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Automatic clustering based on density peak detection using generalized extreme value distribution

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Abstract

Density peaks clustering (DPC) algorithm is able to get a satisfactory result with the help of artificial selecting the clustering centers, but such selection can be hard for a large amount of clustering tasks or the data set with a complex decision diagram. The purpose of this paper is to propose an automatic clustering approach without human intervention. Inspired by the visual selection rule of DPC, the judgment index which equals the lower value within density and distance (after normalization) is proposed for selecting the clustering centers. The judgment index approximately follows the generalized extreme value (GEV) distribution, and each clustering center’s judgment index is much higher. Hence, it is reasonable that the points are selected as clustering centers if their judgment indices are larger than the upper quantile of GEV. This proposed method is called density peaks clustering based on generalized extreme value distribution (DPC-GEV). Furthermore, taking the computational complexity into account, an alternative method based on density peak detection using Chebyshev inequality (DPC-CI) is also given. Experiments on both synthetic and real-world data sets show that DPC-GEV and DPC-CI can achieve the same accuracy as DPC on most data sets but consume much less time.

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Notes

  1. http://mlg.ucd.ie/datasets/3sources.html.

References

  • Andreeva G, Calabrese R, Osmetti SA (2016) A comparative analysis of the UK and Italian small businesses using generalised extreme value models. Eur J Oper Res 249(2):506–516

    Article  Google Scholar 

  • Banfield JD, Raftery AE (1993) Model-based Gaussian and non-Gaussian clustering. Biometrics 49:803–821

    Article  MathSciNet  MATH  Google Scholar 

  • Benson AR, Gleich DF, Leskovec J (2016) Higher-order organization of complex networks. Science 353(6295):163–166

    Article  Google Scholar 

  • Chang H, Yeung DY (2008) Robust path-based spectral clustering. Pattern Recognit 41(1):191–203

    Article  MATH  Google Scholar 

  • Chen Y, Zhao P, Li P et al (2016) Finding communities by their centers. Sci Rep 6. doi:10.1038/srep24017

  • Dikshit AMO (2015) Comparative study on projected clustering methods for hyperspectral imagery classification. Geocarto Int 31(3):1–32

    Google Scholar 

  • Du M, Ding S, Jia H (2016) Study on density peaks clustering based on k-nearest neighbors and principal component analysis. Knowl Based Syst 99:135–145

    Article  Google Scholar 

  • Ester M, Kriegel HP, Sander J et al (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. Kdd 96(34):226–231

    Google Scholar 

  • Fu L, Medico E (2007) FLAME, a novel fuzzy clustering method for the analysis of DNA microarray data. Bmc Bioinform 8(1):1–15

    Article  Google Scholar 

  • Huang Z (1997) Clustering large data sets with mixed numeric and categorical values. In: Proceedings of the 1st Pacific-Asia conference on knowledge discovery and data mining (PAKDD), pp 21–34

  • Jia S, Tang G, Zhu J et al (2016) A novel ranking-based clustering approach for hyperspectral band selection. IEEE Trans Geosci Remote Sens 54(1):88–102

    Article  Google Scholar 

  • Jiang B, Wang N (2013) Cooperative bare-bone particle swarm optimization for data clustering. Soft Comput. 18(6):1079–1091

    Article  Google Scholar 

  • Jordan MI, Mitchell TM (2015) Machine learning: trends, perspectives, and prospects. Science 349(6245):255–60

    Article  MathSciNet  MATH  Google Scholar 

  • Kao YT, Zahara E, Kao IW (2008) A hybridized approach to data clustering. Expert Syst Appl 34(3):1754–1762

    Article  Google Scholar 

  • Kaufman L, Rousseeuw PJ (1990) Finding groups in data: an introduction to cluster analysis. Wiley, New York. doi:10.2307/2532178

  • Kotz S, Nadarajah S (2000) Extreme value distributions: theory and applications. Imperial College Press London, London

    Book  MATH  Google Scholar 

  • Lagarias JC, Reeds JA, Wright MH et al (2006) Convergence properties of the Nelder–Mead simplex method in low dimensions. Siam J Optim 9(1):112–147

    Article  MathSciNet  MATH  Google Scholar 

  • Le HS, Tuan TMA (2015) Cooperative semi-supervised fuzzy clustering framework for dental X-ray image segmentation. Expert Syst Appl 46:38–393

    Google Scholar 

  • Macqueen J (1966) Some methods for classification and analysis of multivariate observations. In: Proceedings of the Berkeley symposium on mathematical, pp 281–297

  • McParland D, Gormley IC (2016) Model based clustering for mixed data: clustMD. Adv Data Anal Classif 10(2):1–15

