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Supervised Clustering --Algorithms and Applications Christoph F. Eick Department of Computer Science University of Houston Organization of the Talk 1. Supervised Clustering 2. Representative-based Supervised Clustering Algorithms 3. Applications: Using Supervised Clustering for a. Dataset Editing b. Class Decomposition c. Distance Function Learning d. Region Discovery in Spatial Datasets 4. Other Activities I am Involved With Ch. Eick: Supervised Clustering --- Algorithms and Applications 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) Ch. Eick: Supervised Clustering --- Algorithms and Applications 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. Ch. Eick: Supervised Clustering --- Algorithms and Applications 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)). Ch. Eick: Supervised Clustering --- Algorithms and Applications Motivation: Finding Subclasses using SC Attribute1 Ford Trucks :Ford :GMC GMC Trucks GMC Van Ford Vans Ford SUV GMC SUV Attribute2 Ch. Eick: Supervised Clustering --- Algorithms and Applications 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 semisupervised 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. Ch. Eick: Supervised Clustering --- Algorithms and Applications 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. Ch. Eick: Supervised Clustering --- Algorithms and Applications Representative-Based Supervised Clustering … (Continued) Attribute1 2 1 3 4 Attribute2 Ch. Eick: Supervised Clustering --- Algorithms and Applications Representative-Based Supervised Clustering … (continued) Attribute1 2 1 3 4 Attribute2 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). Ch. Eick: Supervised Clustering --- Algorithms and Applications SC Algorithms Currently Investigated 1. 2. 3. 4. 5. 6. 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] Ch. Eick: Supervised Clustering --- Algorithms and Applications A Fitness Function for Supervised Clustering q(X) := Impurity(X) + β*Penalty(k) where Impurity(X ) # of Minority Examples , n k c and Penalty(k) n 0 kc 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 kc Penalty(k) Penalty(k) vs k Penalty(k) increase sub-linearly. 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 5 10 26 k 53 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 k Ch. Eick: Supervised Clustering --- Algorithms and Applications Algorithm SRIDHCR (Greedy Hill Climbing) REPEAT r TIMES curr := a randomly created set of representatives (with size between c+1 and 2*c) WHILE NOT DONE DO 1. Create new solutions S by adding a single non-representative to curr and by removing a single representative from curr 2. Determine the element s in S for which q(s) is minimal (if there is more than one minimal element, randomly pick one) 3. 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. 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 Ch. Eick: Supervised Clustering --- Algorithms and Applications Supervised Clustering using Evolutionary Computing: SCEC Initial generation Next generation Mutation Crossover Copy Final generation Best solution Result: Initialize Initialize Solutions Solutions Compose Compose Population Population S S Evaluate Evaluate a a Population Population Clustering Clustering onon S[i] S[i] Loop Loop PSPS times times The complete complete The flow chart chart of of flow SCEC SCEC Loop Loop NN times times Evaluation Evaluation onon S[i] S[i] Intermediate Intermediate Result Result Record Record Best Best Solution, Solution, QQ Exit Exit Best Best Solution, Solution, Q,Q, Summary Summary Create Create next next Generation Generation K-tournament K-tournament Loop Loop PSPS times times Mutation Mutation Crossover Crossover Copy Copy New New S’[i] S’[i] Ch. Eick: Supervised Clustering --- Algorithms and Applications Complex1 Dataset Complex1-Reduced 500 450 Class-0 400 Class-1 350 Class-2 300 Class-3 Class-4 250 200 Class-5 150 Class-6 100 Class-7 50 Class-8 0 0 200 400 600 800 Ch. Eick: Supervised Clustering --- Algorithms and Applications Supervised Clustering Result Complex-1-Reduced, SRIDHCR, Beta=0.25, r=50 500 450 400 350 300 250 200 150 100 50 0 0 100 200 300 400 500 600 700 800 Ch. Eick: Supervised Clustering --- Algorithms and Applications