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Fuzzy weighted c-harmonic regressions clustering algorithm

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Abstract

As a well-known regression clustering algorithm, fuzzy c-regressions (FCR) has been widely studied and applied in various areas. However, FCR appears to be rather sensitive to the undesirable initialization and the presence of noise or outliers in data sets. As a modified alternative, possibilistic c-regressions (PCR) can ameliorate the problem of noise and outliers, but it depends more heavily on initial values. Besides, the number of models should be determined a priori in both algorithms. To overcome these issues, this paper proposes a generalized alternative, called fuzzy weighted c-harmonic regressions (FWCHR), in which, a dynamic-like weight term based on the distinguished feature of the harmonic average is first introduced to enhance robustness. Furthermore, FWCHR can encompass FCR and PCR if some conditions are satisfied. And then a generalized mountain method (GMM) is proposed to automatically determine the number of models and estimate the initial values, which makes the proposed FWCHR algorithm totally unsupervised. Some numerical simulations and real applications are conducted to validate the performance of our algorithms.

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Acknowledgements

The authors would like to thank the editors and the anonymous referees for their helpful comments. This work was supported by National Key Technology R & D Program of the Ministry of Science and Technology of China (2015BAA03B02) and the Key Project of Yunnan Power Grid Co. Ltd. (YNYJ2016043).

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Authors and Affiliations

  1. Key Laboratory of Energy Thermal Conversion and Control of the Ministry of Education, School of Energy and Environment, Southeast University, Nanjing, 210096, China

    Yang Zhao, Pei-hong Wang & Yi-guo Li

  2. Research Institute of Yunnan Power Grid Co. Ltd, Kunming, China

    Meng-yang Li

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  1. Yang Zhao
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  2. Pei-hong Wang
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  3. Yi-guo Li
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  4. Meng-yang Li
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Correspondence to Pei-hong Wang.

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All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Declaration of Helsinki and its later amendments or comparable ethical standards.

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Communicated by V. Loia.

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Zhao, Y., Wang, Ph., Li, Yg. et al. Fuzzy weighted c-harmonic regressions clustering algorithm. Soft Comput 22, 4595–4611 (2018). https://doi.org/10.1007/s00500-017-2642-3

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