Constrained clustering with weak label prior
Jing ZHANG, Ruidong FAN, Hong TAO, Jiacheng JIANG, Chenping HOU
Constrained clustering with weak label prior
Clustering is widely exploited in data mining. It has been proved that embedding weak label prior into clustering is effective to promote its performance. Previous researches mainly focus on only one type of prior. However, in many real scenarios, two kinds of weak label prior information, e.g., pairwise constraints and cluster ratio, are easily obtained or already available. How to incorporate them to improve clustering performance is important but rarely studied. We propose a novel constrained Clustering with Weak Label Prior method (CWLP), which is an integrated framework. Within the unified spectral clustering model, the pairwise constraints are employed as a regularizer in spectral embedding and label proportion is added as a constraint in spectral rotation. To approximate a variant of the embedding matrix more precisely, we replace a cluster indicator matrix with its scaled version. Instead of fixing an initial similarity matrix, we propose a new similarity matrix that is more suitable for deriving clustering results. Except for the theoretical convergence and computational complexity analyses, we validate the effectiveness of CWLP through several benchmark datasets, together with its ability to discriminate suspected breast cancer patients from healthy controls. The experimental evaluation illustrates the superiority of our proposed approach.
clustering / weak label prior / cluster ratio / pairwise constraints
Jing Zhang is a PhD candidate at the National University of Defense Technology, China. She received the BS degree from Sichuan Normal University, China in 2017 and the MS degree from the National University of Defense Technology, China in 2019. Her research interests include machine learning, system science, and data mining
Ruidong Fan is a PhD candidate at the National University of Defense Technology, China. He received the BS degree from Lanzhou University, China in 2018 and the MS degree from the National University of Defense Technology, China in 2020. His research interests include data mining, optimization, and transfer learning
Hong Tao received the PhD degree from the National University of Defense Technology, China in 2019. She is currently a Lecturer with the College of Liberal Arts and Science of the same university. Her research interests include machine learning, system science, and data mining
Jiacheng Jiang received the MS degree from the National University of Defense Technology in 2020, China. He received the BS degree with the same university in 2018. His research interests include data mining and machine learning
Chenping Hou received the PhD degree from the National University of Defense Technology, China in 2009. He is currently a full Professor with the Department of Systems Science of the same university. He has authored 80+ peer-reviewed papers in journals and conferences, such as the IEEE TPAMI, TNNLS/TNN, IEEE TSMCB/TCB, IEEE TIP, the IJCAI, and AAAI. His current research interests include machine learning, data mining, and computer vision
[1] |
Jain A K, Murty M N, Flynn P J . Data clustering: a review. ACM Computing Surveys, 1999, 31( 3): 264–323
|
[2] |
Voss J, Belkin M, Rademacher L. The hidden convexity of spectral clustering. In: Proceedings of the 30th AAAI Conference on Artificial Intelligence. 2016, 2108−2114
|
[3] |
Elhamifar E, Vidal R . Sparse subspace clustering: algorithm, theory, and applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35( 11): 2765–2781
|
[4] |
Kim S, Yoo C D, Nowozin S, Kohli P . Image segmentation using higher-order correlation clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2014, 36( 9): 1761–1774
|
[5] |
