An Efficient k-Means Clustering Algorithm: Analysis and Implementation

  • Authors:

  • Tapas Kanungo;David M. Mount;Nathan S. Netanyahu;Christine D. Piatko;Ruth Silverman;Angela Y. Wu

  • Affiliations:

  • -;-;-;-;-;-

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 2002

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Abstract

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.