Ch. Eick: Supervised Clustering --- Algorithms and Applications Supervised Clustering --- Algorithms and Applications Christoph F. Eick Department of Computer

Ch. Eick: Supervised Clustering --- Algorithms and Applications

Supervised Clustering ---Algorithms and Applications

Christoph F. EickDepartment of Computer Science

University of Houston

Organization of the Talk1. 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


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)


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

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

Different Forms of Clustering


Motivation: Finding Subclasses using SC

Attribute2

Ford TrucksAttribute1

Ford SUV

Ford Vans

GMC Trucks

GMC Van

GMC SUV

:Ford

:GMC


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.


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.


Representative-Based Supervised Clustering … (Continued)

Attribute2

Attribute1

1

2

3

4


Representative-Based Supervised Clustering … (continued)

Attribute2

Attribute1

1

2

3

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).


SC Algorithms Currently Investigated

1. Supervised Partitioning Around Medoids (SPAM).

2. Single Representative Insertion/Deletion Steepest Decent Hill Climbing with Randomized Restart (SRIDHCR).

3. Top Down Splitting Algorithm (TDS).

4. Supervised Clustering using Evolutionary Computing (SCEC)

5. Agglomerative Hierarchical Supervised Clustering (AHSC)

6. Grid-Based Supervised Clustering (GRIDSC)

Remark: For a more detailed discussion of SCEC and SRIDHCR see [EZZ04]


A Fitness Function for Supervised Clustering

q(X) := Impurity(X) + β*Penalty(k)

ck

ck

0

n

ck

Penalty(k) and

,n

ExamplesMinority of # )Impurity(X where 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) vs k

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 5 10 26 53k

Pe

na

lty(k

)

k

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


Algorithm SRIDHCR (Greedy Hill Climbing)

REPEAT r TIMEScurr := 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:=sELSE IF q(s)=q(curr) AND |s|>|curr| THEN Curr:=sELSE 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 .

• Reports the best clustering found in r runs

Initial generation Next generation

Copy

Crossover

Mutation

Final generation

Supervised Clustering using Evolutionary Computing: SCEC

Result:

Best solution


The complete flow chart of SCEC

InitializeSolutions

Clusteringon S[i]

Evaluationon S[i]

IntermediateResult

Record Best Solution, Q

ComposePopulation S

Mutation

New S’[i]

Crossover Copy

K-tournament

Evaluate a Population

Loop PS times

Loop PS times

Create next Generation

Best Solution, Q, SummaryExit

Loop N times

The complete flow chart of SCEC

InitializeSolutions

Clusteringon S[i]

Evaluationon S[i]

IntermediateResult

Record Best Solution, Q

ComposePopulation S

Mutation

New S’[i]

Crossover Copy

K-tournament

Evaluate a Population

Loop PS times

Loop PS times

Create next Generation

Best Solution, Q, SummaryExit

Loop N times


Complex1 Dataset

Complex1-Reduced

0

50

100

150

200

250

300

350

400

450

500

0 200 400 600 800

Class-0

Class-1

Class-2

Class-3

Class-4

Class-5

Class-6

Class-7

Class-8


Supervised Clustering ResultComplex-1-Reduced, SRIDHCR, Beta=0.25, r=50

0

50

100

150

200

250

300

350

400

450

500

0 100 200 300 400 500 600 700 800






a. for Dataset Editing

b. for Class Decomposition

c. for Distance Function Learning

d. for Region Discovery in Spatial Datasets



Nearest Neighbour Rule

Consider a two class problem where each sample consists of two measurements (x,y).

k = 1

k = 3

For a given query point q, assign the class of the nearest neighbour.

Compute the k nearest neighbours and assign the class by majority vote.

Problem: requires “good” distance function


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


Wilson Editing• Wilson 1972• Remove points that do not agree with the majority of their k nearest neighbours

Wilson editing with k=7

Original data

Earlier example

Wilson editing with k=7

Original data

Overlapping classes


RSC Dataset Editing

A

C

E

a. Dataset clustered using supervised clustering.

b. Dataset edited using cluster representatives.

