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Adrian Florea
Adrian Florea

6th presentation @ Papers We Love - Bucharest Chapter on 22nd February, 2016

Software
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k-means Clustering Papers We Love Bucharest Chapter February 22, 2016
I am Adrian Florea Architect Lead @ IBM Bucharest Software Lab Hello!
What is clustering? ◉branch of Machine Learning (unsupervised learning i.e. find underlying patterns in the data) ◉method for identifying data items that closely resemble one another, assembling them into clusters [ODS]
Clustering applications ◉Customer segmentation
Clustering applications ◉Google News
Definitions and notations ◉data to be clustered (N data points) ◉iteratively refined clustering solution ◉cluster membership vector ◉closeness cost function ◉Minkowski distance p=1 (Manhattan), p=2 (Euclidian)
Voronoi diagrams ◉Euclidian distance ◉Manhattan distance
K-means algorithm ◉input: dataset D, number of clusters k ◉output: cluster solution C, cluster membership m ◉initialize C by randomly choose k data points sets from D ◉repeat reasign points in D to closest cluster mean update m update C such that is mean of points in cluster, ◉until convergence of KM(D, C)
K-means iterations example N=12, k=2 randomly choose 2 clusters calculate cluster means reassign points to closest cluster mean update cluster means loop if needed
Poor initialization/Poor clustering Initial (I) Final (I) Initial (II) Final (II) Initial (III) Final (III)
Pros ◉simple ◉common in practice ◉easy to adapt ◉relatively fast ◉sensitive to initial partitions ◉optimal k is difficult to choose ◉restricted to data which has the notion of a center ◉cannot handle well non- convex clusters ◉does not identify outliers (because mean is not a “robust” statistic function) Cons
Tips & tricks ◉run the algorithm multiple times with different initial centroids and select the best result ◉if possible, use the knowledge about the dataset in choosing k ◉trying several k and choosing the one based on closeness cost function is naive ◉use a more appropriate distance measure for the dataset ◉use k-means together with another algorithm ◉Exploit the triangular inequality to avoid to compare each data point with all centroids
Tips & tricks - continued ◉recursively split the least compact cluster in 2 clusters by using 2-means ◉remove outliers in preprocessing (anomaly detection) ◉eliminate small clusters or merge close clusters at postprocessing ◉in case of empty clusters reinitialize their centroids or steal points from the largest cluster
Tools & frameworks ◉Frontline Systems XLMiner (Excel Add-in) ◉SciPy K-means Clustering and Vector Quantization Modules (scipy.cluster.vq.kmeans) ◉stats package in R ◉Azure Machine Learning
Bibliography ◉ H.-H. Bock, "Origins and extensions of the k-means algorithm in cluster analysis", JEHPS, Vol. 4, No. 2, December 2008 ◉ D. Chappell, “Understanding Machine Learning”, PluralSight.com, 4 February 2016 ◉ J. Ghosh, A. Liu, "K-Means", pp. 21-35 in X. Wu, V. Kumar (Eds.), "The Top Ten Algorithms in Data Mining", Chapman & Hall/CRC, 2009 ◉ G.J. Hamerly, "Learning structure and concepts in data through data clustering", PhD Thesis, University of California, San Diego, 2003 ◉ J. Han, M. Kamber, J. Pei, "Chapter 10. Cluster Analysis: Basic Concepts and Methods" in "Data Mining: Concepts and Techniques", Morgan Kaufmann, 2011 ◉ S.P. Lloyd, "Least Squares Quantization in PCM", IEEE Transactions on Information Theory, Vol. 28, No. 2, 1982 ◉ J. MacQueen, “Some Methods for Classification and Analysis of Multivariate Observations”, 5th Berkeley Symposium, 1967 ◉ J. McCaffrey, "Machine Learning Using C# Succinctly", Syncfusion, 2014 ◉ [ODS] G. Upton, I. Cook, “A Dictionary of Statistics”, 3rd Ed., Oxford University Press, 2014 ◉ ***, “k-means clustering”, Wikipedia ◉ ***, “Voronoi diagram”, Wikipedia
Any questions ? You can find me at Thanks!

