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K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality
Abstract
The K-means algorithm is a commonly used technique in cluster analysis. In this paper, several questions about the algorithm are addressed. The clustering problem is first cast as a nonconvex mathematical program. Then, a rigorous proof of the finite convergence of the K-means-type algorithm is given for any metric. It is shown that under certain conditions the algorithm may fail to converge to a local minimum, and that it converges under differentiability conditions to a Kuhn-Tucker point. Finally, a method for obtaining a local-minimum solution is given.
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Cited by
An efficient k-means clustering algorithm: analysis and implementation
Kanungo, T., Mount, D. M., Netanyahu, N. S., Piatko, C. D., Silverman, R., & Wu, A. Y. (2002) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2002.1017616 · Cited by 5,660
A survey of Clustering Algorithms
Rokach, L. (2009) · Data Mining and Knowledge Discovery Handbook · doi:10.1007/978-0-387-09823-4_14 · Cited by 245
Metadata
- Authors
- Selim, S. Z., & Ismail, M. A.
- Venue
- IEEE Transactions on Pattern Analysis and Machine Intelligence
- Published
- 1984-01
- Volume
- PAMI-6
- Issue
- 1
- Pages
- 81-87
- ISSN
- 0162-8828 (ISSN-L)
- OpenAlex
- W2073849744
- Cited by
- 1,212
- References
- 0
- FWCI
- 2.59
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality. https://app.cochat.ai/papers/10.1109/tpami.1984.4767478
- The paper
- Selim, S. Z., & Ismail, M. A. (1984). K-Means-Type Algorithms: A Generalized Convergence Theorem and Characterization of Local Optimality. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/tpami.1984.4767478
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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).
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