540353
[21] A. G. Oskouei, M. Hashemzadeh, B. Asheghi, M. A. Balafar, CGFFCM: Cluster-weight and group-local featureweight
learning in fuzzy c-means clustering algorithm for color image segmentation, Applied Soft Computing, 113
(2021), 108005. https://doi.org/10.1016/j.asoc.2021.108005
[22] A. G. Oskouei, N. Samadi, J. Tanha, Feature-weight and cluster-weight learning in fuzzy c-means method for semisupervised clustering, Applied Soft Computing, 161 (2024), 111712. https://doi.org/10.1016/j.asoc.2024.
111712
[23] T. Qi, X. Feng, B. Gao, K. Wang, An end-to-end graph convolutional network for semi-supervised subspace clustering
via label self-expressiveness, Knowledge-Based Systems, 286 (2024), 111393. https://doi.org/10.1016/j.
knosys.2024.111393
[24] S. Shalev-Shwartz, Y. Singer, Efficient learning of label ranking by soft projections onto polyhedra, The Journal of
Machine Learning Research, 7 (2006), 1567-1599. https://doi.org/10.5555/1248547.1248605
[25] P. Smyth, Model selection for probabilistic clustering using cross-validated likelihood, Statistics and Computing,
10(1) (2000), 63-72. https://doi.org/10.1023/A:1008940618127
[26] N. X. Thao, M. Ali, F. Smarandache, An intuitionistic fuzzy clustering algorithm based on a new correlation
coefficient with application in medical diagnosis, Journal of Intelligent and Fuzzy Systems, 36(1) (2019), 189-198.
https://doi.org/10.3233/JIFS-181084
[27] T. M. Tuan, M. D. Sinh, T. I. Khang, T. T. Ngan, N. L. Giang, A new approach for semi-supervised fuzzy clustering
with multiple fuzzifiers, International Journal of Fuzzy Systems, 24 (2022), 3688-3701. https://doi.org/10.1007/
s40815-022-01363-3
[28] Y. Wan, Y. Zhong, A. Ma, Fully automatic spectral-spatial fuzzy clustering using an adaptive multi-objective
memetic algorithm for multi-spectral imagery, IEEE Transactions on Geoscience and Remote Sensing, 57(4) (2019),
2324-2340. https://doi.org/10.1109/TGRS.2018.2872875
[29] W. Wang, M. A. Carreira-Perpin´an, Projection onto the probability simplex: An efficient algorithm with a simple
proof, and an application, arXiv preprint arXiv:1309.1541, (2013). https://doi.org/10.48550/arXiv.1309.1541
[30] Y. Wang, L. Chen, J. Zhou, T. Li, Y. Yu, Pairwise constraints based semi-supervised fuzzy clustering with
multi-manifold regularization, Information Sciences, 638 (2023), 118994. https://doi.org/10.1016/j.ins.2023.
118994
[31] Z. Wang, S. Wang, L. Bai, W. Wang, Y. Shao, Semi-supervised fuzzy clustering with fuzzy pairwise constraints,
IEEE Transactions on Fuzzy Systems, 30(9) (2022), 3797-3811. https://doi.org/10.1109/TFUZZ.2021.3129848
[32] H. Wang, J. Wang, G. Wang, Clustering validity function fusion method of FCM clustering algorithm based on
dempster-shafer evidence theory, International Journal of Fuzzy Systems, 24(1) (2022), 650-675. https://doi.org/
10.1007/s40815-021-01170-2
[33] G. Wang, J. Wang, H. Wang, J. Liu, Component-wise design method of fuzzy c-means clustering validity function
based on CRITIC combination weighting, The Journal of Supercomputing, 79(13) (2023), 14571-14601. https:
//doi.org/10.1007/s11227-023-05234-y
[34] C. Wu, J. Zhang, Robust semi-supervised spatial picture fuzzy clustering with local membership and KL-divergence
for image segmentation, International Journal of Machine Learning and Cybernetics, 13(4) (2022), 963-987. https:
//doi.org/10.1007/s13042-021-01429-y
[35] C. Wu, J. Zhang, C. Huang, X. Guo, Robust dynamic semi-supervised picture fuzzy clustering with KL divergence
and local information, Cognitive Computation, 14(3) (2022), 970-988. https://doi.org/10.1007/
s12559-021-09988-6
[36] L. Yuan, X. Yang, Z. Xing, Y. Ma, Latent multi-view semi-nonnegative matrix factorization with block diagonal
constraint, Axioms, 11(12) (2022), 722. https://doi.org/10.3390/axioms11120722
[37] L. Zadeh, Fuzzy sets, Information and Control, 8(3) (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)
90241-X
[38] K. Zhang, P. Feng, G. Zhang, T. Xie, J. Hou, X. He, The Bi-level optimal configuration model of the CCHP
system based on the improved FCM clustering algorithm, Processes, 9(6) (2021), 907. https://doi.org/10.3390/
pr9060907
[39] R. Zhang, X. Li, H. Zhang, F. Nie, Deep fuzzy k-means with adaptive loss and entropy regularization, IEEE
Transactions on Fuzzy Systems, 28(11) (2019), 2814-2824. https://doi.org/10.1109/TFUZZ.2019.2945232
[40] Y. Zhang, Y. Ma, X. Yang, Multi-label feature selection based on logistic regression and manifold learning, Applied
Intelligence, 52 (2022), 9256-9273. https://doi.org/10.1007/s10489-021-03008-8
[41] X. Zheng, C. Tang, X. Liu, E. Zhu, Multi-view clustering via matrix factorization assisted k-means, Neurocomputing,
534 (2023), 45-54. https://doi.org/10.1016/j.neucom.2023.03.004
[42] J. Zhou, W. Pedrycz, X. Yue, C. Gao, Z. Lai, J. Wan, Projected fuzzy c-means clustering with locality preservation,
Pattern Recognition, 113 (2021), 107748. https://doi.org/10.1016/j.patcog.2020.107748
Iranian Journal of Fuzzy Systems
Volume 21, Issue 3
May and June 2024
Pages 155-175

Files

Share

How to cite

Statistics