- Big data is growing rapidly in both commercial and scientific databases. Data mining is commonly used to extract useful information from large datasets. It helps with customer service, hypothesis formation, and more. - Recent technological advances are generating large amounts of medical and genomic data. Data mining offers potential solutions for automated analysis of patient histories, gene function prediction, and drug discovery. Traditional techniques may be unsuitable due to data enormity, dimensionality, and heterogeneity. - Data mining involves tasks like classification, association rule mining, clustering, and outlier detection. Various machine learning algorithms are applied including decision trees, naive Bayes, and neural networks.

1. Mining Big Data: Motivation
 Today’s digital society has seen
enormous data growth in both
commercial and scientific databases
 Data Mining is becoming a commonly
used tool to extract information from
large and complex datasets
 Examples:
 Helps provide better customer service in
business/commercial setting
 Helps scientists in hypothesis formation
Computational Simulations
Business Data
Sensor Networks
Geo-spatial data
Homeland Security
Scientific Data

2. Data Mining for Life and Health Sciences
 Recent technological advances are helping to
generate large amounts of both medical and
genomic data
• High-throughput experiments/techniques
- Gene and protein sequences
- Gene-expression data
- Biological networks and phylogenetic profiles
• Electronic Medical Records
- IBM-Mayo clinic partnership has created a DB of 5
million patients
- Single Nucleotides Polymorphisms (SNPs)
 Data mining offers potential solution for analysis of
large-scale data
• Automated analysis of patients history for customized
treatment
• Prediction of the functions of anonymous genes
• Identification of putative binding sites in protein structures
for drugs/chemicals discovery
Protein Interaction Network

3. • Draws ideas from machine learning/AI, pattern
recognition, statistics, and database systems
• Traditional Techniques
may be unsuitable due to
– Enormity of data
– High dimensionality
of data
– Heterogeneous,
distributed nature
of data
Origins of Data Mining
Machine Learning/
Pattern
Recognition
Statistics/
AI
Data Mining
Database
systems

4. Data Mining as Part of the
Knowledge Discovery Process

5. Data Mining Tasks...
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 60K No
7 Yes Divorced 220K No
8 No Single 85K Yes
9 No Married 75K No
10 No Single 90K Yes
11 No Married 60K No
12 Yes Divorced 220K No
13 No Single 85K Yes
14 No Married 75K No
15 No Single 90K Yes
10
Milk
Data

6. August 21, 2022 Data Mining: Concepts and Techniques 6
Data Mining Functions: Generalization
• Materials to be covered in Chapters 2-4
• Information integration and data warehouse construction
– Data cleaning, transformation, integration, and
multidimensional data model
• Data cube technology
– Scalable methods for computing (i.e.,
materializing) multidimensional aggregates
– OLAP (online analytical processing)
• Multidimensional concept description: Characterization and
discrimination
– Generalize, summarize, and contrast data
characteristics, e.g., dry vs. wet regions

7. August 21, 2022 Data Mining: Concepts and Techniques 7
Data Mining Functions: Association and Correlation
• Frequent patterns (or frequent itemsets)
– What items are frequently purchased together in your
Walmart?
• Association, correlation vs. causality
– A typical association rule
• Diaper  Beer [0.5%, 75%] (support, confidence)
– Are strongly associated items also strongly correlated?
• How to mine such patterns and rules efficiently in large datasets?
• How to use such patterns for classification, clustering, and other
applications?

8. August 21, 2022 Data Mining: Concepts and Techniques 8
Data Mining Functions: Classification and Prediction
• Classification and prediction
– Construct models (functions) based on some training examples
– Describe and distinguish classes or concepts for future prediction
• E.g., classify countries based on (climate), or classify cars based on
(gas mileage)
– Predict some unknown or missing numerical values
• Typical methods
– Decision trees, naïve Bayesian classification, support vector machines,
neural networks, rule-based classification, pattern-based classification,
logistic regression, …
• Typical applications:
– Credit card fraud detection, direct marketing, classifying stars, diseases,
web-pages, …

9. August 21, 2022 Data Mining: Concepts and Techniques 9
Data Mining Functions: Cluster and Outlier Analysis
• Cluster analysis
– Unsupervised learning (i.e., Class label is unknown)
– Group data to form new categories (i.e., clusters), e.g., cluster houses to
find distribution patterns
– Principle: Maximizing intra-class similarity & minimizing interclass
similarity
– Many methods and applications
• Outlier analysis
– Outlier: A data object that does not comply with the general behavior of
the data
– Noise or exception? ― One person’s garbage could be another person’s
treasure
– Methods: by product of clustering or regression analysis, …
– Useful in fraud detection, rare events analysis