    Article  MathSciNet  Google Scholar 

  • Murtagh F, Contreras P (2012) Algorithms for hierarchical clustering: an overview. Wiley Interdiscip Rev Data Min Knowl Discov 2(1):86–97

    Article  Google Scholar 

  • Pal NR, Pal K, Keller JM et al (2005) A possibilistic fuzzy c-means clustering algorithm. IEEE Trans. Fuzzy Syst. 13(4):517–530

    Article  Google Scholar 

  • Rodriǵuez A, Alessandro L (2014) Machine learning: clustering by fast search and find of density peaks. Science 344(6191):1492–1496

    Article  Google Scholar 

  • Rokach L (2009) A survey of clustering algorithms. In: Data mining and knowledge discovery handbook, pp 269–298

  • Sandoval CE, Raynal-Villasenor J (2008) Trivariate generalized extreme value distribution in flood frequency analysis. Hydrol Sci J 53(3):550–567

    Article  Google Scholar 

  • Soukissian TH, Tsalis C (2015) The effect of the generalized extreme value distribution parameter estimation methods in extreme wind speed prediction. Nat Hazards 78(3):1777–1809

    Article  Google Scholar 

  • Spath H (1985) Cluster dissection and analysis, theory, FORTRAN programs, examples. Ellis Horwood, Chichester

    MATH  Google Scholar 

  • Tsaparas P, Mannila H, Gionis A (2007) Clustering aggregation. Acm Trans Knowl Discov Data 1(1):341–352

    Google Scholar 

  • Vinh NX, Epps J, Bailey J (2010) Information theoretic measures for clusterings comparison: variants, properties, normalization and correction for chance. J Mach Learn Res 11(1):2837–2854

    MathSciNet  MATH  Google Scholar 

  • Wang XF, Xu Y (2015) Fast clustering using adaptive density peak detection. Stat Methods Med Res 09622802156099482015

  • Xie J, Gao H, Xie W et al (2016) Robust clustering by detecting density peaks and assigning points based on fuzzy weighted K-nearest neighbors. Inf Sci 54:19C40

    Google Scholar 

  • Xu R (2005) Survey of clustering algorithms. IEEE Trans Neural Netw 16(3):645–678

    Article  Google Scholar 

  • Xu J, Wang G, Deng W (2016) DenPEHC: density peak based efficient hierarchical clustering. Inf Sci 373(12):200–218

    Article  Google Scholar 

  • Yaqing S, Peng L, Pinghua L et al (2014) Model-based clustering for RNA-seq data. Bioinformatics 30(2):197–205

    Article  Google Scholar 

  • Zhang K (2013) Adaptive threshold background modeling algorithm based on Chebyshev inequality. Comput Sci 40(4):287–291

    MathSciNet  Google Scholar 

  • Zhang Y, Chen S, Yu G (2016) Efficient distributed density peaks for clustering large data sets in mapreduce. IEEE Trans Knowl Data Eng 28(12):3218–3230

    Article  Google Scholar 

  • Zheng YJ, Ling HF (2013) Emergency transportation planning in disaster relief supply chain management: a cooperative fuzzy optimization approach. Soft Comput 17(7):1301–1314

    Article  Google Scholar 

  • Zheng YJ, Ling HF, Chen SY et al (2014) A hybrid neuro-fuzzy network based on differential biogeography-based optimization for online population classification in earthquakes. IEEE Trans Fuzzy Syst 3(4):1–1

    Google Scholar 

  • Zheng YJ, Ling HF, Xue JY et al (2014) Population classification in fire evacuation: a multiobjective particle swarm optimization approach. IEEE Trans Evolut Comput 18(1):70–81

    Article  Google Scholar 

  • Zhou L, Hu ZC (2012) Chebyshev’s inequality for Banach-space-valued random elements. Stat Probab Lett 82(5):925C931

    MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the financial support from the National Natural Science Foundation of China (61473262, 61503340), Zhejiang Provincial Natural Science Foundation (LQ12A01022) and Educational Commission of Zhejiang Province (Y201121764).

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Authors and Affiliations

  1. College of Information Engineering, Zhejiang University of Technology, Hangzhou, 310023, China

    Jiajun Ding & Xiongxiong He

  2. Department of Applied Mathematics School of Science, Zhejiang University of Technology, Hangzhou, 310023, Zhejiang, China

    Junqing Yuan

  3. College of Education Science and Technology, Zhejiang University of Technology, Hangzhou, 310023, China

    Bo Jiang

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  1. Jiajun Ding
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Correspondence to Xiongxiong He.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by A. Di Nola.

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Ding, J., He, X., Yuan, J. et al. Automatic clustering based on density peak detection using generalized extreme value distribution. Soft Comput 22, 2777–2796 (2018). https://doi.org/10.1007/s00500-017-2748-7

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