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Internal Validity Index for Fuzzy Clustering Based on Relative Uncertainty

Refik Tanju Sirmen1,*, Burak Berk Üstündağ2

1 Graduate School of Science Engineering & Technology, Istanbul Technical University, Istanbul, 34469, Turkey
2 Faculty of Computer & Informatics, Istanbul Technical University, Istanbul, 34469, Turkey

* Corresponding Author: Refik Tanju Sirmen. Email: email

Computers, Materials & Continua 2022, 72(2), 2909-2926.


Unsupervised clustering and clustering validity are used as essential instruments of data analytics. Despite clustering being realized under uncertainty, validity indices do not deliver any quantitative evaluation of the uncertainties in the suggested partitionings. Also, validity measures may be biased towards the underlying clustering method. Moreover, neglecting a confidence requirement may result in over-partitioning. In the absence of an error estimate or a confidence parameter, probable clustering errors are forwarded to the later stages of the system. Whereas, having an uncertainty margin of the projected labeling can be very fruitful for many applications such as machine learning. Herein, the validity issue was approached through estimation of the uncertainty and a novel low complexity index proposed for fuzzy clustering. It involves only uni-dimensional membership weights, regardless of the data dimension, stipulates no specific distribution, and is independent of the underlying similarity measure. Inclusive tests and comparisons returned that it can reliably estimate the optimum number of partitions under different data distributions, besides behaving more robust to over partitioning. Also, in the comparative correlation analysis between true clustering error rates and some known internal validity indices, the suggested index exhibited the highest strong correlations. This relationship has been also proven stable through additional statistical acceptance tests. Thus the provided relative uncertainty measure can be used as a probable error estimate in the clustering as well. Besides, it is the only method known that can exclusively identify data points in dubiety and is adjustable according to the required confidence level.


Cite This Article

APA Style
Sirmen, R.T., Üstündağ, B.B. (2022). Internal validity index for fuzzy clustering based on relative uncertainty. Computers, Materials & Continua, 72(2), 2909-2926.
Vancouver Style
Sirmen RT, Üstündağ BB. Internal validity index for fuzzy clustering based on relative uncertainty. Comput Mater Contin. 2022;72(2):2909-2926
IEEE Style
R.T. Sirmen and B.B. Üstündağ, "Internal Validity Index for Fuzzy Clustering Based on Relative Uncertainty," Comput. Mater. Contin., vol. 72, no. 2, pp. 2909-2926. 2022.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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