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Well-Separated Clusters and Optimal Fuzzy Partitions
Abstract
Two separation indices are considered for partitions P = {X1, …, Xk} of a finite data set X in a general inner product space. Both indices increase as the pairwise distances between the subsets Xi become large compared to the diameters of Xi Maximally separated partitions p' are defined and it is shown that as the indices of p' increase without bound, the characteristic functions of Xi' in P' are approximated more and more closely by the membership functions in fuzzy partitions which minimize certain fuzzy extensions of the k-means squared error criterion function.
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Citations
Cited by
NbClust : An R Package for Determining the Relevant Number of Clusters in a Data Set
Charrad, M., Ghazzali, N., Boiteau, V., & Niknafs, A. (2014) · Journal of Statistical Software · doi:10.18637/jss.v061.i06 · Cited by 3,396
A validity measure for fuzzy clustering
Xie, X. L., & Beni, G. (1991) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.85677 · Cited by 3,385
Performance evaluation of some clustering algorithms and validity indices
Maulik, U., & Bandyopadhyay, S. (2002) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2002.1114856 · Cited by 1,396
Whole genome-based population biology and epidemiological surveillance of Listeria monocytogenes
Moura, A., Criscuolo, A., Pouseele, H., Maury, M. M., Leclercq, A., Tarr, C., Björkman, J. T., Dallman, T., Reimer, A., Enouf, V., et al. (2016) · Nature Microbiology · doi:10.1038/nmicrobiol.2016.185 · Cited by 668
Div-Seq: Single-nucleus RNA-Seq reveals dynamics of rare adult newborn neurons
Habib, N., Li, Y., Heidenreich, M., Swiech, L., Avraham-Davidi, I., Trombetta, J. J., Hession, C., Zhang, F., & Regev, A. (2016) · Science · doi:10.1126/science.aad7038 · Cited by 601
Metadata
- Authors
- Dunn†, J. C.
- Venue
- Journal of Cybernetics
- Publisher
- Informa UK Limited
- Published
- 1974-01
- Volume
- 4
- Issue
- 1
- Pages
- 95-104
- ISSN
- 0022-0280 (ISSN-L)
- OpenAlex
- W2029064186
- Cited by
- 2,510
- References
- 0
- FWCI
- 4.05
- Type
- journal article
- Language
- en
- Open access
- closed
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- Dunn†, J. C. (1974). Well-Separated Clusters and Optimal Fuzzy Partitions. Journal of Cybernetics. https://doi.org/10.1080/01969727408546059
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
