Robust local-coordinate non-negative matrix factorization with adaptive graph for robust clustering. (English) Zbl 07825491
Summary: With its unique geometric properties, non-negative matrix factorization (NMF) has become one of the widely used clustering methods in the field of data mining. Regrettably, most existing NMF methods are sensitive to super-noise (super-outliers). This paper proposes a novel robust clustering method to address this issue. Based on the \(Hx\) loss function, this method establishes a novel robust adaptive local structure learning strategy, reducing the interference of noise (outliers) on data reconstruction and space exploration. In addition, a new orthogonal regularization term is incorporated into the model, ensuring the orthogonality of the factor matrix and enhancing the discriminant ability. Finally, we develop an efficient algorithm to solve the resultant model and analyze its convergence from theoretical and experimental aspects. Experimental results on random synthetic data sets and benchmark databases demonstrate that the proposed method outperforms the existing robust NMF methods in terms of spatial structure learning, discriminant power, and robustness.
MSC:
| 68T09 | Computational aspects of data analysis and big data |
| 15A23 | Factorization of matrices |
| 62H30 | Classification and discrimination; cluster analysis (statistical aspects) |
Keywords:
non-negative matrix factorization; robust adaptive local structure learning strategy; robust model; clusteringReferences:
| [1] | Liu, X., Incomplete multiple kernel alignment maximization for clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence (2021), 1-1 |
| [2] | Wang, R.; Wang, C.; Liu, G., A novel graph clustering method with a greedy heuristic search algorithm for mining protein complexes from dynamic and static ppi networks, Information Sciences, 522, 275-298 (2020) · Zbl 1460.92083 |
| [3] | X. Liu, L. Liu, Q. Liao, S. Wang, Y. Zhang, W. Tu, C. Tang, J. Liu, E. Zhu, One pass late fusion multi-view clustering, in: Proceedings of the 38th International Conference on Machine Learning, Vol. 139, 2021, pp. 6850-6859. |
| [4] | Fu, L.; Yang, J.; Chen, C.; Zhang, C., Low-rank tensor approximation with local structure for multi-view intrinsic subspace clustering, Information Sciences, 606, 877-891 (2022) · Zbl 07814176 |
| [5] | Liu, J.; Liu, X.; Yang, Y.; Wang, S.; Zhou, S., Hierarchical multiple kernel clustering, (Proceedings of the Thirty-fifth AAAI Conference on Artificial Intelligence (2021)), (AAAI-21) |
| [6] | Zhang, Y.; Wang, H.; Yang, Y.; Zhou, W.; Li, T.; Ouyang, X.; Chen, H., Deep matrix factorization with knowledge transfer for lifelong clustering and semi-supervised clustering, Information Sciences, 570, 795-814 (2021) · Zbl 1531.68108 |
| [7] | Yao, S.; Hu, C.; Wang, T.; Cui, X., Autoencoder-like semi-nmf multiple clustering, Information Sciences, 572, 331-342 (2021) |
| [8] | Lee, D. D.; Seung, H. S., Learning the parts of objects by non-negative matrix factorization, Nature, 401, 6755, 788-791 (1999) · Zbl 1369.68285 |
| [9] | Wang, Q.; Chen, M.; Nie, F.; Li, X., Detecting coherent groups in crowd scenes by multiview clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence, 42, 1, 46-58 (2020) |
| [10] | Wan, Z.; Tang, J.; Ren, L.; Xiao, Y.; Liu, S., Optimization techniques to deeply mine the transcriptomic profile of the sub-genomes in hybrid fish lineage, Frontiers in Genetics, 10, 911 (2019) |
| [11] | Wang, D.; Li, T.; Deng, P.; Wang, H.; Zhang, P., Dual graph-regularized sparse concept factorization for clustering, Information Sciences, 607, 1074-1088 (2022) · Zbl 1542.90211 |
