Supervised Clustering --- Algorithms and Applications

1. Supervised Clustering ---Algorithms and Applications Christoph F. Eick Department of Computer Science University of Houston Organization of the Talk Supervised Clustering Representative-based Supervised Clustering Algorithms Applications: Using Supervised Clustering for Dataset Editing Class Decomposition Distance Function Learning Region Discovery in Spatial Datasets Other Activities I am Involved With

2. List of Persons that Contributed to the Work Presented in Today’s Talk • Tae-Wan Ryu (former PhD student; now faculty member Cal State Fullerton) • Ricardo Vilalta (colleague at UH since 2002; Co-Director of the UH’s Data Mining and Knowledge Discovery Group) • Murali Achari (former Master student) • Alain Rouhana (former Master student) • Abraham Bagherjeiran (current PhD student) • Chunshen Chen (current Master student) • Nidal Zeidat (current PhD student) • Sujing Wang (current PhD student) • Kim Wee (current MS student) • Zhenghong Zhao (former Master student)

3. Traditional Clustering • Partition a set of objects into groups of similar objects. Each group is called a cluster. • Clustering is used to “detect classes” in a data set (“unsupervised learning”). • Clustering is based on a fitness function that relies on a distance measure and usually tries to create “tight” clusters.

4. Ch. Eick Different Forms of Clustering Objectives Supervised Clustering: Minimize cluster impurity while keeping the number of clusters low (expressed by a fitness function q(X)).

5. Motivation: Finding Subclasses using SC Attribute1 Ford Trucks :Ford :GMC GMC Trucks GMC Van Ford Vans Ford SUV Attribute2 GMC SUV

6. Related Work Supervised Clustering • Sinkkonen’s [SKN02] discriminative clustering and Tishby’s information bottleneck method [TPB99, ST99] can be viewed as probabilistic supervised clustering algorithms. • There has been a lot of work in the area of semi-supervised clustering that centers on clustering with background information. Although the focus of this work is traditional clustering, there is still a lot of similarity between techniques and algorithms they investigate and the techniques and algorithms we investigate.

7. 2. Representative-Based Supervised Clustering • Aims at finding a set of objects among all objects (called representatives) in the data set that best represent the objects in the data set. Each representative corresponds to a cluster. • The remaining objects in the data set are then clustered around these representatives by assigning objects to the cluster of the closest representative. Remark: The popular k-medoid algorithm, also called PAM, is a representative-based clustering algorithm.

8. Representative-Based Supervised Clustering … (Continued) 2 Attribute1 1 3 Attribute2 4

9. Representative-Based Supervised Clustering … (continued) 2 Attribute1 1 3 Attribute2 4 Objective of RSC: Find a subset OR of O such that the clustering X obtained by using the objects in OR as representatives minimizes q(X).

10. SC Algorithms Currently Investigated • Supervised Partitioning Around Medoids (SPAM). • Single Representative Insertion/Deletion Steepest Decent Hill Climbing with Randomized Restart (SRIDHCR). • Top Down Splitting Algorithm (TDS). • Supervised Clustering using Evolutionary Computing (SCEC) • Agglomerative Hierarchical Supervised Clustering (AHSC) • Grid-Based Supervised Clustering (GRIDSC) Remark: For a more detailed discussion of SCEC and SRIDHCR see [EZZ04]

11. A Fitness Function for Supervised Clustering q(X) := Impurity(X) + β*Penalty(k) k: number of clusters used n: number of examples the dataset c: number of classes in a dataset. β: Weight for Penalty(k), 0< β ≤2.0 Penalty(k) increase sub-linearly. because the effect of increasing the # of clusters from k to k+1 has greater effect on the end result when k is small than when it is large. Hence the formula above

12. REPEAT r TIMES • curr := a randomly created set of representatives (with size between c+1 and 2*c) • WHILE NOT DONE DO • Create new solutions S by adding a single non-representative to curr and by removing a single representative from curr • Determine the element s in S for which q(s) is minimal (if there is more than one minimal element, randomly pick one) • IF q(s)<q(curr) THEN curr:=s • ELSE IF q(s)=q(curr) AND |s|>|curr| THEN Curr:=s • ELSE terminate and return curr as the solution for this run. • Report the best out of the r solutions found. Algorithm SRIDHCR (Greedy Hill Climbing) • Highlights: • k is not an input parameter, SRIDHCR searches for best k within the range that is induced by b. • Reports the best clustering found in r runs