Attribute1

D

B

Attribute2

F

Attribute2

Attribute1


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 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.


Table 2: Prediction Accuracy for the four classifiers.β NR Wilson 1-NN C4.5

Glass (214)0.1 0.636 0.607 0.692 0.6770.4 0.589 0.607 0.692 0.6771.0 0.575 0.607 0.692 0.677

Heart-Stat Log (270)0.1 0.796 0.804 0.767 0.7820.4 0.833 0.804 0.767 0.7821.0 0.838 0.804 0.767 0.782

Diabetes (768)0.1 0.736 0.734 0.690 0.7450.4 0.736 0.734 0.690 0.7451.0 0.745 0.734 0.690 0.745

Vehicle (846)0.1 0.667 0.716 0.700 0.7230.4 0.667 0.716 0.700 0.7231.0 0.665 0.716 0.700 0.723

Heart-H (294)0.1 0.755 0.809 0.783 0.8020.4 0.793 0.809 0.783 0.8021.0 0.809 0.809 0.783 0.802

Waveform (5000)0.1 0.834 0.796 0.768 0.7810.4 0.841 0.796 0.768 0.7811.0 0.837 0.796 0.768 0.781

Iris-Plants (150)0.1 0.947 0.936 0.947 0.9470.4 0.973 0.936 0.947 0.9471.0 0.953 0.936 0.947 0.947

Segmentation (2100)0.1 0.938 0.966 0.956 0.9680.4 0.919 0.966 0.956 0.9681.0 0.890 0.966 0.956 0.968


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

Avg. k [Min-Max]

for SCE

SCE Compression

Rate (%)

Wilson Compression

Rate (%)Glass (214)

0.1 34 [28-39] 84.3 270.4 25 [19-29] 88.4 271.0 6 [6 – 6] 97.2 27

Heart-Stat Log (270)0.1 15 [12-18] 94.4 22.40.4 2 [2 – 2] 99.3 22.41.0 2 [2 – 2] 99.3 22.4

Diabetes (768)0.1 27 [22-33] 96.5 30.00.4 9 [2-18] 98.8 30.01.0 2 [2 – 2] 99.7 30.0

Vehicle (846)0.1 57 [51-65] 97.3 30.50.4 38 [ 26-61] 95.5 30.51.0 14 [ 9-22] 98.3 30.5

Heart-H (294)0.1 14 [11-18] 95.2 21.90.4 2 99.3 21.91.0 2 99.3 21.9

Waveform (5000)0.1 104 [79-117] 97.9 23.40.4 28 [20-39] 99.4 23.41.0 4 [3-6] 99.9 23.4

Iris-Plants (150)0.1 4 [3-8] 97.3 6.00.4 3 [3 – 3] 98.0 6.01.0 3 [3 – 3] 98.0 6.0

Segmentation (2100)0.1 57 [48-65] 97.3 2.80.4 30 [24-37] 98.6 2.81.0 14 99.3 2.8


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].


Future Direction of this Research

Data Set Data Set’

Goal: Find 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.

IDLAIDLA

Classifier C Classifier C’


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

O OOx x xO OOx x xO OOx x x

Figure 4. Supervised clustering editing vs. clustering each class (x and o) separately.

Remark: A traditional clustering algorithm, such as k-medoids, would pick oas the cluster representative, because it is “blind” on how the examples ofother classes distribute, whereas supervised clustering would pick o as the representative; obviously, o is not a good choice for editing, because it attractspoints of the class x, which leads to misclassifications.


Simple classifiers:

• Encompass a small class of approximating functions.