10. August 21, 2022 Data Mining: Concepts and Techniques 10
Data Mining Functions: Trend and Evolution Analysis
• Sequence, trend and evolution analysis
– Trend and deviation analysis: e.g., regression
– Sequential pattern mining
• e.g., first buy digital camera, then large SD memory cards
– Periodicity analysis
– Motifs, time-series, and biological sequence analysis
• Approximate and consecutive motifs
– Similarity-based analysis
• Mining data streams
– Ordered, time-varying, potentially infinite, data
streams

11. August 21, 2022 Data Mining: Concepts and Techniques 11
Data Mining Functions:Structure and Network Analysis
• Graph mining
– Finding frequent subgraphs (e.g., chemical compounds), trees (XML),
substructures (web fragments)
• Information network analysis
– Social networks: actors (objects, nodes) and relationships (edges)
• e.g., author networks in CS, terrorist networks
– Multiple heterogeneous networks
• A person could be multiple information networks: friends, family,
classmates, …
– Links carry a lot of semantic information: Link mining
• Web mining
– Web is a big information network: from PageRank to Google
– Analysis of Web information networks
• Web community discovery, opinion mining, usage mining, …

12. Predictive Modeling
Classification

13. General Approach for Building a Classification
Model
Test
Set
Training
Set
Model
Learn
Classifier
Tid Employed
Level of
Education
# years at
present
address
Credit
Worthy
1 Yes Graduate 5 Yes
2 Yes High School 2 No
3 No Undergrad 1 No
4 Yes High School 10 Yes
… … … … …
10
Tid Employed
Level of
Education
# years at
present
address
Credit
Worthy
1 Yes Undergrad 7 ?
2 No Graduate 3 ?
3 Yes High School 2 ?
… … … … …
10

14. • Predicting tumor cells as benign or malignant
• Classifying secondary structures of protein
as alpha-helix, beta-sheet, or random coil
• Predicting functions of proteins
• Classifying credit card transactions
as legitimate or fraudulent
• Categorizing news stories as finance,
weather, entertainment, sports, etc
• Identifying intruders in the cyberspace
Examples of Classification Task

15. Commonly Used Classification Models
• Base Classifiers
– Decision Tree based Methods
– Rule-based Methods
– Nearest-neighbor
– Neural Networks
– Naïve Bayes and Bayesian Belief Networks
– Support Vector Machines
• Ensemble Classifiers
– Boosting, Bagging, Random Forests

16. Tid Employed
Level of
Education
# years at
present
address
Credit
Worthy
1 Yes Graduate 5 Yes
2 Yes High School 2 No
3 No Undergrad 1 No
4 Yes High School 10 Yes
… … … … …
10
Class
Model for predicting credit
worthiness
Employed
No Education
Number of
years
No Yes
Graduate
{ High school,
Undergrad }
Yes No
> 7 yrs < 7 yrs
Yes
Classification Model: Decision Tree

17. Constructing a Decision Tree
10
Tid Employed
Level of
Education
# years at
present
address
Credit
Worthy
1 Yes Graduate 5 Yes
2 Yes High School 2 No
3 No Undergrad 1 No
4 Yes High School 10 Yes
5 Yes Graduate 2 No
6 No High School 2 No
7 Yes Undergrad 3 No
8 Yes Graduate 8 Yes
9 Yes High School 4 Yes
10 No Graduate 1 No
Employed
Worthy: 4
Not Worthy: 3
Yes
10
Tid Employed
Level of
Education
# years at
present
address
Credit
Worthy
1 Yes Graduate 5 Yes
2 Yes High School 2 No
3 No Undergrad 1 No
4 Yes High School 10 Yes
5 Yes Graduate 2 No
6 No High School 2 No
7 Yes Undergrad 3 No
8 Yes Graduate 8 Yes
9 Yes High School 4 Yes
10 No Graduate 1 No
No
Worthy: 0
Not Worthy: 3
10
Tid Employed
Level of
Education
# years at
present
address
Credit
Worthy
1 Yes Graduate 5 Yes
2 Yes High School 2 No
3 No Undergrad 1 No
4 Yes High School 10 Yes
5 Yes Graduate 2 No
6 No High School 2 No
7 Yes Undergrad 3 No
8 Yes Graduate 8 Yes
9 Yes High School 4 Yes
10 No Graduate 1 No
Graduate High School/
Undergrad
Worthy: 2
Not Worthy: 2
Education
Worthy: 2
Not Worthy: 4
Key Computation
Worthy
Not
Worthy
4 3
0 3
Employed = Yes
Employed = No
10
Tid Employed
Level of
Education
# years at
present
address
Credit
Worthy
1 Yes Graduate 5 Yes
2 Yes High School 2 No
3 No Undergrad 1 No
4 Yes High School 10 Yes
5 Yes Graduate 2 No
6 No High School 2 No
7 Yes Undergrad 3 No
8 Yes Graduate 8 Yes
9 Yes High School 4 Yes
10 No Graduate 1 No
Worthy: 4
Not Worthy: 3
Yes No
Worthy: 0
Not Worthy: 3
Employed

