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Data Mining: Introduction
Part of Lecture Notes for
Introduction to Data Mining
by
Tan, Steinbach, Kumar
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
1
Why Mine Data? Commercial Viewpoint

Lots of data is being collected
and warehoused
– Web data, e-commerce
– purchases at department/
grocery stores
– Bank/Credit Card
transactions

Computers have become cheaper and more powerful

Competitive Pressure is Strong
– Provide better, customized services for an edge (e.g. in
Customer Relationship Management)
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
2
Why Mine Data? Scientific Viewpoint

Data collected and stored at
enormous speeds (GB/hour)
– remote sensors on a satellite
– telescopes scanning the skies
– microarrays generating gene
expression data
– scientific simulations
generating terabytes of data


Traditional techniques infeasible for raw data
Data mining may help scientists
– in classifying and segmenting data
– in Hypothesis Formation
Mining Large Data Sets - Motivation



There is often information “hidden” in the data that is
not readily evident
Human analysts may take weeks to discover useful
information
Much of the data is never analyzed at all
4,000,000
3,500,000
The Data Gap
3,000,000
2,500,000
2,000,000
1,500,000
Total new disk (TB) since 1995
1,000,000
Number of
analysts
500,000
0
1995
1996
1997
1998
1999
©From:
Tan,Steinbach,
R. Grossman,
Kumar
C. Kamath, V. Kumar,
Introduction
“Data Mining
to Data
for Mining
Scientific and Engineering Applications”
4/18/2004
4
What is Data Mining?
 Many
Definitions
– Non-trivial extraction of implicit, previously
unknown and potentially useful information from
data
– Exploration & analysis, by automatic or
semi-automatic means, of
large quantities of data
in order to discover
meaningful patterns
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
5
What is (not) Data Mining?
What is not Data
Mining?

– Look up phone
number in phone
directory
– Query a Web
search engine for
information about
“Amazon”
© Tan,Steinbach, Kumar

What is Data Mining?
– Certain names are more
prevalent in certain US
locations (O’Brien, O’Rurke,
O’Reilly… in Boston area)
– Group together similar
documents returned by
search engine according to
their context (e.g. Amazon
rainforest, Amazon.com,)
Introduction to Data Mining
4/18/2004
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Origins of Data Mining
Draws ideas from machine learning/AI, pattern
recognition, statistics, and database systems
 Traditional Techniques
may be unsuitable due to
Statistics/
Machine Learning/
– Enormity of data
AI
Pattern
Recognition
– High dimensionality
of data
Data Mining
– Heterogeneous,
distributed nature
Database
systems
of data

© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
7
Data Mining Tasks

Prediction Methods
– Use some variables to predict unknown or
future values of other variables.

Description Methods
– Find human-interpretable patterns that
describe the data.
From [Fayyad, et.al.] Advances in Knowledge Discovery and Data Mining, 1996
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
8
Data Mining Tasks...
Classification [Predictive]
 Clustering [Descriptive]
 Association Rule Discovery [Descriptive]
 Sequential Pattern Discovery [Descriptive]
 Regression [Predictive]
 Deviation Detection [Predictive]

© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
9
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.
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
10
Classification Example
ca
go
e
t
al
c
ri
al
us
c
i
o
u
or
in
g
t
e
t
n
ss
a
o
a
c
c
cl
Tid Refund Marital
Status
Taxable
Income Cheat
Refund Marital
Status
Taxable
Income Cheat
1
Yes
Single
125K
No
No
Single
75K
?
2
No
Married
100K
No
Yes
Married
50K
?
3
No
Single
70K
No
No
Married
150K
?
4
Yes
Married
120K
No
Yes
Divorced 90K
?
5
No
Divorced 95K
Yes
No
Single
40K
?
6
No
Married
No
No
Married
80K
?
60K
Test
Set
10
7
Yes
Divorced 220K
No
8
No
Single
85K
Yes
9
No
Married
75K
No
10
No
Single
90K
Yes
10
© Tan,Steinbach, Kumar
Training
Set
Introduction to Data Mining
Learn
Classifier
Model
4/18/2004
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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
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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Classification: Application 1