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"k-means-clustering" presentation @ Papers We Love Bucharest

  • 1. k-means Clustering Papers We Love Bucharest Chapter February 22, 2016
  • 2. I am Adrian Florea Architect Lead @ IBM Bucharest Software Lab Hello!
  • 3. What is clustering? ◉branch of Machine Learning (unsupervised learning i.e. find underlying patterns in the data) ◉method for identifying data items that closely resemble one another, assembling them into clusters [ODS]
  • 6. Definitions and notations ◉data to be clustered (N data points) ◉iteratively refined clustering solution ◉cluster membership vector ◉closeness cost function ◉Minkowski distance p=1 (Manhattan), p=2 (Euclidian)
  • 7. Voronoi diagrams ◉Euclidian distance ◉Manhattan distance
  • 8. K-means algorithm ◉input: dataset D, number of clusters k ◉output: cluster solution C, cluster membership m ◉initialize C by randomly choose k data points sets from D ◉repeat reasign points in D to closest cluster mean update m update C such that is mean of points in cluster, ◉until convergence of KM(D, C)
  • 9. K-means iterations example N=12, k=2 randomly choose 2 clusters calculate cluster means reassign points to closest cluster mean update cluster means loop if needed
  • 10. Poor initialization/Poor clustering Initial (I) Final (I) Initial (II) Final (II) Initial (III) Final (III)
  • 11. Pros ◉simple ◉common in practice ◉easy to adapt ◉relatively fast ◉sensitive to initial partitions ◉optimal k is difficult to choose ◉restricted to data which has the notion of a center ◉cannot handle well non- convex clusters ◉does not identify outliers (because mean is not a “robust” statistic function) Cons
  • 12. Tips & tricks ◉run the algorithm multiple times with different initial centroids and select the best result ◉if possible, use the knowledge about the dataset in choosing k ◉trying several k and choosing the one based on closeness cost function is naive ◉use a more appropriate distance measure for the dataset ◉use k-means together with another algorithm ◉Exploit the triangular inequality to avoid to compare each data point with all centroids
  • 13. Tips & tricks - continued ◉recursively split the least compact cluster in 2 clusters by using 2-means ◉remove outliers in preprocessing (anomaly detection) ◉eliminate small clusters or merge close clusters at postprocessing ◉in case of empty clusters reinitialize their centroids or steal points from the largest cluster
  • 14. Tools & frameworks ◉Frontline Systems XLMiner (Excel Add-in) ◉SciPy K-means Clustering and Vector Quantization Modules (scipy.cluster.vq.kmeans) ◉stats package in R ◉Azure Machine Learning
  • 15. Bibliography ◉ H.-H. Bock, "Origins and extensions of the k-means algorithm in cluster analysis", JEHPS, Vol. 4, No. 2, December 2008 ◉ D. Chappell, “Understanding Machine Learning”, PluralSight.com, 4 February 2016 ◉ J. Ghosh, A. Liu, "K-Means", pp. 21-35 in X. Wu, V. Kumar (Eds.), "The Top Ten Algorithms in Data Mining", Chapman & Hall/CRC, 2009 ◉ G.J. Hamerly, "Learning structure and concepts in data through data clustering", PhD Thesis, University of California, San Diego, 2003 ◉ J. Han, M. Kamber, J. Pei, "Chapter 10. Cluster Analysis: Basic Concepts and Methods" in "Data Mining: Concepts and Techniques", Morgan Kaufmann, 2011 ◉ S.P. Lloyd, "Least Squares Quantization in PCM", IEEE Transactions on Information Theory, Vol. 28, No. 2, 1982 ◉ J. MacQueen, “Some Methods for Classification and Analysis of Multivariate Observations”, 5th Berkeley Symposium, 1967 ◉ J. McCaffrey, "Machine Learning Using C# Succinctly", Syncfusion, 2014 ◉ [ODS] G. Upton, I. Cook, “A Dictionary of Statistics”, 3rd Ed., Oxford University Press, 2014 ◉ ***, “k-means clustering”, Wikipedia ◉ ***, “Voronoi diagram”, Wikipedia
  • 16. Any questions ? You can find me at Thanks!

Editor's Notes

  1. - partition the customer database into several groups, where customers in each group have similar purchasing history and demographics