Abstract
Clustering is one of the most fundamental techniques in statistic and machine learning. Due to the simplicity and efficiency, the most frequently used clustering method is the k-means algorithm. In the past decades, k-means and its various extensions have been proposed and successfully applied in data mining practical problems. However, previous clustering methods are typically designed in a single layer formulation. Thus the mapping between the low-dimensional representation obtained by these methods and the original data may contain rather complex hierarchical information. In this paper, a novel deep k-means model is proposed to learn such hidden representations with respect to different implicit lower-level characteristics. By utilizing the deep structure to conduct k-means hierarchically, the hierarchical semantics of data is learned in a layerwise way. The data points from same class are gathered closer layer by layer, which is beneficial for the subsequent learning task. Experiments on benchmark data sets are performed to illustrate the effectiveness of our method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For simplicity, the layer size (dimensionalities) of layer 1 to layer r is denoted as [\(k_1 \cdots k_r\)] in the experiments.
- 2.
References
Ault, S.V., Perez, R.J., Kimble, C.A., Wang, J.: On speech recognition algorithms. Int. J. Mach. Learn. Comput. 8(6) (2018)
Badea, L.: Clustering and metaclustering with nonnegative matrix decompositions. In: Gama, J., Camacho, R., Brazdil, P.B., Jorge, A.M., Torgo, L. (eds.) ECML 2005. LNCS (LNAI), vol. 3720, pp. 10–22. Springer, Heidelberg (2005). https://doi.org/10.1007/11564096_7
Bengio, Y.: Learning deep architectures for AI. Found. Trends® in Mach. Learn. 2(1), 1–127 (2009)
Boyd, S., Parikh, N., Chu, E., Peleato, B., Eckstein, J., et al.: Distributed optimization and statistical learning via the alternating direction method of multipliers. Found. Trends® Mach. Learn. 3(1), 1–122 (2011)
Buchta, C., Kober, M., Feinerer, I., Hornik, K.: Spherical k-means clustering. J. Stat. Softw. 50(10), 1–22 (2012)
Ding, C., He, X.: K-means clustering via principal component analysis. In: Proceedings of the Twenty-First International Conference on Machine Learning, pp. 29–37 (2004)
Ding, C., Li, T., Jordan, M.I.: Convex and semi-nonnegative matrix factorizations. IEEE Trans. Pattern Anal. Mach. Intell. 32(1), 45–55 (2010)
Ding, C., Li, T., Peng, W., Park, H.: Orthogonal nonnegative matrix t-factorizations for clustering. In: Proceedings of the 12th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 126–135 (2006)
Gokcay, E., Principe, J.C.: Information theoretic clustering. IEEE Trans. Pattern Anal. Mach. Intell. 24(2), 158–171 (2002)
Gönen, M., Margolin, A.A.: Localized data fusion for kernel k-means clustering with application to cancer biology. In: Advances in Neural Information Processing Systems,. pp. 1305–1313 (2014)
Hou, C., Nie, F., Yi, D., Tao, D.: Discriminative embedded clustering: a framework for grouping high-dimensional data. IEEE Trans. Neural Netw. Learn. Syst. 26(6), 1287–1299 (2015)
Huang, S., Kang, Z., Xu, Z.: Self-weighted multi-view clustering with soft capped norm. Knowl. Based Syst. 158, 1–8 (2018)
Huang, S., Ren, Y., Xu, Z.: Robust multi-view data clustering with multi-view capped-norm k-means. Neurocomputing 311, 197–208 (2018)
Huang, S., Wang, H., Li, T., Li, T., Xu, Z.: Robust graph regularized nonnegative matrix factorization for clustering. Data Min. Knowl. Disc. 32(2), 483–503 (2018)
Huang, S., Xu, Z., Kang, Z., Ren, Y.: Regularized nonnegative matrix factorization with adaptive local structure learning. Neurocomputing 382, 196–209 (2020)
Huang, S., Xu, Z., Lv, J.: Adaptive local structure learning for document co-clustering. Knowl.-Based Syst. 148, 74–84 (2018)
Huang, S., Xu, Z., Wang, F.: Nonnegative matrix factorization with adaptive neighbors. In: International Joint Conference on Neural Networks, pp. 486–493 (2017)