Direct Marketing
– Goal: Reduce cost of mailing by targeting a set of
consumers likely to buy a new cell-phone product.
– Approach:
 Use
the data for a similar product introduced before.
 We
know which customers decided to buy and which
decided otherwise. This {buy, don’t buy} decision forms the
class attribute.
 Collect
various demographic, lifestyle, and companyinteraction related information about all such customers.
– Type of business, where they stay, how much they earn, etc.
 Use
this information as input attributes to learn a classifier
model.
From [Berry & Linoff] Data Mining Techniques, 1997
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
13
Classification: Application 2

Fraud Detection
– Goal: Predict fraudulent cases in credit card
transactions.
– Approach:
 Use
credit card transactions and the information on its
account-holder as attributes.
– When does a customer buy, what does he buy, how often he pays on
time, etc
 Label
past transactions as fraud or fair transactions. This
forms the class attribute.
 Learn a model for the class of the transactions.
 Use this model to detect fraud by observing credit card
transactions on an account.
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
14
Classification: Application 3

Customer Attrition/Churn:
– Goal: To predict whether a customer is likely
to be lost to a competitor.
– Approach:
 Use
detailed record of transactions with each of the
past and present customers, to find attributes.
– How often the customer calls, where he calls, what time-of-the
day he calls most, his financial status, marital status, etc.
 Label
the customers as loyal or disloyal.
 Find a model for loyalty.
From [Berry & Linoff] Data Mining Techniques, 1997
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
15
Classification: Application 4

Sky Survey Cataloging
– Goal: To predict class (star or galaxy) of sky objects,
especially visually faint ones, based on the telescopic
survey images (from Palomar Observatory).
– 3000 images with 23,040 x 23,040 pixels per image.
– Approach:
 Segment
the image.
 Measure
image attributes (features) - 40 of them per object.
 Model
the class based on these features.
 Success
Story: Could find 16 new high red-shift quasars,
some of the farthest objects that are difficult to find!
From [Fayyad, et.al.] Advances in Knowledge Discovery and Data Mining, 1996
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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Classifying Galaxies
Courtesy: http://aps.umn.edu
Early
Class:
• Stages of Formation
Attributes:
• Image features,
• Characteristics of light
waves received, etc.
Intermediate
Late
Data Size:
• 72 million stars, 20 million galaxies
• Object Catalog: 9 GB
• Image Database: 150 GB
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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Clustering Definition


Given a set of data points, each having a set of
attributes, and a similarity measure among them,
find clusters such that
– Data points in one cluster are more similar to
one another.
– Data points in separate clusters are less
similar to one another.
Similarity Measures:
– Euclidean Distance if attributes are
continuous.
– Other Problem-specific Measures.
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
18
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
Inter-cluster
distances are
maximized
Intra-cluster
distances are
minimized
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
19
Notion of a Cluster can be Ambiguous
How many clusters?
Six Clusters
Two Clusters
Four Clusters
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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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
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
21
Partitional Clustering
Original Points
© Tan,Steinbach, Kumar
A Partitional Clustering
Introduction to Data Mining
4/18/2004
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Hierarchical Clustering
p1 p2
Traditional Hierarchical Clustering
p1
p3
p3 p4
Traditional Dendrogram
p4
p2
p1 p2
Non-traditional Hierarchical Clustering
© Tan,Steinbach, Kumar
p3 p4
Non-traditional Dendrogram
Introduction to Data Mining
4/18/2004
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Types of Clusters

Well-separated clusters

Center-based clusters

Contiguous clusters

Density-based clusters

Property or Conceptual

Described by an Objective Function
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
24
Types of Clusters: Well-Separated

Well-Separated Clusters:
– A cluster is a set of points such that any point in a cluster is
closer (or more similar) to every other point in the cluster than
to any point not in the cluster.
3 well-separated clusters
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
25
Types of Clusters: Center-Based

Center-based
– A cluster is a set of objects such that an object in a cluster is
closer (more similar) to the “center” of a cluster, than to the
center of any other cluster
– The center of a cluster is often a centroid, the average of all
the points in the cluster, or a medoid, the most “representative”
point of a cluster
4 center-based clusters
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
26
Types of Clusters: Contiguity-Based

Contiguous Cluster (Nearest neighbor or
Transitive)
– A cluster is a set of points such that a point in a cluster is
closer (or more similar) to one or more other points in the
cluster than to any point not in the cluster.
8 contiguous clusters
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
27
Types of Clusters: Density-Based

Density-based
– A cluster is a dense region of points, which is separated by
low-density regions, from other regions of high density.
– Used when the clusters are irregular or intertwined, and when
noise and outliers are present.
6 density-based clusters
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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Types of Clusters: Conceptual Clusters

Shared Property or Conceptual Clusters
– Finds clusters that share some common property or represent
a particular concept.
.
2 Overlapping Circles
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
29
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
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
30
K-means Clustering – Details

Initial centroids are often chosen randomly.
–
Clusters produced vary from one run to another.