| [12] | Tang, J.; Wan, Z., Orthogonal dual graph-regularized nonnegative matrix factorization for co-clustering, Journal of Scientific Computing, 87, 3, 1-37 (2021) · Zbl 1466.62359 |
| [13] | Ding, C.; Li, T.; Peng, W.; Park, H., Orthogonal nonnegative matrix t-factorizations for clustering, (Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2006)), 126-135 |
| [14] | He, P.; Xu, X.; Ding, J.; Fan, B., Low-rank nonnegative matrix factorization on stiefel manifold, Information Sciences, 514, 131-148 (2020) · Zbl 1462.62773 |
| [15] | Xia, H.; Shao, S.; Hu, C.; Zhang, R.; Qiu, T.; Xiao, F., Robust clustering model based on attention mechanism and graph convolutional network, IEEE Transactions on Knowledge and Data Engineering (2022), 1-1 |
| [16] | Zhou, J.; Pedrycz, W.; Wan, J.; Gao, C.; Lai, Z.-H.; Yue, X., Low-rank linear embedding for robust clustering, IEEE Transactions on Knowledge and Data Engineering (2022), 1-1 |
| [17] | Zhen, L.; Peng, D.; Wang, W.; Yao, X., Kernel truncated regression representation for robust subspace clustering, Information Sciences, 524, 59-76 (2020) · Zbl 1458.62093 |
| [18] | Huang, S.; Xu, Z.; Kang, Z.; Ren, Y., Regularized nonnegative matrix factorization with adaptive local structure learning, Neurocomputing, 382, 196-209 (2020) |
| [19] | Wang, Q.; He, X.; Jiang, X.; Li, X., Robust bi-stochastic graph regularized matrix factorization for data clustering, IEEE Transactions on Pattern Analysis and Machine Intelligence (2020), 1-1 |
| [20] | Zhang, L.; Liu, Z.; Pu, J.; Song, B., Adaptive graph regularized nonnegative matrix factorization for data representation, Applied Intelligence, 50, 2, 438-447 (2020) |
| [21] | D. Kong, C. Ding, H. Huang, Robust nonnegative matrix factorization using ℓ_21)norm, in: Proceedings of the 20th ACM International Conference on Information and Knowledge Management, no. 10, 2011, pp. 673-682. doi:10.1145/2063576.2063676. |
| [22] | Nie, F.; Wang, X.; Huang, H., Clustering and projected clustering with adaptive neighbors, (Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining (2014)), 977-986 |
| [23] | J. Huang, F. Nie, H. Huang, C. Ding, Robust manifold nonnegative matrix factorization, ACM Trans. Knowl. Discov. Data 8 (3). doi:10.1145/2601434. |
| [24] | Nie, F.; Wang, I. J.M.; Xiaoqian, H. Huang, The constrained laplacian rank algorithm for graph-based clustering, (Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence (2016)), 1969-1976 |
| [25] | Zhou, Z.; Si, G.; Sun, H.; Qu, K.; Hou, W., A robust clustering algorithm based on the identification of core points and knn kernel density estimation, Expert Systems with Applications, 195, Article 116573 pp. (2022) |
| [26] | P. Zhou, L. Du, Y.-D. Shen, X. Li, Tri-level robust clustering ensemble with multiple graph learning, in: Thirty-Fifth AAAI Conference on Artificial Intelligence, 2021, pp. 11125-11133. |
| [27] | Liu, H.; Yang, Z.; Yang, J.; Wu, Z.; Li, X., Local coordinate concept factorization for image representation, IEEE Transactions on Neural Networks and Learning Systems, 25, 6, 1071-1082 (2014) |
| [28] | Yoo, J.; Choi, S., Orthogonal nonnegative matrix tri-factorization for co-clustering: Multiplicative updates on stiefel manifolds, Information Processing and Management, 46, 5, 559-570 (2010) |
| [29] | He, X.; Yan, S.; Hu, Y.; Niyogi, P.; Zhang, H.-J., Face recognition using laplacianfaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 3, 328-340 (2005) |
| [30] | Huang, Q.; Yin, X.; Chen, S.; Wang, Y.; Chen, B., Robust nonnegative matrix factorization with structure regularization, Neurocomputing, 412, 72-90 (2020) |
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