Soft Computing

, Volume 22, Issue 3, pp 861–872 | Cite as

Self-adaptive kernel K-means algorithm based on the shuffled frog leaping algorithm

  • Shuyan Fan
  • Shifei DingEmail author
  • Yu Xue
Methodologies and Application


Kernel K-means can handle nonlinearly separate datasets by mapping the input datasets into a high-dimensional feature space. The kernel matrix reflects the inner structure of data, so it is a key to construct an appropriate kernel matrix. However, many kernel-based methods need to be set kernel parameter artificially in advance. It is difficult to set an appropriate kernel parameter for each dataset artificially, which limits the performance of the kernel K-means algorithm to some extent. It is necessary to design a method which can adjust the kernel parameter automatically according to the data structure. In addition, the number of clusters also needs to be set. To overcome these challenges, this paper proposed a self-adaptive kernel K-means based on the shuffled frog leaping algorithm, which regard the kernel parameter and the number of clusters as the position information of the frog. We designed a clustering validity index named Between-Within Proportion suitable for the kernel space (KBWP) by modifying the clustering validity index Between-Within Proportion (BWP). Treat KBWP as fitness in the shuffled frog leaping algorithm, and then do local and global optimization until the max iterations. The kernel parameter and the number of clusters corresponding to the maximum fitness are optimal. We experimentally verify our algorithm on artificial datasets and real datasets. Experimental results demonstrate the effectiveness and good performance of the proposed algorithm.


Kernel K-means Shuffled frog leaping algorithm Clustering validity index Clustering analysis 



This work is supported by the National Natural Science Foundation of China under Grant Nos. 61379101 and 61672522, the National Basic Research Program of China under Grant No. 2013CB329502, A Project Funded by the Priority Academic Program Development of Jiangsu Higer Education Institutions (PAPD), and Jiangsu Collaborative Innovation Center on Atmospheric Environment and Equipment Technology (CICAEET).

Compliance with ethical standards

Conflict of interest

Shuyan Fan declares that she has no conflict of interest. Shifei Ding declares that he has no conflict of interest. Yu Xue declares that he has no conflict of interest.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.School of Computer Science and TechnologyChina University of Mining and TechnologyXuzhouChina
  2. 2.Key Laboratory of Intelligent Information Processing, Institute of Computing TechnologyChinese Academy of SciencesBeijingChina
  3. 3.School of Computer and SoftwareNanjing University of Information Science and TechnologyNanjingChina

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