Huang, S., Zhao, P., Ren, Y., Li, T., Xu, Z.: Self-paced and soft-weighted nonnegative matrix factorization for data representation. Knowl.-Based Syst. 164, 29–37 (2018)
Kang, Z., Peng, C., Cheng, Q.: Kernel-driven similarity learning. Neurocomputing 267, 210–219 (2017)
Kang, Z., et al.: Multi-graph fusion for multi-view spectral clustering. Knowl. Based Syst. 189, 105102 (2020)
Kang, Z., Wen, L., Chen, W., Xu, Z.: Low-rank kernel learning for graph-based clustering. Knowl.-Based Syst. 163, 510–517 (2019)
Kang, Z., Xu, H., Wang, B., Zhu, H., Xu, Z.: Clustering with similarity preserving. Neurocomputing 365, 211–218 (2019)
Kang, Z., et al.: Partition level multiview subspace clustering. Neural Netw. 122, 279–288 (2020)
Kong, D., Ding, C., Huang, H.: Robust nonnegative matrix factorization using l21-norm. In: Proceedings of the 20th ACM International Conference on Information and Knowledge Management, pp. 673–682. ACM (2011)
Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: Advances in Neural Information Processing Systems, vol. 13, pp. 556–562 (2001)
Macqueen, J.: Some methods for classification and analysis of multivariate observations. In: Proceedings of Berkeley Symposium on Mathematical Statistics and Probability, pp. 281–297 (1967)
Newling, J., Fleuret, F.: Fast k-means with accurate bounds. In: International Conference on Machine Learning, pp. 936–944 (2016)
Newling, J., Fleuret, F.: Nested mini-batch k-means. In: Advances in Neural Information Processing Systems, pp. 1352–1360 (2016)
Ng, A.Y., Jordan, M.I., Weiss, Y.: On spectral clustering: analysis and an algorithm. In: Advances in Neural Information Processing Systems, pp. 849–856 (2002)
Ren, Y., Domeniconi, C., Zhang, G., Yu, G.: Weighted-object ensemble clustering: methods and analysis. Knowl. Inf. Syst. 51(2), 661–689 (2017)
Ren, Y., Hu, K., Dai, X., Pan, L., Hoi, S.C., Xu, Z.: Semi-supervised deep embedded clustering. Neurocomputing 325, 121–130 (2019)
Ren, Y., Huang, S., Zhao, P., Han, M., Xu, Z.: Self-paced and auto-weighted multi-view clustering. Neurocomputing 383, 248–256 (2020)
Ren, Y., Kamath, U., Domeniconi, C., Xu, Z.: Parallel boosted clustering. Neurocomputing 351, 87–100 (2019)
Ren, Y., Que, X., Yao, D., Xu, Z.: Self-paced multi-task clustering. Neurocomputing 350, 212–220 (2019)
Trigeorgis, G., Bousmalis, K., Zafeiriou, S., Schuller, B.W.: A deep matrix factorization method for learning attribute representations. IEEE Trans. Pattern Anal. Mach. Intell. 39(3), 417–429 (2017)
Tunali, V., Bilgin, T., Camurcu, A.: An improved clustering algorithm for text mining: multi-cluster spherical k-means. Int. Arab J. Inf. Technol. 13(1), 12–19 (2016)
Wang, J., et al.: Enhancing multiphoton upconversion through energy clustering at sublattice level. Nat. Mater. 13(2), 157 (2014)
Wang, L., Pan, C.: Robust level set image segmentation via a local correntropy-based k-means clustering. Pattern Recogn. 47(5), 1917–1925 (2014)
Wu, X., et al.: Top 10 algorithms in data mining. Knowl. Inf. Syst. 14(1), 1–37 (2008)
Acknowledgments
This work was partially supported by the National Key Research and Development Program of China under Contract 2017YFB1002201, the National Natural Science Fund for Distinguished Young Scholar under Grant 61625204, the State Key Program of the National Science Foundation of China under Grant 61836006, and the Fundamental Research Funds for the Central Universities under Grant 1082204112364.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Huang, S., Kang, Z., Xu, Z. (2020). Deep K-Means: A Simple and Effective Method for Data Clustering. In: Zhang, H., Zhang, Z., Wu, Z., Hao, T. (eds) Neural Computing for Advanced Applications. NCAA 2020. Communications in Computer and Information Science, vol 1265. Springer, Singapore. https://doi.org/10.1007/978-981-15-7670-6_23
Download citation
DOI: https://doi.org/10.1007/978-981-15-7670-6_23
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-7669-0
Online ISBN: 978-981-15-7670-6
eBook Packages: Computer ScienceComputer Science (R0)