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Density-based IFCM along with its interval valued and probabilistic extensions, and a review of intuitionistic fuzzy clustering methods

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Abstract

Fuzzy clustering has been useful in capturing the uncertainty present in the data during clustering. Most of the c-Means algorithms such as FCM (Fuzzy c-Means), IFCM (Intuitionistic Fuzzy c-Means), and the recently reported PIFCM (Probabilistic Intuitionistic Fuzzy c-means) randomly initialize cluster centroids. Performance of these techniques is very reliant on the initialized cluster centroids. So, a good initialization technique can significantly affect the cluster formation. Recently, density-based initialization technique for FCM (DFCM) was proposed, which initializes datapoints with high density as cluster centroids. In DFCM, points within some distance contribute in the density of the data points. In this paper, we propose a new way to compute fuzzy density of datapoints based on the distance measure. Uncertainty can be better captured by intuitionistic fuzzy set (IFS) and interval-valued IFS (IVIFS). Thus, we propose a new density-based initialization technique for IFCM, called ‘Density based Intuitionistic Fuzzy c-Means (DIFCM) Algorithm’. The proposed DIFCM has been further developed for IVIFS, which we term ‘Interval-valued Density based Intuitionistic Fuzzy c-Means (IVDIFCM) Algorithm’, is also introduced in this paper. PIFCM incorporates probabilistic weights between membership, non-membership and hesitancy component. In this paper, we also introduce the density based initialized cluster centroids for PIFCM algorithm to propose the ‘Density Based Probabilistic Intuitionistic Fuzzy c-Means (DPIFCM) Algorithm’. There were many clustering approaches based on IFSs but there do not exist any literature review on the IFS based clustering approaches. Therefore,  this article also provides a detailed review of the recently proposed clustering algorithms based on IFS theory. Experiments over various UCI datasets proves that our proposed algorithms has better clustering results than their existing counterparts.

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Notes

  1. Since the Seed data set and the Wine dataset have more than two dimensions, there are some overlapping points belonging to different classes as they are significantly different for other dimensions.

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Acknowledgments

Authors are thankful to the editors and the reviewers for all their valuable comments which have helped a lot in improving the work. First author gratefully acknowledges the financial assistance obtained from South Asian University (SAU), New Delhi, India in the form of a master’s scholarship. All authors are also thankful to the SAU, New Delhi for providing the infrastructural facilities to conduct this research through the Computational Intelligence research lab.

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  1. Ayush K. Varshney

    Present address: Department of Computing Science, Umeå University 90187, Umea, Sweden

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  1. Department of Computer Science, South Asian University, New Delhi, 110021, India

    Ayush K. Varshney & Pranab K. Muhuri

  2. Department of Mathematics, South Asian University, New Delhi 110021, India

    Q. M. Danish Lohani

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Varshney, A.K., Muhuri, P.K. & Lohani, Q.M.D. Density-based IFCM along with its interval valued and probabilistic extensions, and a review of intuitionistic fuzzy clustering methods. Artif Intell Rev 56, 3755–3795 (2023). https://doi.org/10.1007/s10462-022-10236-y

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