Abstract
Clustering with a criterion which minimizes the sum of squared distances to cluster centroids is usually done in a heuristic way. An exact polynomial algorithm, with a complexity in O(N p+1 logN), is proposed for minimum sum of squares hierarchical divisive clustering of points in a p-dimensional space with small p. Empirical complexity is one order of magnitude lower. Data sets with N = 20000 for p = 2, N = 1000 for p = 3, and N = 200 for p = 4 are clustered in a reasonable computing time.
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Hansen, P., Jaumard, B. & Mladenovic, N. Minimum Sum of Squares Clustering in a Low Dimensional Space. J. of Classification 15, 37–55 (1998). https://doi.org/10.1007/s003579900019
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DOI: https://doi.org/10.1007/s003579900019