13. Supervised Clustering using Evolutionary Computing: SCEC Initial generation Next generation Mutation Crossover Copy Best solution Final generation Result:

14. Initialize Solutions Initialize Solutions Compose Population S Compose Population S Evaluate a Population Evaluate a Population Clustering on S[i] Clustering on S[i] Loop PS times Loop PS times Loop N times Loop N times Evaluation on S[i] Evaluation on S[i] Intermediate Result Intermediate Result Record Best Solution, Q Record Best Solution, Q Best Solution, Q, Summary Best Solution, Q, Summary Exit Exit Create next Generation Create next Generation K-tournament K-tournament Loop PS times Loop PS times Mutation Mutation Crossover Crossover Copy Copy New S’[i] New S’[i] The complete flow chart of SCEC The complete flow chart of SCEC

15. Complex1 Dataset

16. Supervised Clustering Result

17. Supervised Clustering ---Algorithms and Applications Organization of the Talk Supervised Clustering Representative-based Supervised Clustering Algorithms Applications: Using Supervised Clustering for for Dataset Editing for Class Decomposition for Distance Function Learning for Region Discovery in Spatial Datasets Other Activities I am Involved With

18. Nearest Neighbour Rule Consider a two class problem where each sample consists of two measurements (x,y). For a given query point q, assign the class of the nearest neighbour. k = 1 Compute the k nearest neighbours and assign the class by majority vote. k = 3 Problem: requires “good” distance function

19. 3a. Dataset Reduction: Editing • Training data may contain noise, overlapping classes • Editing seeks to remove noisy points and produce smooth decision boundaries – often by retaining points far from the decision boundaries • Main Goal of Editing: enhance the accuracy of classifier (% of “unseen” examples classified correctly) • Secondary Goal of Editing: enhance the speed of a k-NN classifier

20. Wilson Editing • Wilson 1972 • Remove points that do not agree with the majority of their k nearest neighbours Earlier example Overlapping classes Original data Original data Wilson editing with k=7 Wilson editing with k=7

21. RSC  Dataset Editing Attribute1 Attribute1 B A D C F E Attribute2 Attribute2 a. Dataset clustered using supervised clustering. b. Dataset edited using cluster representatives.

22. Experimental Evaluation • We compared a traditional 1-NN, 1-NN using Wilson Editing, Supervised Clustering Editing (SCE), and C4.5 (that was run using its default parameter setting). • A benchmark consisting of 8 UCI datasets was used for this purpose. • Accuracies were computed using 10-fold cross validation. • SRIDHCR was used for supervised clustering. • SCE was tested using different compression rates by associating different penalties with the number of clusters found (by setting parameter b to: 0.1, 0.4 and 1.0). • Compression rates of SCE and Wilson Editing were computed using: 1-(k/n) with n being the size of the original dataset and k being the size of the edited dataset.

23. Table 2: Prediction Accuracy for the four classifiers.

24. Table 3: Dataset Compression Rates for SCE and Wilson Editing.

25. Summary SCE and Wilson Editing • Wilson editing enhances the accuracy of a traditional 1-NN classifier for six of the eight datasets tested. It achieved compression rates of approx. 25%, but much lower compression rates for “easy” datasets. • SCE achieved very high compression rates without loss in accuracy for 6 of the 8 datasets tested. • SCE accomplished a significant improvement in accuracy for 3 of the 8 datasets tested. • Surprisingly, many UCI datasets can be compressed by just using a single representative per class without a significant loss in accuracy. • SCE tends to pick representatives that are in the center of a region that is dominated by a single class; it removes examples that are classified correctly as well as examples that are classified incorrectly from the dataset. This explains its much higher compression rates. Remark: For a more detailed evaluation of SCE, Wilson Editing, and other editing techniques see [EZV04] and [ZWE05].

26. Future Direction of this Research p Data Set’ Data Set IDLA IDLA Classifier C Classifier C’ Goal: Find p, such that C’ is more accurate than C or C and C’ have approximately the same accuracy, but C’ can be learnt more quickly and/or C’ classifies new examples more quickly.