Mittal H, Pandey A C, Saraswat M, Kumar S, Pal R, Modwel G . A comprehensive survey of image segmentation: clustering methods, performance parameters, and benchmark datasets. Multimedia Tools and Applications, 2022, 81( 24): 35001–35026
|
[6] |
Shi J, Malik J . Normalized cuts and image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22( 8): 888–905
|
[7] |
Zhang J, Zhou K, Luximon Y, Li P, Iftikhar H . 3D-guided facial shape clustering and analysis. Multimedia Tools and Applications, 2022, 81( 6): 8785–8806
|
[8] |
Liu H, Liu T, Wu J, Tao D, Fu Y. Spectral ensemble clustering. In: Proceedings of the 21st ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. 2015, 715−724
|
[9] |
Hartigan J A, Wong M A . A k-means clustering algorithm. Journal of the Royal Statistical Society Series C: Applied Statistics, 1979, 28( 1): 100–108
|
[10] |
Kanungo T, Mount D M, Netanyahu N S, Piatko C D, Silverman R, Wu A . An efficient k-means clustering algorithm: analysis and implementation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2002, 24( 7): 881–892
|
[11] |
Johnson S C . Hierarchical clustering schemes. Psychometrika, 1967, 32( 3): 241–254
|
[12] |
Levin M S. Towards hierarchical clustering. In: Proceedings of the 2nd international conference on Computer Science: theory and applications. 2007, 205−215
|
[13] |
Von Luxburg U . A tutorial on spectral clustering. Statistics and Computing, 2007, 17( 4): 395–416
|
[14] |
Lu C, Yan S, Lin Z . Convex sparse spectral clustering: single-view to multi-view. IEEE Transactions on Image Processing, 2016, 25( 6): 2833–2843
|
[15] |
Khan A A, Mohanty S K . A fast spectral clustering technique using MST based proximity graph for diversified datasets. Information Sciences, 2022, 609: 1113–1131
|
[16] |
Lu C, Feng J, Lin Z, Mei T, Yan S . Subspace clustering by block diagonal representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2019, 41( 2): 487–501
|
[17] |
Gao H, Nie F, Li X, Huang H. Multi-view subspace clustering. In: Proceedings of 2015 IEEE International Conference on Computer Vision. 2015, 4238−4246
|
[18] |
Dong W, Wu X J, Kittler J . Subspace clustering via joint ℓ1,2 and ℓ2,1 norms. Information Sciences, 2022, 612: 675–686
|
[19] |
Parmar M, Wang D, Zhang X, Tan A H, Miao C, Jiang J, Zhou Y . Redpc: a residual error-based density peak clustering algorithm. Neurocomputing, 2019, 348: 82–96
|
[20] |
Parmar M D, Pang W, Hao D, Jiang J, Liupu W, Wang L, Zhou Y. FREDPC: a feasible residual error-based density peak clustering algorithm with the fragment merging strategy. IEEE Access, 2019, 7: 89789−89804
|
[21] |
Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y . Robust recovery of subspace structures by low-rank representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013, 35( 1): 171–184
|
[22] |
Tao Z, Liu H, Li S, Ding Z, Fu Y . Robust spectral ensemble clustering via rank minimization. ACM Transactions on Knowledge Discovery from Data, 2019, 13( 1): 1–25
|
[23] |
Zhu Y, Kwok J T, Zhou Z H . Multi-label learning with global and local label correlation. IEEE Transactions on Knowledge and Data Engineering, 2018, 30( 6): 1081–1094
|
[24] |
Saha S, Alok A K, Ekbal A . Brain image segmentation using semi-supervised clustering. Expert Systems with Applications, 2016, 52: 50–63
|
[25] |
Śmieja M, Myronov O, Tabor J . Semi-supervised discriminative clustering with graph regularization. Knowledge-Based Systems, 2018, 151: 24–36
|
[26] |
Nie F, Zhang H, Wang R, Li X. Semi-supervised clustering via pairwise constrained optimal graph. In: Proceedings of the 29th International Joint Conference on Artificial Intelligence. 2021, 437
|
[27] |
Zhu Z, Gao Q . Semi-supervised clustering via cannot link relationship for multiview data. IEEE Transactions on Circuits and Systems for Video Technology, 2022, 32( 12): 8744–8755
|
[28] |
