1. Data Mining Classification and Clustering Techniques Introduction to Data Mining by Tan, Steinbach, Kumar © Tan,Steinbach, Kumar Introduction to Data Mining 4/18/2004 1 Thank you very much for all materials

2. Classification: Definition Given a collection of records (training set ) –Each record contains a set of attributes, one of the attributes is the class. Find a model for class attribute as a function of the values of other attributes. Goal: previously unseen records should be assigned a class as accurately as possible. –A test set is used to determine the accuracy of the model. Usually, the given data set is divided into training and test sets, with training set used to build the model and test set used to validate it.

3. Illustrating Classification Task

4. Examples of Classification Task Predicting tumor cells as benign or malignant Classifying credit card transactions as legitimate or fraudulent Classifying secondary structures of protein as alpha-helix, beta-sheet, or random coil Categorizing news stories as finance, weather, entertainment, sports, etc

5. Classification Techniques Decision Tree based Methods Rule-based Methods Memory based reasoning Neural Networks Naïve Bayes and Bayesian Belief Networks Support Vector Machines

6. Example of a Decision Tree categorical continuous class Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Splitting Attributes Training Data Model: Decision Tree

7. Another Example of Decision Tree categorical continuous class MarSt Refund TaxInc YES NO Yes No Married Single, Divorced < 80K> 80K There could be more than one tree that fits the same data!

8. Decision Tree Classification Task Decision Tree

9. Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data Start from the root of tree.

10. Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

11. Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

12. Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

13. Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data

14. Apply Model to Test Data Refund MarSt TaxInc YES NO YesNo Married Single, Divorced < 80K> 80K Test Data Assign Cheat to “No”

15. What is Cluster Analysis? Finding groups of objects such that the objects in a group will be similar (or related) to one another and different from (or unrelated to) the objects in other groups Inter-cluster distances are maximized Intra-cluster distances are minimized

16. Applications of Cluster Analysis Understanding –Group related documents for browsing, group genes and proteins that have similar functionality, or group stocks with similar price fluctuations Summarization –Reduce the size of large data sets Clustering precipitation in Australia

17. Notion of a Cluster can be Ambiguous How many clusters? Four ClustersTwo Clusters Six Clusters

18. Types of Clusterings A clustering is a set of clusters Important distinction between hierarchical and partitional sets of clusters Partitional Clustering –A division data objects into non-overlapping subsets (clusters) such that each data object is in exactly one subset Hierarchical clustering –A set of nested clusters organized as a hierarchical tree

19. Partitional Clustering Original Points A Partitional Clustering

20. Hierarchical Clustering Traditional Hierarchical Clustering Non-traditional Hierarchical Clustering Non-traditional Dendrogram Traditional Dendrogram

21. Clustering Algorithms K-means and its variants Hierarchical clustering

22. K-means Clustering Partitional clustering approach Each cluster is associated with a centroid (center point) Each point is assigned to the cluster with the closest centroid Number of clusters, K, must be specified The basic algorithm is very simple

23. K-means: Example

25. Sub-optimal ClusteringOptimal Clustering Original Points Importance of Choosing Initial Centroids …

28. Problems with Selecting Initial Points If there are K ‘real’ clusters then the chance of selecting one centroid from each cluster is small. –Chance is relatively small when K is large –If clusters are the same size, n, then –For example, if K = 10, then probability = 10!/10 10 = 0.00036 –Sometimes the initial centroids will readjust themselves in ‘right’ way, and sometimes they don’t –Consider an example of five pairs of clusters

29. Solutions to Initial Centroids Problem Multiple runs –Helps, but probability is not on your side Sample and use hierarchical clustering to determine initial centroids Select more than k initial centroids and then select among these initial centroids –Select most widely separated Postprocessing

30. Limitations of K-means K-means has problems when clusters are of differing –Sizes –Densities –Non-globular shapes K-means has problems when the data contains outliers.

31. Limitations of K-means: Differing Sizes Original Points K-means (3 Clusters)

32. Limitations of K-means: Differing Density Original Points K-means (3 Clusters)

33. Limitations of K-means: Non-globular Shapes Original Points K-means (2 Clusters)

34. Overcoming K-means Limitations Original PointsK-means Clusters One solution is to use many clusters. Find parts of clusters, but need to put together.