The centroid is (typically) the mean of the points in the
cluster.

‘Closeness’ is measured by Euclidean distance, cosine
similarity, correlation, etc.

K-means will converge for common similarity measures
mentioned above.

Most of the convergence happens in the first few
iterations.
–

Often the stopping condition is changed to ‘Until relatively few
points change clusters’
Complexity is O( n * K * I * d )
–
n = number of points, K = number of clusters,
I = number of iterations, d = number of attributes
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
31
Two different K-means Clusterings
3
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Optimal Clustering
© Tan,Steinbach, Kumar
-2
Introduction to Data Mining
Sub-optimal Clustering
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Importance of Choosing Initial Centroids
Iteration 6
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© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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Importance of Choosing Initial Centroids
Iteration 1
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© Tan,Steinbach, Kumar
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Introduction to Data Mining
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Evaluating K-means Clusters

Most common measure is Sum of Squared Error (SSE)
– For each point, the error is the distance to the nearest cluster
– To get SSE, we square these errors and sum them.
K
SSE    dist 2 (mi , x )
i 1 xCi
– x is a data point in cluster Ci and mi is the representative point for
cluster Ci

can show that mi corresponds to the center (mean) of the cluster
– Given two clusters, we can choose the one with the smallest
error
– One easy way to reduce SSE is to increase K, the number of
clusters
A good clustering with smaller K can have a lower SSE than a poor
clustering with higher K

© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
35
Importance of Choosing Initial Centroids …
Iteration 5
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© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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Importance of Choosing Initial Centroids …
Iteration 1
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© Tan,Steinbach, Kumar
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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
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
38
10 Clusters Example
Iteration 4
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Starting with two initial centroids in one cluster of each pair of clusters
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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10 Clusters Example
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Starting with two initial centroids in one cluster of each pair of clusters
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
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10 Clusters Example
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Starting with some pairs of clusters having three initial centroids, while other have only
one.
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
41
10 Clusters Example
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Starting with some pairs of clusters having three initial centroids, while other have only
one.
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
42
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
 Bisecting K-means
– Not as susceptible to initialization issues

© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
43
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
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© Tan,Steinbach, Kumar
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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 dendogram at the
proper level

They may correspond to meaningful taxonomies
– Example in biological sciences (e.g., animal
kingdom, phylogeny reconstruction, …)
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
45
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
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
46
Agglomerative Clustering Algorithm

More popular hierarchical clustering technique

Basic algorithm is straightforward
1.
Compute the proximity matrix
2.
Let each data point be a cluster
3.
Repeat
4.
Merge the two closest clusters
5.
Update the proximity matrix
6.

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
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
47
Starting Situation

Start with clusters of individual points and a
proximity matrix
p1 p2
p3
p4 p5
...
p1
p2
p3
p4
p5
.
.
Proximity Matrix
.
...
p1
© Tan,Steinbach, Kumar
Introduction to Data Mining
p2
p3
p4
p9
p10
4/18/2004
p11
p12
48
Intermediate Situation

After some merging steps, we have some clusters
C1
C2
C3
C4
C5
C1
C2
C3
C3
C4
C4
C5
Proximity Matrix
C1
C2
C5
...
p1
© Tan,Steinbach, Kumar
Introduction to Data Mining
p2
p3
p4
p9
p10
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p11
p12
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Intermediate Situation

We want to merge the two closest clusters (C2 and C5) and
update the proximity matrix.
C1 C2
C3
C4 C5
C1
C2
C3
C3
C4
C4
C5
Proximity Matrix
C1
C2
C5
...
p1
© Tan,Steinbach, Kumar
Introduction to Data Mining
p2
p3
p4
p9
p10
4/18/2004
p11
p12
50
After Merging