Wang X, Qian B, Davidson I . On constrained spectral clustering and its applications. Data Mining and Knowledge Discovery, 2014, 28( 1): 1–30
|
[29] |
Chen L M, Xiu B X, Ding Z Y . Multiple weak supervision for short text classification. Applied Intelligence, 2022, 52( 8): 9101–9116
|
[30] |
Rasti R, Teshnehlab M, Phung S L . Breast cancer diagnosis in DCE-MRI using mixture ensemble of convolutional neural networks. Pattern Recognition, 2017, 72: 381–390
|
[31] |
Lai K T, Yu F X, Chen M S, Chang S F. Video event detection by inferring temporal instance labels. In: Proceedings of 2014 IEEE Conference on Computer Vision and Pattern Recognition. 2014, 2243−2250
|
[32] |
Poyiadzi R, Santos-Rodríguez R, Twomey N. Label propagation for learning with label proportions. In: Proceedings of the 28th IEEE International Workshop on Machine Learning for Signal Processing. 2018, 1−6
|
[33] |
Sun N, Luo T, Zhuge W, Tao H, Hou C, Hu D . Semi-supervised learning with label proportion. IEEE Transactions on Knowledge and Data Engineering, 2023, 35( 1): 877–890
|
[34] |
Ng A, Jordan M, Weiss Y. On spectral clustering: Analysis and an algorithm. In: Proceedings of the 14th International Conference on Neural Information Processing Systems. 2011
|
[35] |
Zhang X, You Q. An improved spectral clustering algorithm based on random walk. Frontiers of Computer Science in China, 2011, 5(3): 268–278
|
[36] |
Yu S X, Shi J. Multiclass spectral clustering. In: Proceedings of the 9th IEEE International Conference on Computer Vision. 2003, 313−313
|
[37] |
Liu W, He J, Chang S. Large graph construction for scalable semi-supervised learning. In: Proceedings of the 27th International Conference on International Conference on Machine Learning. 2010, 679−686
|
[38] |
Huang J, Nie F, Huang H. Spectral rotation versus k-means in spectral clustering. In: Proceedings of the 27th AAAI Conference on Artificial Intelligence. 2013, 431−437
|
[39] |
Nie F P, Wang X Q, Jordan M, Huang H. The constrained laplacian rank algorithm for graph-based clustering. In: Proceedings of the 37th AAAI Conference on Artificial Intelligence. 2016, 1969−1976
|
[40] |
Pang Y, Xie J, Nie F, Li X . Spectral clustering by joint spectral embedding and spectral rotation. IEEE Transactions on Cybernetics, 2020, 50( 1): 247–258
|
[41] |
Nie F, Zhang R, Li X . A generalized power iteration method for solving quadratic problem on the stiefel manifold. Science China Information Sciences, 2017, 60( 11): 112101
|
[42] |
Zhu X, Ghahramani Z. Learning from labeled and unlabeled data with label propagation. Pittsburgh: Carnegie Mellon University, 2002
|
[43] |
Hagen L, Kahng A B. New spectral methods for ratio cut partitioning and clustering. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 1992, 11(9): 1074−1085
|
[44] |
MacQueen J. Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability. 1967, 281−297
|
[45] |
Van Craenendonck T, Dumančic S, Blockeel H. COBRA: a fast and simple method for active clustering with pairwise constraints. In: Proceedings of the 26th International Joint Conference on Artificial Intelligence. 2018
|
[46] |
Nie F, Zhu W, Li X . Unsupervised large graph embedding based on balanced and hierarchical k-means. IEEE Transactions on Knowledge and Data Engineering, 2020, 34( 4): 2008–2019
|
[47] |
Zhu J, Tao L, Yang H, Nie F . Unsupervised optimized bipartite graph embedding. IEEE Transactions on Knowledge and Data Engineering, 2023, 35( 3): 3224–3238
|
[48] |
Wang J, Ma Z, Nie F, Li X. Efficient discrete clustering with anchor graph. IEEE Transactions on Neural Networks and Learning Systems, 2023, 1–9, doi:
|
[49] |
Zhou D, Bousquet O, Lal T N, Weston J, Schölkopf B. Learning with local and global consistency. In: Proceedings of the 16th International Conference on Neural Information Processing Systems. 2003, 321−328
|
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