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On uniqueness of the set of k-means
- Publication Year :
- 2024
-
Abstract
- We provide necessary and sufficient conditions for the uniqueness of the k-means set of a probability distribution. This uniqueness problem is related to the choice of k: depending on the underlying distribution, some values of this parameter could lead to multiple sets of k-means, which hampers the interpretation of the results and/or the stability of the algorithms. We give a general assessment on consistency of the empirical k-means adapted to the setting of non-uniqueness and determine the asymptotic distribution of the within cluster sum of squares (WCSS). We also provide statistical characterizations of k-means uniqueness in terms of the asymptotic behavior of the empirical WCSS. As a consequence, we derive a bootstrap test for uniqueness of the set of k-means. The results are illustrated with examples of different types of non-uniqueness and we check by simulations the performance of the proposed methodology.<br />Comment: 41 pages, 14 figures
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2410.13495
- Document Type :
- Working Paper