The question is “How do we update the proximity matrix?”
C1
C1
C4
C3
C4
?
?
?
?
C2 U C5
C3
C2
U
C5
?
C3
?
C4
?
Proximity Matrix
C1
C2 U C5
...
p1
© Tan,Steinbach, Kumar
Introduction to Data Mining
p2
p3
p4
p9
p10
4/18/2004
p11
p12
51
How to Define Inter-Cluster Similarity
p1
Similarity?
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
– Ward’s Method uses squared error
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
52
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
– Ward’s Method uses squared error
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
53
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
– Ward’s Method uses squared error
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
54
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
– Ward’s Method uses squared error
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
55
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
– Ward’s Method uses squared error
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
56
Graph-Based Clustering

Graph-Based clustering uses the proximity graph
– Start with the proximity matrix
– Consider each point as a node in a graph
– Each edge between two nodes has a weight
which is the proximity between the two points
– Initially the proximity graph is fully connected
– MIN (single-link) and MAX (complete-link) can
be viewed as starting with this graph
In the simplest case, clusters are connected
components in Introduction
the graph.
© Tan,Steinbach, Kumar
to Data Mining
4/18/2004

57
MST: Divisive Hierarchical Clustering

Build MST (Minimum Spanning Tree)
– Start with a tree that consists of any point
– In successive steps, look for the closest pair of points (p, q)
such that one point (p) is in the current tree but the other (q) is
not
– Add q to the tree and put an edge between p and q
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
58
MST: Divisive Hierarchical Clustering

Use MST for constructing hierarchy of clusters
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
59
Clustering: Application 1

Market Segmentation:
– Goal: subdivide a market into distinct subsets of
customers where any subset may conceivably be
selected as a market target to be reached with a
distinct marketing mix.
– Approach:
 Collect
different attributes of customers based on their
geographical and lifestyle related information.
 Find clusters of similar customers.
 Measure the clustering quality by observing buying patterns
of customers in same cluster vs. those from different
clusters.
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
60
Clustering: Application 2

Document Clustering:
– Goal: To find groups of documents that are
similar to each other based on the important
terms appearing in them.
– Approach: To identify frequently occurring
terms in each document. Form a similarity
measure based on the frequencies of different
terms. Use it to cluster.
– Gain: Information Retrieval can utilize the
clusters to relate a new document or search
term to clustered documents.
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
61
Illustrating Document Clustering


Clustering Points: 3204 Articles of Los Angeles Times.
Similarity Measure: How many words are common in
these documents (after some word filtering).
Category
© Tan,Steinbach, Kumar
Financial
Total
Articles
555
Correctly
Placed
364
Foreign
341
260
National
273
36
Metro
943
746
Sports
738
573
Entertainment
354
278
Introduction to Data Mining
4/18/2004
62
Clustering of S&P 500 Stock Data
❚ Observe Stock Movements every day.
❚ Clustering points: Stock-{UP/DOWN}
❚ Similarity Measure: Two points are more similar if the events
described by them frequently happen together on the same day.
❚ We used association rules to quantify a similarity measure.
Discovered Clusters
1
2
Applied-Matl-DOW N,Bay-Net work-Down,3-COM-DOWN,
Cabletron-Sys-DOW N,CISCO-DOWN,HP-DOWN,
DSC-Co mm-DOW N,INT EL-DOW N,LSI-Logic -DOW N,
Micron-Tech-DOW N,Te xas-Inst-Down,Te llabs-Inc-Down,
Natl-Se miconduct-DOW N,Orac l-DOW N,SGI-DOW N,
Sun-DOW N
Apple-Co mp-DOW N,Autodesk-DOW N,DEC-DOW N,
ADV-M icro-Device -DOWN,Andrew-Corp-DOWN,
Co mputer-Assoc-DOW N,Circuit-City-DOWN,
Co mpaq-DOW N, EM C-Corp-DOWN, Gen-Inst-DOWN,
Motorola-DOW N,Mic rosoft-DOW N,Sc ientific-Atl-DOW N
3
4
© Tan,Steinbach, Kumar
Fannie-Mae-DOW N,Fed-Ho me-Loan-DOW N,
MBNA-Corp -DOWN,Morgan-Stanley-DOWN
Bake r-Hughes-UP,Dresser-Inds-UP,Halliburton-HLD-UP,
Louisiana-Land-UP,Phillips-Petro-UP,Unocal-UP,
Schlu mberger-UP
Introduction to Data Mining
Industry Group
Techno lo gy1-DOWN
Techno lo gy2-DOWN
Financial-DOWN
Oil-UP
4/18/2004
63
Association Rule Mining

