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<p>In k\hbox{-}{\rm{means}} clustering, we are given a set of n data points in d\hbox{-}{\rm{dimensional}} space {\bf{R}}^d and an integer k and the problem is to determine a set of k points in {\bf{R}}^d, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k\hbox{-}{\rm{means}} clustering is Lloyd's algorithm. In this paper, we present a simple and efficient implementation of Lloyd's k\hbox{-}{\rm{means}} clustering algorithm, which we call the filtering algorithm. This algorithm is easy to implement, requiring a kd-tree as the only major data structure. We establish the practical efficiency of the filtering algorithm in two ways. First, we present a data-sensitive analysis of the algorithm's running time, which shows that the algorithm runs faster as the separation between clusters increases. Second, we present a number of empirical studies both on synthetically generated data and on real data sets from applications in color quantization, data compression, and image segmentation.</p>
Pattern recognition, machine learning, data mining, k-means clustering, nearest-neighbor searching, k-d tree, computational geometry, knowledge discovery.

T. Kanungo, D. M. Mount, N. S. Netanyahu, C. D. Piatko, R. Silverman and A. Y. Wu, "An Efficient k-Means Clustering Algorithm: Analysis and Implementation," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 24, no. , pp. 881-892, 2002.
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