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Data Mining
Classification and Clustering Techniques
Introduction to Data Mining
by
Tan, Steinbach, Kumar
Thank you very much for all materials
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
1
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.
Illustrating Classification Task
Tid
Attrib1
Attrib2
Attrib3
Class
1
Yes
Large
125K
No
2
No
Medium
100K
No
3
No
Small
70K
No
4
Yes
Medium
120K
No
5
No
Large
95K
Yes
6
No
Medium
60K
No
7
Yes
Large
220K
No
8
No
Small
85K
Yes
9
No
Medium
75K
No
10
No
Small
90K
Yes
Learning
algorithm
Induction
Learn
Model
Model
10
Training Set
Tid
Attrib1
Attrib2
11
No
Small
55K
?
12
Yes
Medium
80K
?
13
Yes
Large
110K
?
14
No
Small
95K
?
15
No
Large
67K
?
10
Test Set
Attrib3
Apply
Model
Class
Deduction
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
Classification Techniques
•
•
•
•
•
Decision Tree based Methods
Rule-based Methods
Memory based reasoning
Neural Networks
Naïve Bayes and Bayesian Belief
Networks
• Support Vector Machines
Example of a Decision Tree
Tid Refund Marital
Status
Taxable
Income Cheat
1
Yes
Single
125K
No
2
No
Married
100K
No
3
No
Single
70K
No
4
Yes
Married
120K
No
5
No
Divorced 95K
Yes
6
No
Married
No
7
Yes
Divorced 220K
No
8
No
Single
85K
Yes
9
No
Married
75K
No
10
No
Single
90K
Yes
60K
Splitting Attributes
Refund
Yes
No
NO
MarSt
Single, Divorced
TaxInc
< 80K
NO
NO
> 80K
YES
10
Training Data
Married
Model: Decision Tree
Another Example of Decision
Tree
MarSt
10
Tid Refund Marital
Status
Taxable
Income Cheat
1
Yes
Single
125K
No
2
No
Married
100K
No
3
No
Single
70K
No
4
Yes
Married
120K
No
5
No
Divorced 95K
Yes
6
No
Married
No
7
Yes
Divorced 220K
No
8
No
Single
85K
Yes
9
No
Married
75K
No
10
No
Single
90K
Yes
60K
Married
NO
Single,
Divorced
Refund
No
Yes
NO
TaxInc
< 80K
NO
> 80K
YES
There could be more than one tree that
fits the same data!
Decision Tree Classification
Task
Tid
Attrib1
Attrib2
Attrib3
Class
1
Yes
Large
125K
No
2
No
Medium
100K
No
3
No
Small
70K
No
4
Yes
Medium
120K
No
5
No
Large
95K
Yes
6
No
Medium
60K
No
7
Yes
Large
220K
No
8
No
Small
85K
Yes
9
No
Medium
75K
No
10
No
Small
90K
Yes
Tree
Induction
algorithm
Induction
Learn
Model
Model
10
Training Set
Tid
Attrib1
Attrib2
11
No
Small
55K
?
12
Yes
Medium
80K
?
13
Yes
Large
110K
?
14
No
Small
95K
?
15
No
Large
67K
?
10
Test Set
Attrib3
Apply
Model
Class
Deduction
Decision
Tree
Apply Model to Test Data
Test Data
Start from the root of tree.
Refund
Yes
10
No
NO
MarSt
Single, Divorced
TaxInc
< 80K
NO
Married
NO
> 80K
YES
Refund Marital
Status
Taxable
Income Cheat
No
80K
Married
?
Apply Model to Test Data
Test Data
Refund
Yes
10
No
NO
MarSt
Single, Divorced
TaxInc
< 80K
NO
Married
NO
> 80K
YES
Refund Marital
Status
Taxable
Income Cheat
No
80K
Married
?
Apply Model to Test Data
Test Data
Refund
Yes
10
No
NO
MarSt
Single, Divorced
TaxInc
< 80K
NO
Married
NO
> 80K
YES
Refund Marital
Status
Taxable
Income Cheat
No
80K
Married
?
Apply Model to Test Data
Test Data
Refund
Yes
10
No
NO
MarSt
Single, Divorced
TaxInc
< 80K
NO
Married
NO
> 80K
YES
Refund Marital
Status
Taxable
Income Cheat
No
80K
Married
?
Apply Model to Test Data
Test Data
Refund
Yes
10
No
NO
MarSt
Single, Divorced
TaxInc
< 80K
NO
Married
NO
> 80K
YES
Refund Marital
Status
Taxable
Income Cheat
No
80K
Married
?
Apply Model to Test Data
Test Data
Refund
Yes
Refund Marital
Status
Taxable
Income Cheat
No
80K
Married
?
10
No
NO
MarSt
Single, Divorced
TaxInc
< 80K
NO
Married
NO
> 80K
YES
Assign Cheat to “No”
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
Intra-cluster
distances are
minimized
Inter-cluster
distances are
maximized
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
Discovered Clusters
1
2
3
4
Applied-Matl-DOWN,Bay-Network-Down,3-COM-DOWN,
Cabletron-Sys-DOWN,CISCO-DOWN,HP-DOWN,
DSC-Comm-DOWN,INTEL-DOWN,LSI-Logic-DOWN,
Micron-Tech-DOWN,Texas-Inst-Down,Tellabs-Inc-Down,
Natl-Semiconduct-DOWN,Oracl-DOWN,SGI-DOWN,
Sun-DOWN
Apple-Comp-DOWN,Autodesk-DOWN,DEC-DOWN,
ADV-Micro-Device-DOWN,Andrew-Corp-DOWN,
Computer-Assoc-DOWN,Circuit-City-DOWN,
Compaq-DOWN, EMC-Corp-DOWN, Gen-Inst-DOWN,
Motorola-DOWN,Microsoft-DOWN,Scientific-Atl-DOWN
Fannie-Mae-DOWN,Fed-Home-Loan-DOWN,
MBNA-Corp-DOWN,Morgan-Stanley-DOWN
Baker-Hughes-UP,Dresser-Inds-UP,Halliburton-HLD-UP,
Louisiana-Land-UP,Phillips-Petro-UP,Unocal-UP,