Given a set of transactions, i.e. a set of records each of
which contain some number of items from a given
collection, find rules that will predict the occurrence of an
item based on the occurrences of other items in the
transaction
Market-Basket transactions
Example of Association
Rules
TID
Items
1
Bread, Milk
2
3
4
5
Bread, Diaper, Beer, Eggs
Milk, Diaper, Beer, Coke
Bread, Milk, Diaper, Beer
Bread, Milk, Diaper, Coke
© Tan,Steinbach, Kumar
Introduction to Data Mining
{Diaper}  {Beer},
{Milk, Bread}  {Eggs,Coke},
{Beer, Bread}  {Milk},
Implication means co-occurrence,
not causality!
4/18/2004
64
Definition: Frequent Itemset

Itemset
– A collection of one or more items

Example: {Milk, Bread, Diaper}
– k-itemset


An itemset that contains k items
Support count ()
– Frequency of occurrence of an itemset
– E.g. ({Milk, Bread,Diaper}) = 2

Support
TID
Items
1
Bread, Milk
2
3
4
5
Bread, Diaper, Beer, Eggs
Milk, Diaper, Beer, Coke
Bread, Milk, Diaper, Beer
Bread, Milk, Diaper, Coke
– Fraction of transactions that contain an
itemset
– E.g. s({Milk, Bread, Diaper}) = 2/5

Frequent Itemset
– An itemset whose support is greater
than or equal to a minsup threshold
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
65
Definition: Association Rule

Association Rule
– An implication expression of the form
X  Y, where X and Y are itemsets
– Example:
{Milk, Diaper}  {Beer}

Rule Evaluation Metrics
– Support (s)

Measures how often items in Y
appear in transactions that
contain X
1
Bread, Milk
2
3
4
5
Bread, Diaper, Beer, Eggs
Milk, Diaper, Beer, Coke
Bread, Milk, Diaper, Beer
Bread, Milk, Diaper, Coke
{Milk, Diaper}  Beer
s
c
© Tan,Steinbach, Kumar
Items
Example:
Fraction of transactions that contain
both X and Y
– Confidence (c)

TID
Introduction to Data Mining
 (Milk, Diaper, Beer) 2
  0.4
|T|
5
 (Milk, Diaper, Beer) 2
  0.67
 (Milk, Diaper )
3
4/18/2004
66
Association Rule Mining Task

Given a set of transactions T, the goal of
association rule mining is to find all rules having
– support ≥ minsup threshold
– confidence ≥ minconf threshold

Brute-force approach:
– List all possible association rules
– Compute support and confidence for each rule
– Prune rules that fail the minsup and minconf
thresholds
 Computationally prohibitive!
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
67
Mining Association Rules
Example of Rules:
TID
Items
1
Bread, Milk
2
3
4
Bread, Diaper, Beer, Eggs
Milk, Diaper, Beer, Coke
Bread, Milk, Diaper, Beer
5
Bread, Milk, Diaper, Coke
{Milk,Diaper}  {Beer} (s=0.4, c=0.67)
{Milk,Beer}  {Diaper} (s=0.4, c=1.0)
{Diaper,Beer}  {Milk} (s=0.4, c=0.67)
{Beer}  {Milk,Diaper} (s=0.4, c=0.67)
{Diaper}  {Milk,Beer} (s=0.4, c=0.5)
{Milk}  {Diaper,Beer} (s=0.4, c=0.5)
Observations:
• All the above rules are binary partitions of the same itemset:
{Milk, Diaper, Beer}
• Rules originating from the same itemset have identical support but
can have different confidence
• Thus, we may decouple the support and confidence requirements
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
68
Mining Association Rules

Two-step approach:
1. Frequent Itemset Generation
–
Generate all itemsets whose support  minsup
1. Rule Generation
–

