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Excerpt from Asymptotic Properties of Univariate Sample K-Means Clusters
This method for division of a sample into k groups to minimize the with in groups sum of squares locally is known in the clustering literature as k-means. In one dimension, the partition will be specified by k-1 cutpoints; the observations lying between common cutpoints are in the same group. See Hartigan (1975) for a detailed description of the k-means method, and see Hartigan and Wong (1979) for an efficient computational algorithm. This method has been widely used in various clustering applications (see Blashfield and Aldenderfer, Its asymptotic properties (when N for fixed k have been studied by macqueen Hartigan and Pollard Here, the sampling properties of k-means clusters when k approaches with N are presented.
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