18. Constructing a Decision Tree
Employed =
Yes
Employed =
No
10
Tid Employed
Level of
Education
# years at
present
address
Credit
Worthy
1 Yes Graduate 5 Yes
2 Yes High School 2 No
3 No Undergrad 1 No
4 Yes High School 10 Yes
5 Yes Graduate 2 No
6 No High School 2 No
7 Yes Undergrad 3 No
8 Yes Graduate 8 Yes
9 Yes High School 4 Yes
10 No Graduate 1 No
10
Tid Employed
Level of
Education
# years at
present
address
Credit
Worthy
1 Yes Graduate 5 Yes
2 Yes High School 2 No
4 Yes High School 10 Yes
5 Yes Graduate 2 No
7 Yes Undergrad 3 No
8 Yes Graduate 8 Yes
9 Yes High School 4 Yes
10
Tid Employed
Level of
Education
# years at
present
address
Credit
Worthy
3 No Undergrad 1 No
6 No High School 2 No
10 No Graduate 1 No

19. Classification Errors
• Training errors (apparent errors)
– Errors committed on the training set
• Test errors
– Errors committed on the test set
• Generalization errors
– Expected error of a model over random selection
of records from same distribution

20. Example Data Set
Two class problem:
+ : 5200 instances
• 5000 instances generated from a
Gaussian centered at (10,10)
• 200 noisy instances added
o : 5200 instances
• Generated from a uniform
distribution
10 % of the data used for
training and 90% of the data
used for testing

21. Design Issues of Decision Tree Induction
• How should training records be split?
– Method for specifying test condition
• depending on attribute types
– Measure for evaluating the goodness of a test condition
• How should the splitting procedure stop?
– Stop splitting if all the records belong to the same class or
have identical attribute values
– Early termination

22. Model Overfitting
Underfitting: when model is too simple, both training and test errors are large
Overfitting: when model is too complex, training error is small but test error is large

23. Model Overfitting
Using twice the number of data instances
• If training data is under-representative, testing errors increase and training errors
decrease on increasing number of nodes
• Increasing the size of training data reduces the difference between training and testing
errors at a given number of nodes

24. Reasons for Model Overfitting
• Presence of Noise
• Lack of Representative Samples
• Multiple Comparison Procedure

25. Notes on Overfitting
• Overfitting results in decision trees that are
more complex than necessary
• Training error does not provide a good
estimate of how well the tree will perform on
previously unseen records
• Need ways for incorporating model complexity
into model development

26. Clustering Algorithms
• K-means and its variants
• Hierarchical clustering
• Other types of clustering

27. K-means Clustering
• Partitional clustering approach
• Number of clusters, K, must be specified
• Each cluster is associated with a centroid (center point)
• Each point is assigned to the cluster with the closest
centroid
• The basic algorithm is very simple

28. Example of K-means Clustering
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
3
x
y Iteration 1
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
3
x
y Iteration 2
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
3
x
y Iteration 3
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
3
x
y Iteration 4
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
3
x
y Iteration 5
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
3
x
y Iteration 6

29. K-means Clustering – Details
• The centroid is (typically) the mean of the points in the
cluster
• Initial centroids are often chosen randomly
– Clusters produced vary from one run to another
• ‘Closeness’ is measured by Euclidean distance, cosine
similarity, correlation, etc
• Complexity is O( n * K * I * d )
– n = number of points, K = number of clusters,
I = number of iterations, d = number of attributes