Supervised Clustering --Algorithms and Applications Organization of the Talk 1. Supervised Clustering 2. Representative-based Supervised Clustering Algorithms 3. Applications: Using Supervised Clustering for a. for Dataset Editing b. for Class Decomposition c. for Distance Function Learning d. for Region Discovery in Spatial Datasets 4. Other Activities I am Involved With Ch. Eick: Supervised Clustering --- Algorithms and Applications 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 Ch. Eick: Supervised Clustering --- Algorithms and Applications 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 Ch. Eick: Supervised Clustering --- Algorithms and Applications Wilson Editing • • Wilson 1972 Remove points that do not agree with the majority of their k nearest neighbours Earlier example Original data Wilson editing with k=7 Overlapping classes Original data Wilson editing with k=7 Ch. Eick: Supervised Clustering --- Algorithms and Applications RSC Dataset Editing Attribute1 A Attribute1 B D C F E Attribute2 a. Dataset clustered using supervised clustering. Attribute2 b. Dataset edited using cluster representatives. Ch. Eick: Supervised Clustering --- Algorithms and Applications 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. Ch. Eick: Supervised Clustering --- Algorithms and Applications Table 2: Prediction Accuracy for the four classifiers. β NR Wilson 1-NN C4.5 0.636 0.589 0.575 0.607 0.607 0.607 0.692 0.692 0.692 0.677 0.677 0.677 0.796 0.833 0.838 0.804 0.804 0.804 0.767 0.767 0.767 0.782 0.782 0.782 0.736 0.736 0.745 0.734 0.734 0.734 0.690 0.690 0.690 0.745 0.745 0.745 0.667 0.667 0.665 0.716 0.716 0.716 0.700 0.700 0.700 0.723 0.723 0.723 0.755 0.793 0.809 0.809 0.809 0.809 0.783 0.783 0.783 0.802 0.802 0.802 0.834 0.841 0.837 0.796 0.796 0.796 0.768 0.768 0.768 0.781 0.781 0.781 0.947 0.973 0.953 0.936 0.936 0.936 0.947 0.947 0.947 0.947 0.947 0.947 0.938 0.919 0.890 0.966 0.966 0.966 0.956 0.956 0.956 0.968 0.968 0.968 Glass (214) 0.1 0.4 1.0 Heart-Stat Log (270) 0.1 0.4 1.0 Diabetes (768) 0.1 0.4 1.0 Vehicle (846) 0.1 0.4 1.0 Heart-H (294) 0.1 0.4 1.0 Waveform (5000) 0.1 0.4 1.0 Iris-Plants (150) 0.1 0.4 1.0 Segmentation (2100) 0.1 0.4 1.0 Ch. Eick: Supervised Clustering --- Algorithms and Applications Table 3: Dataset Compression Rates for SCE and Wilson Editing. b Glass (214) 0.1 0.4 1.0 Heart-Stat Log (270) 0.1 0.4 1.0 Diabetes (768) 0.1 0.4 1.0 Vehicle (846) 0.1 0.4 1.0 Heart-H (294) 0.1 0.4 1.0 Waveform (5000) 0.1 0.4 1.0 Iris-Plants (150) 0.1 0.4 1.0 Segmentation (2100) 0.1 0.4 1.0 Avg. k [Min-Max] for SCE SCE Compression Rate (%) Wilson Compression Rate (%) 34 [28-39] 25 [19-29] 6 [6 – 6] 84.3 88.4 97.2 27 27 27 15 [12-18] 2 [2 – 2] 2 [2 – 2] 94.4 99.3 99.3 22.4 22.4 22.4 27 [22-33] 9 [2-18] 2 [2 – 2] 96.5 98.8 99.7 30.0 30.0 30.0 57 [51-65] 38 [ 26-61] 14 [ 9-22] 97.3 95.5 98.3 30.5 30.5 30.5 14 [11-18] 2 2 95.2 99.3 99.3 21.9 21.9 21.9 104 [79-117] 28 [20-39] 4 [3-6] 97.9 99.4 99.9 23.4 23.4 23.4 4 [3-8] 3 [3 – 3] 3 [3 – 3] 97.3 98.0 98.0 6.0 6.0 6.0 57 [48-65] 30 [24-37] 14 97.3 98.6 99.3 2.8 2.8 2.8 Ch. Eick: Supervised Clustering --- Algorithms and Applications 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]. Ch. Eick: Supervised Clustering --- Algorithms and Applications Future Direction of this Research Data Set IDLA Classifier C p Data Set’ IDLA 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. Ch. Eick: Supervised Clustering --- Algorithms and Applications Supervised Clustering vs. Clustering the Examples of Each Separately Approaches to discover subclasses of a given class: 1. Cluster the examples of each class separately 2. Use supervised clustering Figure 4. Supervised clustering editing vs. clustering each class (x and o) separately. O O O OOx OOx OOx x x x x x x 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. Ch. Eick: Supervised Clustering --- Algorithms and Applications Applications of Supervised Clustering 3.b Class Decomposition (see also [VAE03]) Attribute 1 Attribute 1 Attribute 2 Attribute 2 Simple classifiers: Attribute 1 • Encompass a small class of approximating functions. • Limited flexibility in their decision boundaries Attribute 2 Ch. Eick: Supervised Clustering --- Algorithms and Applications Naïve Bayes vs. Naïve Bayes