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An efficient k-means clustering algorithm: analysis and implementation

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6 Author(s)
Kanungo, Tapas ; Almaden Res. Center, San Jose, CA, USA ; Mount, D.M. ; Netanyahu, N.S. ; Piatko, C.D.
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In k-means clustering, we are given a set of n data points in d-dimensional space Rd and an integer k and the problem is to determine a set of k points in Rd, called centers, so as to minimize the mean squared distance from each data point to its nearest center. A popular heuristic for k-means clustering is Lloyd's (1982) algorithm. We present a simple and efficient implementation of Lloyd's k-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

Published in:

Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:24 ,  Issue: 7 )

Date of Publication:

Jul 2002

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