35. Overcoming K-means Limitations Original PointsK-means Clusters

36. Overcoming K-means Limitations Original PointsK-means Clusters

37. Clustering Algorithms K-means and its variants Hierarchical clustering

38. Hierarchical Clustering Produces a set of nested clusters organized as a hierarchical tree Can be visualized as a dendrogram –A tree like diagram that records the sequences of merges or splits

39. Strengths of Hierarchical Clustering Do not have to assume any particular number of clusters –Any desired number of clusters can be obtained by ‘cutting’ the dendrogram at the proper level They may correspond to meaningful taxonomies –Example in biological sciences (e.g., animal kingdom, phylogeny reconstruction, …)

40. Hierarchical Clustering Two main types of hierarchical clustering –Agglomerative: Start with the points as individual clusters At each step, merge the closest pair of clusters until only one cluster (or k clusters) left –Divisive: Start with one, all-inclusive cluster At each step, split a cluster until each cluster contains a point (or there are k clusters) Traditional hierarchical algorithms use a similarity or distance matrix –Merge or split one cluster at a time

41. Agglomerative Clustering Algorithm More popular hierarchical clustering technique Basic algorithm is straightforward 1.Compute the proximity matrix 2.Let each data point be a cluster 3.Repeat 4.Merge the two closest clusters 5.Update the proximity matrix 6.Until only a single cluster remains Key operation is the computation of the proximity of two clusters –Different approaches to defining the distance between clusters distinguish the different algorithms

42. Starting Situation Start with clusters of individual points and a proximity matrix p1 p3 p5 p4 p2 p1p2p3p4p5......... Proximity Matrix

43. Intermediate Situation After some merging steps, we have some clusters C1C1 C4C4 C2C2 C5C5 C3C3 C2C1 C3 C5 C4 C2 C3C4C5 Proximity Matrix

44. Intermediate Situation We want to merge the two closest clusters (C2 and C5) and update the proximity matrix. C1C1 C4C4 C2C2 C5C5 C3C3 C2C1 C3 C5 C4 C2 C3C4C5 Proximity Matrix

45. After Merging The question is “How do we update the proximity matrix?” C1C1 C4C4 C2 U C5 C3C3 ? ? ? ? ? C2 U C5 C1 C3 C4 C2 U C5 C3C4 Proximity Matrix

46. How to Define Inter-Cluster Similarity p1 p3 p5 p4 p2 p1p2p3p4p5......... Similarity? l MIN l MAX l Group Average l Distance Between Centroids l Other methods driven by an objective function Proximity Matrix

47. How to Define Inter-Cluster Similarity p1 p3 p5 p4 p2 p1p2p3p4p5......... Proximity Matrix l MIN l MAX l Group Average l Distance Between Centroids l Other methods driven by an objective function

48. How to Define Inter-Cluster Similarity p1 p3 p5 p4 p2 p1p2p3p4p5......... Proximity Matrix l MIN l MAX l Group Average l Distance Between Centroids l Other methods driven by an objective function

49. How to Define Inter-Cluster Similarity p1 p3 p5 p4 p2 p1p2p3p4p5......... Proximity Matrix l MIN l MAX l Group Average l Distance Between Centroids l Other methods driven by an objective function

50. How to Define Inter-Cluster Similarity p1 p3 p5 p4 p2 p1p2p3p4p5......... Proximity Matrix l MIN l MAX l Group Average l Distance Between Centroids l Other methods driven by an objective function 

51. Hierarchical Clustering: Problems and Limitations Once a decision is made to combine two clusters, it cannot be undone No objective function is directly minimized Different schemes have problems with one or more of the following: –Sensitivity to noise and outliers –Difficulty handling different sized clusters and convex shapes –Breaking large clusters

52. Cluster Validity For supervised classification we have a variety of measures to evaluate how good our model is –Accuracy, precision, recall For cluster analysis, the analogous question is how to evaluate the “goodness” of the resulting clusters? But “clusters are in the eye of the beholder”! Then why do we want to evaluate them? –To avoid finding patterns in noise –To compare clustering algorithms –To compare two sets of clusters –To compare two clusters

53. Order the similarity matrix with respect to cluster labels and inspect visually. Using Similarity Matrix for Cluster Validation

54. “The validation of clustering structures is the most difficult and frustrating part of cluster analysis. Without a strong effort in this direction, cluster analysis will remain a black art accessible only to those true believers who have experience and great courage.” Algorithms for Clustering Data, Jain and Dubes Final Comment on Cluster Validity