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Supervised Clustering --- Algorithms and Applications

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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

- 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)

- 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)).

Attribute1

Ford Trucks

:Ford

:GMC

GMC Trucks

GMC Van

Ford Vans

Ford SUV

Attribute2

GMC SUV

- 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.

- 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.

2

Attribute1

1

3

Attribute2

4

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).

- 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]

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

- 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

Supervised Clustering using Evolutionary Computing: SCEC

Initial generation

Next generation

Mutation

Crossover

Copy

Best solution

Final generation

Result:

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

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

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

- 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 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

Attribute1

Attribute1

B

A

D

C

F

E

Attribute2

Attribute2

a. Dataset clustered using supervised clustering.

b. Dataset edited using cluster representatives.

- 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.

- 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].

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.

O OOx x x

OOOx x x

O OOx x x

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.

- 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

3c. Using Clustering in Distance Function Learning

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

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]

- 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.

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

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

Graph produced by Abraham Bagherjeiran

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]

…

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.

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.

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+,R-0) relying on the following interpolation

function (e.g. g1=0.8,g2=1.2,R+ =1, R-=1):

qC(X)= ScX (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

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

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])

Data Set Examples

Data Set Feature Representation

Distance Function

Clustering Algorithm Parameters

Fitness Function Parameters

Background Knowledge

- 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

[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