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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs K-means*: Clustering by Gradual Data Transformation Mikko Malinen and Pasi Fränti Speech and Image Processing Unit School of Computing University of Eastern Finland
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs K-means* clustering Gradual transformation of data Model Data Fit the data to a model IntermediateFinal
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs K-means clustering Iterate between two steps: 1. Assignment step Assign the points to the nearest centroids 2. Update step Update the location of centroids
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs K-means* clustering
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Example of clustering (s 2 dataset)
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs 0% done
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Empty clusters problem
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Initialization Data set transform Empty clusters removal K-means Algorithm total Time Complexity
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Time Complexity Fixed k-means Initialization Data set transform Empty clusters removal K-means Algorithm total
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs s1 d = 2 n = 5000 k = 15 s2 d = 2 n = 5000 k = 15 s3 d = 2 n = 5000 k = 15 s4 d = 2 n = 5000 k = 15 bridge d = 16 n = 4096 k= 256 missa d = 16 n = 6480 k= 256 house d = 3 n=34000 k=256 thyroid d = 5 n = 215 k = 2 iris d = 4 n = 150 k = 2 wine d = 13 n = 178 k = 3 Datasets
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Mean square error Datasetk-meansproposedGKMoptimal s11.851.010.89 s21.941.521.33 s31.971.711.69 s41.691.631.57 bridge168.2164.7164.1160.7 missa5.335.155.345.12 house9.889.485.945.86 thyroid6.976.921.52 iris3.70 2.02 wine1.921.900.88
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Mean square error vs. number of steps
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Mean square error vs. number of steps
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Mean square error vs. number of steps
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Mean square error vs. number of steps
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Mean square error vs. number of steps
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Mean square error vs. number of steps
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Mean square error vs. number of steps
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs All correct: Number of incorrect clusters proposed: 36% k-means: 14%
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs 1 incorrect: Number of incorrect clusters proposed: 64% k-means: 38%
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs 2 incorrect: Number of incorrect clusters proposed: 0% k-means: 34%
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs 3 incorrect: Number of incorrect clusters proposed: 0% k-means: 10%
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University of Eastern Finland School of Computing P.O. Box 111 FIN- 80101 Joensuu FINLAND Tel. +358 13 251 7959 fax +358 13 251 7955 www.uef.fi/cs Summary We have presented a clustering method based on gradual transformation of data and k-means. Instead of fitting the model to data, we fit the data to a model. The proposed method gives better mean square error than k-means.
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