with Class Decomposition Dataset Diabetes Heart-H Segment Vehicle Naïve Bayes (NB) 76.56 79.73 68.00 45.02 NB with Class Decomposition 77.08 70.27 75.045 68.25 Improvement 0.52% 9.46% 7.05% 23.23% Ch. Eick: Supervised Clustering --- Algorithms and Applications 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 Ch. Eick: Supervised Clustering --- Algorithms and Applications CAL-FULL/UH Database Clustering & Similarity Assessment Environments Library of clustering algorithms Training Data A set of clusters Learning Tool Object View Data Extraction Tool DBMS For more details: see [RE05] Clustering Tool User Interface Similarity measure Similarity Measure Tool Default choices and domain information Library of similarity measures Type and weight information Today’s topic Ch. Eick: Supervised Clustering --- Algorithms and Applications Similarity Assessment Framework and Objectives q (o , o ) i j p qf (oi oj ) * wf f 1 p wf f 1 , • 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. Ch. Eick: Supervised Clustering --- Algorithms and Applications Idea: Coevolving Clusters and Distance Functions Weight Updating Scheme / Search Strategy Clustering X Cluster q(X) Clustering Evaluation Goodness of the Distance Function Q Distance Function Q “Bad” distance function Q1 “Good” distance function Q2 o o x oox x x o x o x o oo o o o x x x x Ch. Eick: Supervised Clustering --- Algorithms and Applications 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 Idea: Move examples of the majority class closer to each other Cluster1: distances with respect to Att2 o o xx o o Action: Decrease weight for Att2 Ch. Eick: Supervised Clustering --- Algorithms and Applications Sample Run of IOWU for Diabetes Dataset Graph produced by Abraham Bagherjeiran Ch. Eick: Supervised Clustering --- Algorithms and Applications Research Framework Distance Function Learning Weight-Updating Scheme / Search Strategy Distance Function Evaluation Inside/Outside Weight Updating K-Means [ERBV04] Randomized Hill Climbing Other Research [BECV05] Adaptive Clustering … Supervised Clustering Work By Karypis NN-Classifier … Ch. Eick: Supervised Clustering --- Algorithms and Applications 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. Ch. Eick: Supervised Clustering --- Algorithms and Applications Wyoming Map Ch. Eick: Supervised Clustering --- Algorithms and Applications Household Income in 1999: Wyoming Park County Ch. Eick: Supervised Clustering --- Algorithms and Applications 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. Ch. Eick: Supervised Clustering --- Algorithms and Applications 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 (g11g2; R+,R0) relying on the following interpolation function (e.g. g1=0.8,g2=1.2,R+ =1, R=1): qC(X)= cX (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) Ch. Eick Example: Discovery of “Interesting Regions” in Wyoming Census 2000 Datasets Ch. Eick: Supervised Clustering --- Algorithms and Applications Supervised Clustering --Algorithms and Applications Organization of the Talk 1. Supervised Clustering 2. Representative-based Supervised Clustering Algorithms 3. Applications: Using Supervised Clustering for a. for Dataset Editing b. for Class Decomposition c. for Distance Function Learning d. for Region Discovery in Spatial Datasets 4. Other Activities I am Involved With Ch. Eick: Supervised Clustering --- Algorithms and Applications An Environment for Adaptive (Supervised) Clustering for Summary Generation Applications Inputs Clustering Algorithm Clustering Summary changes Adaptation System Evaluation System feedback Past Experience quality Domain Expert q(X), Fitness … Functions (predefined) 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]) Ch. Eick: Supervised Clustering --- Algorithms and Applications Clustering Algorithm Inputs Data Set Examples Data Set Feature Representation Distance Function Clustering Algorithm Parameters Fitness Function Parameters Background Knowledge Ch. Eick: Supervised Clustering --- Algorithms and Applications 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 Ch. Eick: Supervised Clustering --- Algorithms and Applications 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 Ch. Eick: Supervised Clustering --- Algorithms and Applications