Soft Computing

, Volume 22, Issue 9, pp 2777–2796 | Cite as

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

  • Jiajun Ding
  • Xiongxiong He
  • Junqing Yuan
  • Bo Jiang


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.


Density peak Judgment index Generalized extreme value distribution Chebyshev inequality Optimization 



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).

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

Ethical standard

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

Informed consent

Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Jiajun Ding
    • 1
  • Xiongxiong He
    • 1
  • Junqing Yuan
    • 2
  • Bo Jiang
    • 3
  1. 1.College of Information EngineeringZhejiang University of TechnologyHangzhouChina
  2. 2.Department of Applied Mathematics School of ScienceZhejiang University of TechnologyHangzhouChina
  3. 3.College of Education Science and TechnologyZhejiang University of TechnologyHangzhouChina

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