27. O OOx x x OOOx x x O OOx x x Supervised Clustering vs. Clustering the Examples of Each Separately Approaches to discover subclasses of a given class: • Cluster the examples of each class separately • Use supervised clustering Figure 4. Supervised clustering editing vs. clustering each class (x and o) separately. Remark: A traditional clustering algorithm, such as k-medoids, would pick o as the cluster representative, because it is “blind” on how the examples of other classes distribute, whereas supervised clustering would pick o as the representative; obviously, o is not a good choice for editing, because it attracts points of the class x, which leads to misclassifications.

28. Applications of Supervised Clustering • 3.b Class Decomposition (see also [VAE03]) Attribute 1 Attribute 1 Attribute 2 Attribute 2 Attribute 1 • Simple classifiers: • Encompass a small class of approximating functions. • Limited flexibility in their decision boundaries Attribute 2

29. Naïve Bayes vs. Naïve Bayes with Class Decomposition

30. 3c. Using Clustering in Distance Function Learning Example: How to Find Similar Patients? The following relation is given (with 10000 tuples): Patient(ssn, weight, height, cancer-sev, eye-color, age,…) • Attribute Domains • ssn: 9 digits • weight between 30 and 650; mweight=158 sweight=24.20 • height between 0.30 and 2.20 in meters; mheight=1.52 sheight=19.2 • cancer-sev: 4=serious 3=quite_serious 2=medium 1=minor • eye-color: {brown, blue, green, grey } • age: between 3 and 100; mage=45 sage=13.2 Task: Define Patient Similarity

31. CAL-FULL/UH Database Clustering & Similarity Assessment Environments Training Data A set of clusters Library of clustering algorithms Learning Tool Object View Similarity measure Clustering Tool Library of similarity measures Similarity Measure Tool Data Extraction Tool User Interface Today’s topic Type and weight information Default choices and domain information DBMS For more details: see [RE05]

32. Similarity Assessment Framework and Objectives • Objective: Learn a good distance function q for classification tasks. • Our approach: Apply a clustering algorithm with the distance function q to be evaluated that returns a number of clusters k. The more pure the obtained clusters are the better is the quality of q. • Our goal is to learn the weights of an object distance function q such that all the clusters are pure (or as pure is possible); for more details see [ERBV05] and [BECV05] papers.

33. Idea: Coevolving Clusters and Distance Functions Weight Updating Scheme / Search Strategy Clustering X Distance Function Q Cluster “Bad” distance function Q1 “Good” distance function Q2 q(X) Clustering Evaluation o o o x x o x o o o x o o o Goodness of the Distance Function Q o o x x x x x x

34. Idea Inside/Outside Weight Updating o:=examples belonging to majority class x:= non-majority-class examples Cluster1: distances with respect to Att1 xo oo ox Action: Increase weight of Att1 Cluster1: distances with respect to Att2 Idea: Move examples of the majority class closer to each other o o xx o o Action: Decrease weight for Att2

35. Sample Run of IOWU for Diabetes Dataset Graph produced by Abraham Bagherjeiran

36. Research Framework Distance Function Learning Distance Function Evaluation Weight-Updating Scheme / Search Strategy K-Means Inside/Outside Weight Updating [ERBV04] Supervised Clustering Work By Karypis Randomized Hill Climbing NN-Classifier Adaptive Clustering Other Research … [BECV05] …

37. 3.d Discovery of Interesting Regions for Spatial Data Mining Task: 2D/3D datasets are given; discover interesting regions in the dataset that maximize a given fitness function; examples of region discovery include: • Discover regions that have significant deviations from the prior probability of a class; e.g. regions in the state of Wyoming were people are very poor or not poor at all • Discover regions that have significant variation in the income (fitness is defined based on the variance with respect to income in a region) • Discover regions for congressional redistricting • Discover congested regions for traffic control Remark: We use (supervised) clustering to discover such regions; regions are implicitly defined by the set of points that belong to a cluster.

38. Wyoming Map

39. Household Income in 1999: Wyoming Park County

40. Clusters  Regions Example: 2 clusters in red and blue are given; regions are defined by using a Voronoi diagram based on a NN classifier with k=7; region are in grey and white.