Schlumberger-UP
• Summarization
– Reduce the size of large
data sets
Clustering
precipitation in
Australia
Industry Group
Technology1-DOWN
Technology2-DOWN
Financial-DOWN
Oil-UP
Notion of a Cluster can be
Ambiguous
How many clusters?
Six Clusters
Two Clusters
Four Clusters
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
Partitional Clustering
Original Points
A Partitional Clustering
Hierarchical Clustering
p1
p3
p4
p2
p1 p2
Traditional Hierarchical
Clustering
p3 p4
Traditional Dendrogram
p1
p3
p4
p2
p1 p2
Non-traditional Hierarchical
Clustering
p3 p4
Non-traditional Dendrogram
Clustering Algorithms
• K-means and its variants
• Hierarchical clustering
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
K-means: Example
Iteration 6
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2
3
4
5
3
2.5
2
y
1.5
1
0.5
0
-2
-1.5
-1
-0.5
0
x
0.5
1
1.5
2
K-means: Example
Iteration 1
Iteration 2
Iteration 3
2.5
2.5
2.5
2
2
2
1.5
1.5
1.5
y
3
y
3
y
3
1
1
1
0.5
0.5
0.5
0
0
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-2
-1.5
-1
-0.5
x
0
0.5
1
1.5
2
-2
Iteration 4
Iteration 5
2.5
2
2
2
1.5
1.5
1.5
1
1
1
0.5
0.5
0.5
0
0
0
-0.5
0
x
0.5
1
1.5
2
0
0.5
1
1.5
2
1
1.5
2
y
2.5
y
2.5
y
3
-1
-0.5
Iteration 6
3
-1.5
-1
x
3
-2
-1.5
x
-2
-1.5
-1
-0.5
0
x
0.5
1
1.5
2
-2
-1.5
-1
-0.5
0
x
0.5
Importance of Choosing Initial Centroids …
3
2.5
Original Points
2
y
1.5
1
0.5
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
x
2.5
2.5
2
2
1.5
1.5
y
3
y
3
1
1
0.5
0.5
0
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
x
Optimal Clustering
2
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
x
Sub-optimal Clustering
Importance of Choosing Initial Centroids …
Iteration 5
1
2
3
4
3
2.5
2
y
1.5
1
0.5
0
-2
-1.5
-1
-0.5
0
x
0.5
1
1.5
2
Importance of Choosing Initial Centroids …
Iteration 1
Iteration 2
2.5
2.5
2
2
1.5
1.5
y
3
y
3
1
1
0.5
0.5
0
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
-2
-1.5
-1
-0.5
x
0
0.5
Iteration 3
2.5
2
2
2
1.5
1.5
1.5
y
2.5
y
2.5
y
3
1
1
1
0.5
0.5
0.5
0
0
0
-1
-0.5
0
x
0.5
2
Iteration 5
3
-1.5
1.5
Iteration 4
3
-2
1
x
1
1.5
2
-2
-1.5
-1
-0.5
0
x
0.5
1
1.5
2
-2
-1.5
-1
-0.5
0
x
0.5
1
1.5
2
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!/1010 = 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
–
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
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.
Limitations of K-means: Differing Sizes
Original Points
K-means (3 Clusters)
Limitations of K-means: Differing Density
Original Points
K-means (3 Clusters)
Limitations of K-means: Non-globular Shapes
Original Points
K-means (2 Clusters)
Overcoming K-means Limitations
Original Points
K-means Clusters
One solution is to use many clusters.
Find parts of clusters, but need to put together.
Overcoming K-means Limitations
Original Points
K-means Clusters
Overcoming K-means Limitations
Original Points
K-means Clusters
Clustering Algorithms
• K-means and its variants
• Hierarchical clustering
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
5
6
0.2
4
3
4
2
0.15
5
2
0.1
1
0.05
3
0
1
3
2
5
4
6
1
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, …)
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
Agglomerative Clustering
Algorithm
•
More popular hierarchical clustering technique
•
Basic algorithm is straightforward
1.
2.
3.
4.
5.
6.
•
Compute the proximity matrix
Let each data point be a cluster
Repeat
Merge the two closest clusters
Update the proximity matrix
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
Starting Situation
• Start with clusters of individual
points and
p1 p2 p3 p4 p5 . . .
p1
a proximity matrix
p2
p3
p4
p5
.
.
Proximity Matrix
.
...
p1
p2
p3
p4
p9
p10
p11
p12
Intermediate Situation
• After some merging steps, we have someC1
clusters
C2 C3 C4 C5
C1
C2
C3
C
3
C4
C
4
C5
Proximity Matrix
C
1
C
2
C
5
...
p1
p2
p3
p4
p9
p10
p11
p12
Intermediate Situation
• We want to merge the two closest clustersC1(C2
C2and
C3C5)
C4 and
C5
update the proximity matrix.
C1
C2
C3
C
3
C4
C
4
C5
Proximity Matrix
C
1
C
2
C
5
...
p1
p2
p3
p4
p9
p10
p11
p12
After Merging
C2 matrix?”
• The question is “How do we update the proximity
C1
C1
C
3
?
?
C2 U
C5 C3
C
4
U
C3
C5
?
?
C4
?
?
?
C4
Proximity Matrix
C
1
C2 U
C5
...
p1
p2
p3
p4
p9
p10
p11
p12
How to Define Inter-Cluster Similarity
p1 p2
Similarity?
p3
p4 p5
p1
p2
p3
p4





