doi:10.1016/S0031-3203(02)00060-2
Copyright © 2002 Pattern Recognition Society. Published by Elsevier Science B.V.
The global k-means clustering algorithm
a Department of Computer Science, University of Ioannina, 45110, Ioannina, Greece
b Computer Science Institute, University of Amsterdam, Kruislaan 403, 1098 SJ, Amsterdam, The Netherlands
Received 23 March 2001;
accepted 4 March 2002.
Available online 14 May 2002.
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Abstract
We present the global k-means algorithm which is an incremental approach to clustering that dynamically adds one cluster center at a time through a deterministic global search procedure consisting of N (with N being the size of the data set) executions of the k-means algorithm from suitable initial positions. We also propose modifications of the method to reduce the computational load without significantly affecting solution quality. The proposed clustering methods are tested on well-known data sets and they compare favorably to the k-means algorithm with random restarts.
Author Keywords: Clustering; k-Means algorithm; Global optimization; k-d Trees; Data mining
Fig. 1. Performance results for data drawn from a Gaussian mixture with 15 components.
Fig. 2. Performance results for the Iris data set.
Fig. 3. Performance results for the synthetic data set.
Fig. 4. Performance results for the image segmentation data set.
Fig. 5. Results for the texture segmentation problem using as many clusters as textures.
Fig. 6. Results for the texture segmentation problem using twice as many clusters as textures.
Fig. 7. Some example two-dimensional data sets with five sources and separation (from left to right) 0.5, 0.75 and 1.
Fig. 8. Experimental results on artificial data sets with d=2 and 4.
Fig. 9. Experimental results on artificial data sets with d=6 and 8.
Fig. 10. The number of allowed trials for the randomly initialized k-means as a function of the number of clusters.