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A necessary condition about the optimum partition on a finite set of samples and its application to clustering analysis

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Abstract

This paper presents another necessary condition about the optimum partition on a finite set of samples. From this condition, a correspondinggeneralized sequential hard k-means (GSHKM) clustering algorithm is built and many well-known clustering algorithms are found to be included in it. Under some assumptions the well-known MacQueen’s SHKM (Sequential Hard K-Means) algorithm, FSCL (Frequency Sensitive Competitive Learning) algorithm and RPCL (Rival Penalized Competitive Learning) algorithm are derived. It is shown that FSCL in fact still belongs to the kind of GSHKM clustering algorithm and is more suitable for producing means of K-partition of sample data, which is illustrated by numerical experiment. Meanwhile, some improvements on these algorithms are also given.

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Authors and Affiliations

  1. Institute of Computing Technology, The Chinese Academy of Sciences, 100080, Beijing

    Ye Shiwei & Shi Zhongzhi

Authors
  1. Ye Shiwei
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  2. Shi Zhongzhi
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Additional information

Ye Shiwei is a Ph.D. candidate at Institute of Computing Technology. His research interests include artificial neural networks, wavelets analysis and image processing.

Shi Zhongzhi is a Professor at Institute of Computing Technology. His research interests include artificial neural networks and artificial life.

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Ye, S., Shi, Z. A necessary condition about the optimum partition on a finite set of samples and its application to clustering analysis. J. of Comput. Sci. & Technol. 10, 545–556 (1995). https://doi.org/10.1007/BF02943512

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  • DOI: https://doi.org/10.1007/BF02943512

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