Generate high confidence rules from each
frequent itemset, where each rule is a binary
partitioning of a frequent itemset
Frequent itemset generation is still
computationally expensive
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
69
Frequent Itemset Generation
null
A
B
C
D
E
AB
AC
AD
AE
BC
BD
BE
CD
CE
DE
ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BDE
CDE
ABCD
ABCE
ABDE
ACDE
ABCDE
© Tan,Steinbach, Kumar
Introduction to Data Mining
BCDE
Given d items, there
are 2d possible
candidate itemsets
4/18/2004
70
Frequent Itemset Generation

Brute-force approach:
– Each itemset in the lattice is a candidate frequent itemset
– Count the support of each candidate by scanning the
database
Transactions
N
TID
1
2
3
4
5
Items
Bread, Milk
Bread, Diaper, Beer, Eggs
Milk, Diaper, Beer, Coke
Bread, Milk, Diaper, Beer
Bread, Milk, Diaper, Coke
List of
Candidates
M
w
– Match each transaction against every candidate
– Complexity ~ O(NMw) => Expensive since M = 2d !!!
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
71
Computational Complexity

Given d unique items:
– Total number of itemsets = 2d
– Total number of possible association rules:
 d   d  k 
R       

 k   j 
 3  2 1
d 1
d k
k 1
j 1
d
d 1
If d=6, R = 602 rules
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
72
Frequent Itemset Generation Strategies

Reduce the number of candidates (M)
– Complete search: M=2d
– Use pruning techniques to reduce M

Reduce the number of transactions (N)
– Reduce size of N as the size of itemset increases
– Used by DHP and vertical-based mining algorithms

Reduce the number of comparisons (NM)
– Use efficient data structures to store the candidates or
transactions
– No need to match every candidate against every
transaction
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
73
Reducing Number of Candidates

Apriori principle:
– If an itemset is frequent, then all of its subsets must also
be frequent

Apriori principle holds due to the following property
of the support measure:
X , Y : ( X  Y )  s( X )  s(Y )
– Support of an itemset never exceeds the support of its
subsets
– This is known as the anti-monotone property of support
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
74
Illustrating Apriori Principle
null
A
Found to be
Infrequent
B
D
E
AB
AC
AD
AE
BC
BD
BE
CD
CE
DE
ABC
ABD
ABE
ACD
ACE
ADE
BCD
BCE
BDE
CDE
ABCD
ABCE
Pruned
supersets
© Tan,Steinbach, Kumar
C
Introduction to Data Mining
ABDE
ACDE
BCDE
ABCDE
4/18/2004
75
Illustrating Apriori Principle
Item
Bread
Coke
Milk
Beer
Diaper
Eggs
Count
4
2
4
3
4
1
Items (1-itemsets)
Itemset
{Bread,Milk}
{Bread,Beer}
{Bread,Diaper}
{Milk,Beer}
{Milk,Diaper}
{Beer,Diaper}
Minimum Support = 3
Pairs (2-itemsets)
(No need to generate
candidates involving Coke
or Eggs)
Triplets (3-itemsets)
If every subset is considered,
6
C1 + 6C2 + 6C3 = 41
With support-based pruning,
6 + 6 + 1 = 13
© Tan,Steinbach, Kumar
Count
3
2
3
2
3
3
Introduction to Data Mining
Itemset
{Bread,Milk,Diaper}
Count
3
4/18/2004
76
Apriori Algorithm

Method:
– Let k=1
– Generate frequent itemsets of length 1
– Repeat until no new frequent itemsets are identified
 Generate
length (k+1) candidate itemsets from length k
frequent itemsets
 Prune candidate itemsets containing subsets of length k that
are infrequent
 Count the support of each candidate by scanning the DB
 Eliminate candidates that are infrequent, leaving only those
that are frequent
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
77
Rule Generation

Given a frequent itemset L, find all non-empty
subsets f  L such that f  L – f satisfies the
minimum confidence requirement
– If {A,B,C,D} is a frequent itemset, candidate rules:
ABC D,
A BCD,
AB CD,
BD AC,

ABD C,
B ACD,
AC  BD,
CD AB,
ACD B,
C ABD,
AD  BC,
BCD A,
D ABC
BC AD,
If |L| = k, then there are 2k – 2 candidate
association rules (ignoring L   and   L)
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
78
Rule Generation

