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THEORETICAL ANALYSIS OF PICTURE FUZZY CLUSTERING: CONVERGENCE AND PROPERTY

Pham Thi Minh Phuong, Pham Huy Thong, Le Hoang Son

Abstract


Recently, picture fuzzy clustering (FC-PFS) has been introduced as a new computational intelligence tool for various problems in knowledge discovery and pattern recognition. However, an important question that was lacked in the related researches is examination of mathematical properties behind the picture fuzzy clustering algorithm such as the convergence, the boundary or the convergence rate, etc. In this paper, we will prove that FC-PFS converges to at least one local minimum. The similarities and differences between this algorithm and other clustering methods are compared. Analysis on the loss function is also considered.


Keywords


Convergence analysis, picture fuzzy sets, picture fuzzy clustering.

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DOI: https://doi.org/10.15625/1813-9663/34/1/12725

Journal of Computer Science and Cybernetics ISSN: 1813-9663

Published by Vietnam Academy of Science and Technology