Abstract
Cluster analysis is a method of unsupervised learning technology which is playing a more and more important role in data mining. However, one basic and difficult question for clustering is how to gain the number of clusters automatically. The traditional solution for the problem is to introduce a single validity index which may lead to failure because the index is bias to some specific condition. On the other hand, most of the existing clustering algorithms are based on hard partitioning which can not reflect the uncertainty of the data in the clustering process. To combat these drawbacks, this paper proposes a method to determine the number of clusters automatically based on three-way decision and multi-validity index which includes three parts: (1) the k-means clustering algorithm is devised to obtain the three-way clustering results; (2) multi-validity indexes are employed to evaluate the results and each evaluated result is weighed according to the mean similarity between the corresponding clustering result and the others based on the idea of the median partition in clustering ensemble; and (3) the comprehensive evaluation results are sorted and the best ranked k value is selected as the optional number of clusters. The experimental results show that the proposed method is better than the single evaluation method used in the fusion at determining the number of clusters automatically.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Azimi, R., Ghayekhloo, M., Ghofrani, M., et al.: A novel clustering algorithm based on data transformation approaches. Expert Syst. Appl. Int. J. 76(C), 59–70 (2017)
Chen, H.P., Shen, X.J., Lv, Y.D.: A novel automatic fuzzy clustering algorithm based on soft partition and membership information. Neurocomputing 236, 104–112 (2016)
Cristofor, D., Simovici, D.: Finding median partitions using information-theoretical-based genetic algorithms. J. Univers. Comput. Sci. 8(2), 153–172 (2002)
Gionis, A., Mannila, H., Tsaparas, P.: Clustering aggregation. In: International Conference on Data Engineering, 2005, ICDE 2005. Proceedings. IEEE, pp. 341–352 (2005)
Huang, D., Wang, C., Lai, J., et al.: Clustering ensemble by decision weighting. JCAAI Trans. Intell. Syst. 11(3), 418–424 (2016)
Jaskowiak, P.A., Moulavi, D., Furtado, A.C.S.: On strategies for building effective ensembles of relative clustering validity criteria. Knowl. Inf. Syst. 47(2), 329–354 (2016)
Ling, H.L., Wu, J.S., Zhou, Y., et al.: How many clusters? A robust PSO-based local density model. Neurocomputing 207(C), 264–275 (2016)
Mok, P.Y., Huang, H.Q., Kwok, Y.L.: A robust adaptive clustering analysis method for automatic identification of clusters. Pattern Recogn. 45(8), 3017–3033 (2012)
Naldi, M.C., Carvalho, A.C., Campello, R.J.: Cluster ensemble selection based on relative validity indexes. Data Min. Knowl. Discov. 27(2), 259–289 (2013)
Singhbiostatistics, V.: Ensemble clustering using semidefiniteprogramming. Mach. Learn. 79(1–2), 177–200 (2008)
Vega-Pons, S., Avesani, P.: On pruning the search space for clustering ensemble problems. Neurocomputing 150(1), 481–489 (2015)
Yangtao, W., Lihui, C., Jianping, M.: Incremental fuzzy clustering with multiple medoids for large data. IEEE Trans. Fuzzy Syst. 22(6), 1557–1568 (2014)
Wu, X., Kumar, V., Quinlan, J.R.: Top 10 algorithms in data mining. Knowl. Inf. Syst. 14(1), 1–37 (2007)
Xie, X.L., Beni, G.: A validity measure for fuzzy clustering. IEEE Trans. Pami 13(13), 841–847 (1991)
Yao, Y.Y.: Three-way decisions with probabilistic rough sets. Inf. Sci. 180(3), 341–353 (2010)
Yu, H., Liu, Z., Wang, G.: An automatic method to determine the number of clusters using decision-theoretic rough set. Int. J. Approximate Reasoning 55(1), 101–115 (2014)
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61533020, 61751312 and 61379114.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this paper
Cite this paper
Sun, N., Yu, H. (2018). A Method to Determine the Number of Clusters Based on Multi-validity Index. In: Nguyen, H., Ha, QT., Li, T., Przybyła-Kasperek, M. (eds) Rough Sets. IJCRS 2018. Lecture Notes in Computer Science(), vol 11103. Springer, Cham. https://doi.org/10.1007/978-3-319-99368-3_33
Download citation
DOI: https://doi.org/10.1007/978-3-319-99368-3_33
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-99367-6
Online ISBN: 978-3-319-99368-3
eBook Packages: Computer ScienceComputer Science (R0)