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Comparing Different Approaches to Archetypal Analysis as a Fuzzy Clustering Tool

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Abstract

We summarize the results of an intensive simulation study carried out to compare the performance of three approaches to archetypal analysis regarded as a fuzzy clustering tool: the original approach, namely that of Cutler and Breiman (Technometrics 36(4):338–347, 1994), the Ding et al. (IEEE Trans Pattern Anal Mach Intell 32(1):45–55, 2010) proposal, and the factorized fuzzy c-means algorithm. The artificial data we use in our experiment are generated from polytopes in low-dimensional \({\mathbb {R}}^{n}\) spaces \(\left( 2\le n\le 7\right) \), and comprise a diversity of cluster contexts. The simulation results show that the original proposal is generally a more accurate method to uncover the cluster structure hidden in the data and to reproduce the data themselves. However, this supremacy, if any, is not clear for the data generated from real life problems, and devoted to unsupervised clustering problems.

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Notes

  1. A special session entitled ’SS_37: Matrix Factorization for Fuzzy Clustering and Related Approaches’ took place at 2017 IEEE International Conference on Fuzzy Systems, in Naples, Italy: https://www.fuzzieee2017.org/specialSessions.php.

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Acknowledgements

The author expresses his gratitude to two anonymous reviewers for their many suggestions, careful reading and helpful comments on the earlier version of this manuscript. This work was supported by Fundação para a Ciência e a Tecnologia (FCT), Grant UIDB/00315/2020.

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  1. Instituto Universitário de Lisboa (ISCTE-IUL), Business Research Unit (BRU-IUL), Lisboa, Portugal

    Abdul Suleman

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Suleman, A. Comparing Different Approaches to Archetypal Analysis as a Fuzzy Clustering Tool. Int. J. Fuzzy Syst. 23, 2182–2199 (2021). https://doi.org/10.1007/s40815-021-01088-9

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