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A Central Limit Theorem for $k$-Means Clustering
Open accessAbstract
A set of $n$ points in Euclidean space is partitioned into the $k$ groups that minimize the within groups sum of squares. Under the assumption that the $n$ points come from independent sampling on a fixed distribution, conditions are found to assure asymptotic normality of the vector of means of the $k$ groups. The method of proof makes novel application of a functional central limit theorem for empirical processes--a generalization of Donsker's theorem due to Dudley.
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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
Grouped Patterns of Heterogeneity in Panel Data
Bonhomme, S., & Manresa, E. (2015) · Econometrica · doi:10.3982/ecta11319 · Cited by 451
Metadata
- Authors
- Pollard, D.
- Venue
- The Annals of Probability
- Publisher
- Institute of Mathematical Statistics
- Published
- 1982-11-01
- Volume
- 10
- Issue
- 4
- ISSN
- 0091-1798 (ISSN-L)
- OpenAlex
- W2050744541
- Cited by
- 240
- References
- 0
- FWCI
- 3.05
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Pollard, D. (1982). A Central Limit Theorem for $k$-Means Clustering. The Annals of Probability. https://doi.org/10.1214/aop/1176993713
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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.