How to efficiently generate rules from frequent
itemsets?
– In general, confidence does not have an antimonotone property
c(ABC D) can be larger or smaller than c(AB D)
– But confidence of rules generated from the same
itemset has an anti-monotone property
– e.g., L = {A,B,C,D}:
c(ABC  D)  c(AB  CD)  c(A  BCD)
 Confidence is anti-monotone w.r.t. number of items on the
RHS of the rule
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
79
Rule Generation for Apriori Algorithm
Lattice of rules
Low
Confidence
Rule
CD=>AB
ABCD=>{ }
BCD=>A
ACD=>B
BD=>AC
D=>ABC
BC=>AD
C=>ABD
ABD=>C
AD=>BC
B=>ACD
ABC=>D
AC=>BD
AB=>CD
A=>BCD
Pruned
Rules
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
80
Rule Generation for Apriori Algorithm

Candidate rule is generated by merging two rules
that share the same prefix
in the rule consequent
CD=>AB


BD=>AC
join(CD=>AB,BD=>AC)
would produce the candidate
rule D => ABC
Prune rule D=>ABC if its
subset AD=>BC does not have
high confidence
© Tan,Steinbach, Kumar
Introduction to Data Mining
D=>ABC
4/18/2004
81
Association Rule Discovery: Application 1

Marketing and Sales Promotion:
– Let the rule discovered be
{Bagels, … } --> {Potato Chips}
– Potato Chips as consequent => Can be used to
determine what should be done to boost its sales.
– Bagels in the antecedent => Can be used to see
which products would be affected if the store
discontinues selling bagels.
– Bagels in antecedent and Potato chips in consequent
=> Can be used to see what products should be sold
with Bagels to promote sale of Potato chips!
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
82
Association Rule Discovery: Application 2

Supermarket shelf management.
– Goal: To identify items that are bought
together by sufficiently many customers.
– Approach: Process the point-of-sale data
collected with barcode scanners to find
dependencies among items.
– A classic rule - If
a customer buys diaper and milk, then he is very
likely to buy beer.
 So, don’t be surprised if you find six-packs stacked
next to diapers!
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
83
Association Rule Discovery: Application 3

Inventory Management:
– Goal: A consumer appliance repair company wants to
anticipate the nature of repairs on its consumer
products and keep the service vehicles equipped with
right parts to reduce on number of visits to consumer
households.
– Approach: Process the data on tools and parts
required in previous repairs at different consumer
locations and discover the co-occurrence patterns.
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
84
Sequential Pattern Discovery: Definition

Given is a set of objects, with each object associated with its own timeline of
events, find rules that predict strong sequential dependencies among different
events.
(A B)

(C)
(D E)
Rules are formed by first disovering patterns. Event occurrences in the
patterns are governed by timing constraints.
(A B)
<= xg
(C) (D E)
>ng
<= ws
<= ms
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
85
Sequential Pattern Discovery: Examples

In telecommunications alarm logs,
– (Inverter_Problem Excessive_Line_Current)
(Rectifier_Alarm) --> (Fire_Alarm)

In point-of-sale transaction sequences,
– Computer Bookstore:
(Intro_To_Visual_C) (C++_Primer) -->
(Perl_for_dummies,Tcl_Tk)
– Athletic Apparel Store:
(Shoes) (Racket, Racketball) --> (Sports_Jacket)
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
86
Regression



Predict a value of a given continuous valued variable
based on the values of other variables, assuming a
linear or nonlinear model of dependency.
Greatly studied in statistics, neural network fields.
Examples:
– Predicting sales amounts of new product based on
advetising expenditure.
– Predicting wind velocities as a function of
temperature, humidity, air pressure, etc.
– Time series prediction of stock market indices.
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
87
Deviation/Anomaly Detection
Detect significant deviations from normal behavior
 Applications:
– Credit Card Fraud Detection

– Network Intrusion
Detection
Typical network traffic at University level may reach over 100 million connections per
day
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
88
Challenges of Data Mining







Scalability
Dimensionality
Complex and Heterogeneous Data
Data Quality
Data Ownership and Distribution
Privacy Preservation
Streaming Data
© Tan,Steinbach, Kumar
Introduction to Data Mining
4/18/2004
89