p5
MIN
.
MAX
.
Group Average
.
Proximity Matrix
Distance Between Centroids
Other methods driven by an objective
function
...
How to Define Inter-Cluster Similarity
p1 p2
p3
p4 p5
p1
p2
p3
p4





p5
MIN
.
MAX
.
Group Average
.
Proximity Matrix
Distance Between Centroids
Other methods driven by an objective
function
...
How to Define Inter-Cluster Similarity
p1 p2
p3
p4 p5
p1
p2
p3
p4





p5
MIN
.
MAX
.
Group Average
.
Proximity Matrix
Distance Between Centroids
Other methods driven by an objective
function
...
How to Define Inter-Cluster Similarity
p1 p2
p3
p4 p5
p1
p2
p3
p4





p5
MIN
.
MAX
.
Group Average
.
Proximity Matrix
Distance Between Centroids
Other methods driven by an objective
function
...
How to Define Inter-Cluster Similarity
p1 p2
p3
p4 p5
p1


p2
p3
p4





p5
MIN
.
MAX
.
Group Average
.
Proximity Matrix
Distance Between Centroids
Other methods driven by an objective
function
...
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
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
Using Similarity Matrix for Cluster Validation
• Order the similarity matrix with respect to cluster
labels and inspect visually.
1
1
0.9
0.8
0.7
Points
y
0.6
0.5
0.4
0.3
0.2
0.1
0
10
0.9
20
0.8
30
0.7
40
0.6
50
0.5
60
0.4
70
0.3
80
0.2
90
0.1
100
0
0.2
0.4
0.6
x
0.8
1
20
40
60
Points
80
0
100 Similarity
Final Comment on Cluster Validity
“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