41. An Evaluation Scheme for Discovering Regions that Deviate from the Prior Probability of a Class C Let prior(C)= |C|/n p(c,C)= percentage of examples in c that belong to class C Reward(c) is computed based on p(c.C), prior(C) , and based on the following parameters: g1,g2,R+,R- (g11g2; R+,R-0) relying on the following interpolation function (e.g. g1=0.8,g2=1.2,R+ =1, R-=1): qC(X)= ScX (t(p(c,C),prior(C),g1,g2,R+,R-) *|c|)b/n) with b>1 (typically, 1.0001<b<2); the idea is that increases in cluster-size rewarded nonlinearly, favoring clusters with more points as long as |c|*t(…) increases. Reward(c) R+ R- t(p(C),prior(C),g1,g2,R+,R-) prior(C)*g1 prior(C) prior(C)*g2 1 p(c,C)

42. Ch. Eick Example: Discovery of “Interesting Regions” in Wyoming Census 2000 Datasets

43. Supervised Clustering ---Algorithms and Applications Organization of the Talk Supervised Clustering Representative-based Supervised Clustering Algorithms Applications: Using Supervised Clustering for for Dataset Editing for Class Decomposition for Distance Function Learning for Region Discovery in Spatial Datasets Other Activities I am Involved With

44. An Environment for Adaptive (Supervised) Clusteringfor Summary Generation Applications Clustering Summary Clustering Algorithm Inputs changes Adaptation System Evaluation System feedback Past Experience Domain Expert quality Fitness Functions (predefined) q(X), … Idea: Development of a Generic Clustering/Feedback/Adaptation Architecture whose objective is to facilitate the search for clusterings that maximize an internally and/or an externally given reward function (for some initial ideas see [BECV05])

45. Clustering Algorithm Inputs Data Set Examples Data Set Feature Representation Distance Function Clustering Algorithm Parameters Fitness Function Parameters Background Knowledge

46. Research Topics 2005/2006 • Inductive Learning/Data Mining • Decision trees, nearest neighbor classifiers • Using clustering to enhance classification algorithms • Making sense of data • Supervised Clustering • Learning subclasses • Supervised clustering algorithms that learn clusters with arbitrary shape • Using supervised clustering for region discovery • Adaptive clustering • Tools for Similarity Assessment and Distance Function Learning • Data Set Compression and Creating Meta Knowledge for Local Learning Techniques • Comparative studies • Creating maps and other data set signatures for datasets based on editing, SC, and other techniques • Traditional Clustering • Data Mining and Information Retrieval for Structured Data • Other: Evolutionary Computing, File Prediction, Ontologies, Heuristic Search, Reinforcement Learning, Data Models. Remark: Topics that were “covered” in this talk are in blue

47. Links to 7 Papers [VAE03] R. Vilalta, M. Achari, C. Eick, Class Decomposition via Clustering: A New Framework for Low-Variance Classifiers, in Proc. IEEE International Conference on Data Mining (ICDM), Melbourne, Florida, November 2003. http://www.cs.uh.edu/~ceick/kdd/VAE03.pdf [EZZ04] C. Eick, N. Zeidat, Z. Zhao, Supervised Clustering --- Algorithms and Benefits, short version appeared in Proc. International Conference on Tools with AI (ICTAI), Boca Raton, Florida, November 2004. http://www.cs.uh.edu/~ceick/kdd/EZZ04.pdf [EZV04] C. Eick, N. Zeidat, R. Vilalta, Using Representative-Based Clustering for Nearest Neighbor Dataset Editing, in Proc. IEEE International Conference on Data Mining (ICDM), Brighton, England, November 2004. http://www.cs.uh.edu/~ceick/kdd/EZV04.pdf [RE05] T. Ryu and C. Eick, A Clustering Methodology and Tool, in Information Sciences 171(1-3): 29-59 (2005). http://www.cs.uh.edu/~ceick/kdd/RE05.doc [ERBV04] C. Eick, A. Rouhana, A. Bagherjeiran, R. Vilalta, Using Clustering to Learn Distance Functions for Supervised Similarity Assessment, in Proc. MLDM'05, Leipzig, Germany, July 2005. http://www.cs.uh.edu/~ceick/kdd/ERBV05.pdf [ZWE05] N. Zeidat, S. Wang, C. Eick,, Editing Techniques: a Comparative Study, submitted for publication. http://www.cs.uh.edu/~ceick/kdd/ZWE05.pdf [BECV05] A. Bagherjeiran, C. Eick, C.-S. Chen, R. Vilalta, Adaptive Clustering: Obtaining Better Clusters Using Feedback and Past Experience, submitted for publication. http://www.cs.uh.edu/~ceick/kdd/BECV05.pdf