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Clustering methods

Clustering methods. Partitional clustering in which clusters are represented by their centroids (proc FASTCLUS) Agglomerative hierarchical clustering in which the closest clusters are repeatedly merged (proc CLUSTER)

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Clustering methods

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  1. Clustering methods • Partitional clustering in which clusters are represented by their centroids (proc FASTCLUS) • Agglomerative hierarchical clustering in which the closest clusters are repeatedly merged (proc CLUSTER) • Density-based clustering in which core points and associated border points are clustered (proc MODECLUS) Data mining and statistical learning - lecture 14

  2. Proc FASTCLUS • Select k initial centroids • Repeat the following until the clusters remain unchanged: • Form k clusters by assigning each point to its nearest centroid • Update the centroid of each cluster Data mining and statistical learning - lecture 14

  3. Identification of water samples with incorrecttotal nitrogen levels Data mining and statistical learning - lecture 14

  4. Identification of water samples with incorrect total nitrogen levels- 2-means clustering Initialization problems? Data mining and statistical learning - lecture 14

  5. Limitations of K-means clustering • Difficult to detect clusters with non-spherical shapes • Difficult to detect clusters of widely different sizes • Difficult to detect clusters of different densities Data mining and statistical learning - lecture 14

  6. Proc MODECLUS • Use a smoother to estimate the (local) density of the given dataset • A cluster is loosely defined as a region surrounding a local maximum of the probability density function Data mining and statistical learning - lecture 14

  7. Identification of water samples with incorrecttotal nitrogen levels- proc MODECLUS, R = 1000 What will happen if R is increased? Data mining and statistical learning - lecture 14

  8. Identification of water samples with incorrecttotal nitrogen levels- proc MODECLUS, R = 4000 Data mining and statistical learning - lecture 14

  9. Identification of water samples with incorrecttotal nitrogen levels- proc MODECLUS, method 6 Why did the clustering fail? Data mining and statistical learning - lecture 14

  10. Limitations of density-based clustering • Difficult to control (requires repeated runs) • Collapses in high dimensions Data mining and statistical learning - lecture 14

  11. Strength of density-based clustering Given a sufficiently large sample, nonparametric density-based clustering methods are capable of detecting clusters of unequal size and dispersion and with highly irregular shapes Data mining and statistical learning - lecture 14

  12. Identification of water samples with incorrecttotal nitrogen levels- transformed data Data mining and statistical learning - lecture 14

  13. Identification of water samples with incorrecttotal nitrogen levels- proc MODECLUS, R = 2000, transformed data Data mining and statistical learning - lecture 14

  14. Preprocessing • Standardization • Linear transformation • Dimension reduction Data mining and statistical learning - lecture 14

  15. Postprocessing • Split a cluster • Usually, the cluster with the largest SSE is split • Introduce a new cluster centroid • Often the point that is farthest from any cluster center is chosen • Disperse a cluster • Remove one centroid and reassign the points to other clusters • Merge two clusters • Typically, the clusters with the closest centroids are chosen Data mining and statistical learning - lecture 14

  16. Profiling website visitors • A total of 296 pages at a Microsoft website are grouped into 13 homogenous categories • Initial • Support • Entertainment • Office • Windows • Othersoft • Download • ….. • For each of 32711 visitors we have recorded how many times they have visited the different categories of pages • We would like to make a behavioural segmentation of the users ( a cluster analysis) that can be used in future marketing decisions Data mining and statistical learning - lecture 14

  17. Profiling website visitors- the dataset Why is it necessary to group the pages into categories? Data mining and statistical learning - lecture 14

  18. Profiling website visitors- 10-means clustering Data mining and statistical learning - lecture 14

  19. Profiling website visitors- cluster proximities Data mining and statistical learning - lecture 14

  20. Profiling website visitors- profiles Data mining and statistical learning - lecture 14

  21. Profiling website visitors- Kohonen Map of cluster frequencies Data mining and statistical learning - lecture 14

  22. Profiling website visitors- Kohonen Maps of means by variable and grid cell Data mining and statistical learning - lecture 14

  23. Characteristics of Kohonen maps • The centroids vary smoothly over the map • The set of clusters having unusually large (or small) values of a given variable tend to form connected spatial patterns • Clusters with similar centroids need not be close to each other in a Kohonen map • The sizes of the clusters in Kohonen maps tend to be less variable than those obtained by K-means clustering Data mining and statistical learning - lecture 14

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