• Limited flexibility in their decision boundaries

Attribute 1

Attribute 2

Attribute 1

Attribute 2

Attribute 2

Applications of Supervised Clustering3.b Class Decomposition (see also [VAE03])

Attribute 1


Naïve Bayes vs. Naïve Bayes with Class Decomposition

Dataset Naïve Bayes (NB)

NB with Class Decomposition

Improvement

Diabetes 76.56 77.08 0.52% Heart-H 79.73 70.27 9.46% Segment 68.00 75.045 7.05% Vehicle 45.02 68.25 23.23%


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

3c. Using Clustering in Distance Function Learning


Data Extraction Tool

DBMS

Clustering Tool

User Interface

A set of clusters

Similarity measure

Similarity Measure Tool

Default choices and domain information

Library of similarity measures

Type and weight

information

ObjectView

Library of clustering algorithms

CAL-FULL/UH Database Clustering & Similarity Assessment Environments

CAL-FULL/UH Database Clustering & Similarity Assessment Environments

LearningTool

TrainingData

Today’stopic

For more details: see [RE05]


Similarity Assessment Framework and Objectives

• Objective: Learn a good distance function for classification tasks.• Our approach: Apply a clustering algorithm with the distance function to

be evaluated that returns a number of clusters k. The more pure the obtained clusters are the better is the quality of .

• Our goal is to learn the weights of an object distance function such that all the clusters are pure (or as pure is possible); for more details see [ERBV05] and [BECV05] papers.

f

fjif

ji

wpf

woopfoo

1

*)(1

,),(


Idea: Coevolving Clusters and Distance Functions

Clustering X DistanceFunction Cluster

Goodness of the Distance Function

q(X) Clustering Evaluation

Weight Updating Scheme /Search Strategy

x

x x

x

o

oo

o

xx

oo

xx

oo

oo

“Bad” distance function “Good” distance function

xx

oo


Idea Inside/Outside Weight Updating

Cluster1: distances with respect to Att1

Action: Increase weight of Att1

Action: Decrease weight for Att2

Cluster1: distances with respect to Att2Idea: Move examples of the majority class closer to each other

xo oo ox

o o xx o o

o:=examples belonging to majority classx:= non-majority-class examples


Sample Run of IOWU for Diabetes Dataset

Graph produced by Abraham Bagherjeiran


Research Framework Distance Function Learning

RandomizedHill Climbing

AdaptiveClustering

Inside/OutsideWeight Updating

K-Means

SupervisedClustering

NN-Classifier

Weight-Updating Scheme /Search Strategy

Distance FunctionEvaluation

… …

WorkBy Karypis

[BECV05]

Other Research

[ERBV04]


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.


Wyoming Map


Household Income in 1999: Wyoming Park County


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.

An Evaluation Scheme for Discovering Regions that Deviate from the Prior Probability of a Class C

Letprior(C)= |C|/np(c,C)= percentage of examples in c that belong to class CReward(c) is computed based on p(c.C), prior(C) , and based on the following parameters: 1,2,R+,R112; R+,R0) relying on the following interpolation function (e.g. 1=0.8,2=1.2,R+ =1, R=1):

p(c,C)

Reward(c)

1prior(C)prior(C)*1 prior(C)*2

R+

R

qC(X)= cX ((p(c,C),prior(C),1,2,R+,R-) |c|)/n)with >1 (typically, 1.0001<<2); the idea is that increases incluster-size rewarded nonlinearly, favoring clusters with more points as long as |c|*(…) increases.

(p(C),prior(C),1,2,R+,R


Example: Discovery of “Interesting Regions” in Wyoming Census 2000 Datasets

Ch. Eick






a. for Dataset Editing

b. for Class Decomposition

c. for Distance Function Learning

d. for Region Discovery in Spatial Datasets



An Environment for Adaptive (Supervised) Clusteringfor Summary Generation Applications

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])

ClusteringAlgorithm

Inputs Clustering

quality

AdaptationSystem

changes

Past Experience

feedback

EvaluationSystem

Summary

Domain Expert

q(X),…

FitnessFunctions

(predefined)


Clustering Algorithm Inputs

Data Set Examples

Data Set Feature Representation

Distance Function

Clustering Algorithm Parameters

Fitness Function Parameters

Background Knowledge


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


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

Documents

Ch. Eick: Supervised Clustering --- Algorithms and Applications Supervised Clustering --- Algorithms and Applications Christoph F. Eick Department of Computer