V. Faber, "Clustering and the continuous k-means algorithm," Los Alamos Science 22, pp. 138--144, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....which is often called the k means algorithm. Define the neighborhood of a center point to be the set of data points for which this center is the closest. It is easy to prove that any locally minimal solution must be centroidal, meaning that that each center lies at the centroid of its neighborhood [10, 14]. Lloyd s algorithm starts with any feasible solution, and it repeatedly computes the neighborhood of each center and then moves the center to the centroid of its neighborhood, until some convergence criterion is satisfied. It can be shown that Lloyd s algorithm eventually converges to a locally ....

V. Faber. Clustering and the continuous k-means algorithm. Los Alamos Science, 22:138--144, 1994.

....Further development of this method may be found in the work by P. Agarwal and C. Procopiuc [1] Another simple and efficient algorithm for clustering data, an extremely popular k means algorithm, was conceptually described by S.P. Lloyd [30] and later improved by J. MacQueen [31] Many papers [5, 8, 23, 40] suggest various improvements to the k means algorithm, mostly based on the use of the random sub sampling of the data sets at various stages of the algorithm. K. Fu and R. Gonzalez [13] suggested a split and merge algorithm to cluster areas using a decreasing resolution technique. A 2D version ....

V. Faber, Clustering and the Continuous k-Means Algorithm, Los Alamos Science Magazine, Number 22, 1994

....nearest neighbor. Equivalently, V i is the set of data points lying in the Voronoi cell of c i relative to the set of centers. For the next iteration of the algorithm, replace c i with the centroid of V i . These two steps are repeated until some convergence conditions have been met. See Faber [15] for descriptions of other variants of this algorithm. For points in general position, the algorithm will eventually converge to a point that is a local minimum. This is true because any local minimum for this problem corresponds to a centroidal Voronoi configuration (see [15, 12] However, the ....

....been met. See Faber [15] for descriptions of other variants of this algorithm. For points in general position, the algorithm will eventually converge to a point that is a local minimum. This is true because any local minimum for this problem corresponds to a centroidal Voronoi configuration (see [15, 12]) However, the result is not necessarily a global minimum. See [7, 30, 33, 35] for further discussion of its statistical and convergence properties. Because of its simplicity and flexibility it is a very popular algorithm and is widely used in statistical analysis, in spite of its apparent ....

V. Faber. Clustering and the continuous k-means algorithm. Los Alamos Science, 22:138--144, 1994.

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V. Faber, "Clustering and the continuous k-means algorithm," Los Alamos Science 22, pp. 138--144, 1994.

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