30. 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
• x is a data point in cluster Ci and mi is the representative point for
cluster Ci
– Given two sets of clusters, we prefer the one with the smallest error
– One easy way to reduce SSE is to increase K, the number of clusters

 

K
i C
x
i
i
x
m
dist
SSE
1
2
)
,
(

31. Two different K-means Clusterings
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
3
x
y
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
3
x
y
Sub-optimal Clustering
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
0
0.5
1
1.5
2
2.5
3
x
y
Optimal Clustering
Original Points

32. 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.

33. Limitations of K-means: Differing Sizes
Original Points K-means (3 Clusters)

34. Limitations of K-means: Differing Density
Original Points K-means (3 Clusters)

35. Limitations of K-means: Non-globular Shapes
Original Points K-means (2 Clusters)

36. 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 1
2
3
4
5
6
1
2
3
4
5
3 6 2 5 4 1
0
0.05
0.1
0.15
0.2

37. 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, …)

38. 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

39. 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

40. Starting Situation
• Start with clusters of individual points and a
proximity matrix
p1
p3
p5
p4
p2
p1 p2 p3 p4 p5 . . .
.
.
.
Proximity Matrix
...
p1 p2 p3 p4 p9 p10 p11 p12

41. Intermediate Situation
• After some merging steps, we have some clusters
C1
C4
C2 C5
C3
C2
C1
C1
C3
C5
C4
C2
C3 C4 C5
Proximity Matrix
...
p1 p2 p3 p4 p9 p10 p11 p12

42. Intermediate Situation
• We want to merge the two closest clusters (C2 and C5)
and update the proximity matrix.
C1
C4
C2 C5
C3
C2
C1
C1
C3
C5
C4
C2
C3 C4 C5
Proximity Matrix
...
p1 p2 p3 p4 p9 p10 p11 p12

43. After Merging
• The question is “How do we update the proximity
matrix?”
C1
C4
C2 U C5
C3
? ? ? ?
?
?
?
C2 U
C5
C1
C1
C3
C4
C2 U C5
C3 C4
Proximity Matrix
...
p1 p2 p3 p4 p9 p10 p11 p12

44. How to Define Inter-Cluster Distance
p1
p3
p5
p4
p2
p1 p2 p3 p4 p5 . . .
.
.
.
Similarity?
• MIN
• MAX
• Group Average
• Distance Between Centroids
• Other methods driven by an objective
function
– Ward’s Method uses squared error
Proximity Matrix

45. How to Define Inter-Cluster Similarity
p1
p3
p5
p4
p2
p1 p2 p3 p4 p5 . . .
.
.
.
Proximity Matrix
• MIN
• MAX
• Group Average
• Distance Between Centroids
• Other methods driven by an objective
function
– Ward’s Method uses squared error

46. How to Define Inter-Cluster Similarity
p1
p3
p5
p4
p2
p1 p2 p3 p4 p5 . . .
.
.
.
Proximity Matrix
• MIN
• MAX
• Group Average
• Distance Between Centroids
• Other methods driven by an objective
function
– Ward’s Method uses squared error

47. How to Define Inter-Cluster Similarity
p1
p3
p5
p4
p2
p1 p2 p3 p4 p5 . . .
.
.
.
Proximity Matrix
• MIN
• MAX
• Group Average
• Distance Between Centroids
• Other methods driven by an objective
function
– Ward’s Method uses squared error

48. How to Define Inter-Cluster Similarity
p1
p3
p5
p4
p2
p1 p2 p3 p4 p5 . . .
.
.
.
Proximity Matrix
• MIN
• MAX
• Group Average
• Distance Between Centroids
• Other methods driven by an objective
function
– Ward’s Method uses squared error
 

49. Other Types of Cluster Algorithms
• Hundreds of clustering algorithms
• Some clustering algorithms
– K-means
– Hierarchical
– Statistically based clustering algorithms
• Mixture model based clustering
– Fuzzy clustering
– Self-organizing Maps (SOM)
– Density-based (DBSCAN)
• Proper choice of algorithms depends on the type of clusters
to be found, the type of data, and the objective

50. 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

51. Clusters found in Random Data
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
Random
Points
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
K-means
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
DBSCAN
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
Complete
Link

