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Clustering method based on the elastic energy functional of directed signed weighted graphs

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  • Tselykh, Alexander
  • Vasilev, Vladislav
  • Tselykh, Larisa

Abstract

This article proposes a new method of clustering based on minimizing the elastic energy functional (EEF) of directed weighted signed graphs. The new method has three distinctive features: the weights on the edges of the graph are set by the original model of the system (fuzzy cognitive map), and each weight represents a causal relationship between the graph vertices (system factors); a clearly formalized criterion for division into clusters; and the order of the vertices generated by the algorithm reflects the ratio of intra-cluster and extra-cluster energy. The proposed functional of the elastic energy reflects the nature of the factor relationship in a socio-economic system. Minimization of the functional is monotonic and does not require user intervention. The algorithm is computationally efficient.

Suggested Citation

  • Tselykh, Alexander & Vasilev, Vladislav & Tselykh, Larisa, 2019. "Clustering method based on the elastic energy functional of directed signed weighted graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 392-407.
    • Handle: RePEc:eee:phsmap:v:523:y:2019:i:c:p:392-407
    DOI: 10.1016/j.physa.2019.02.031
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    References listed on IDEAS

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    1. Yang, Bo & He, He & Hu, Xiaoming, 2017. "Detecting community structure in networks via consensus dynamics and spatial transformation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 156-170.
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    3. Ferreira, Fernando A.F. & Jalali, Marjan S. & Ferreira, João J.M., 2016. "Integrating qualitative comparative analysis (QCA) and fuzzy cognitive maps (FCM) to enhance the selection of independent variables," Journal of Business Research, Elsevier, vol. 69(4), pages 1471-1478.
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