52. • Distinguishing whether non-random structure actually exists in the data
• Comparing the results of a cluster analysis to externally known results,
e.g., to externally given class labels
• Evaluating how well the results of a cluster analysis fit the data without
reference to external information
• Comparing the results of two different sets of cluster analyses to
determine which is better
• Determining the ‘correct’ number of clusters
Different Aspects of Cluster Validation

53. • Order the similarity matrix with respect to cluster
labels and inspect visually.
Using Similarity Matrix for Cluster Validation
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
Points
Points
20 40 60 80 100
10
20
30
40
50
60
70
80
90
100
Similarity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1

54. Using Similarity Matrix for Cluster Validation
• Clusters in random data are not so crisp
Points
Points
20 40 60 80 100
10
20
30
40
50
60
70
80
90
100
Similarity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
DBSCAN
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y

55. Points
Points
20 40 60 80 100
10
20
30
40
50
60
70
80
90
100
Similarity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Using Similarity Matrix for Cluster Validation
• Clusters in random data are not so crisp
K-means
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y

56. Using Similarity Matrix for Cluster Validation
• Clusters in random data are not so crisp
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
Points
Points
20 40 60 80 100
10
20
30
40
50
60
70
80
90
100
Similarity
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Complete Link

57. • Numerical measures that are applied to judge various aspects of cluster
validity, are classified into the following three types of indices.
– External Index: Used to measure the extent to which cluster labels match
externally supplied class labels.
• Entropy
– Internal Index: Used to measure the goodness of a clustering structure
without respect to external information.
• Sum of Squared Error (SSE)
– Relative Index: Used to compare two different clusterings or clusters.
• Often an external or internal index is used for this function, e.g., SSE
or entropy
• For futher details please see “Introduction to Data
Mining”, Chapter 8.
– http://www-users.cs.umn.edu/~kumar/dmbook/ch8.pdf
Measures of Cluster Validity

58. Association Analysis

59. Association Analysis
• Given a set of records, find dependency rules which will predict
occurrence of an item based on occurrences of other items in
the record
• Applications
– Marketing and Sales Promotion
– Supermarket shelf management
– Traffic pattern analysis (e.g., rules such as "high congestion on Intersection 58
implies high accident rates for left turning traffic")
TID Items
1 Bread, Coke, Milk
2 Beer, Bread
3 Beer, Coke, Diaper, Milk
4 Beer, Bread, Diaper, Milk
5 Coke, Diaper, Milk
Rules Discovered:
{Milk} --> {Coke} (s=0.6, c=0.75)
{Diaper, Milk} --> {Beer}
(s=0.4, c=0.67)
ons
transacti
Total
Y
and
X
contain
that
ons
transacti
#
s
Support, 
X
contain
that
ons
transacti
#
Y
and
X
contain
that
ons
transacti
#
c
,
Confidence 

60. 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: Two Steps
– Frequent Itemset Generation
• Generate all itemsets whose support  minsup
– 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 computationally expensive

61. Efficient Pruning Strategy (Ref: Agrawal & Srikant 1994)
If an itemset is infrequent,
then all of its supersets must
also be infrequent
null
AB AC AD AE BC BD BE CD CE DE
A B C D E
ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE
ABCD ABCE ABDE ACDE BCDE
ABCDE
Found to be
Infrequent
null
AB AC AD AE BC BD BE CD CE DE
A B C D E
ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE
ABCD ABCE ABDE ACDE BCDE
ABCDE
null
AB AC AD AE BC BD BE CD CE DE
A B C D E
ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE
ABCD ABCE ABDE ACDE BCDE
ABCDE
Pruned
supersets

62. Illustrating Apriori Principle
Item Count
Bread 4
Coke 2
Milk 4
Beer 3
Diaper 4
Eggs 1
Itemset Count
{Bread,Milk} 3
{Bread,Beer} 2
{Bread,Diaper} 3
{Milk,Beer} 2
{Milk,Diaper} 3
{Beer,Diaper} 3
Itemset Count
{Bread,Milk,Diaper} 3
Items (1-itemsets)
Pairs (2-itemsets)
(No need to generate
candidates involving Coke
or Eggs)
Triplets (3-itemsets)
Minimum Support = 3
If every subset is considered,
6C1 + 6C2 + 6C3 = 41
With support-based pruning,
6 + 6 + 1 = 13