Data Mining:
Mining Frequent Patterns,
Association and Correlations
1
Mining Frequent Patterns, Association and
Correlations
 Basic concepts and a road map
 Efficient and scalable frequent itemset mining
methods
 Mining various kinds of association rules
 From association mining to correlation
analysis
 Summary
2
What Is Frequent Pattern Analysis?

Frequent pattern: a pattern (a set of items, subsequences, substructures,
etc.) that occurs frequently in a data set

First proposed by Agrawal, Imielinski, and Swami [AIS93] in the context
of frequent itemsets and association rule mining



Motivation: Finding inherent regularities in data

What products were often purchased together?— Beer and diapers?!

What are the subsequent purchases after buying a PC?

What kinds of DNA are sensitive to this new drug?

Can we automatically classify web documents?
Assume all data are categorical.
No good algorithm for numeric data.
3
Why Is Freq. Pattern Mining Important?

Discloses an intrinsic and important property of data sets

Forms the foundation for many essential data mining tasks

Association, correlation, and causality analysis

Sequential, structural (e.g., sub-graph) patterns

Pattern analysis in spatiotemporal, multimedia, timeseries, and stream data

Classification: associative classification

Cluster analysis: frequent pattern-based clustering

Data warehousing: cube-gradient

Broad applications
4
Association Rules


Rules for customers that buy PC for buying
antivirus software
 PC  antivirus-sw [support =2%, conf= 60%]
 Support  2% of customers both PC and
antivirus-sw together
 Confidence  60% of PC buyers also buys
antivirus-sw
Needs to satisfy minimum support and confidence
5
Definitions




Let
be set of all items
 I = {bread, milk, beer, chocolate, egg, diaper}
Transaction
 T1 = {milk, egg}
Itemset
 Set of items
 k-itemset: itemset with k items
Frequent itemset
 Itemsets that satisfies a frequency threshold
called minimum support count
6
Transaction data: a set of documents

A text document data set. Each
document is treated as a “bag” of
keywords
doc1:
doc2:
doc3:
doc4:
doc5:
doc6:
doc7:
CS583, Bing Liu, UIC
Student, Teach, School
Student, School
Teach, School, City, Game
Baseball, Basketball
Basketball, Player, Spectator
Baseball, Coach, Game, Team
Basketball, Team, City, Game
7
Association Rules



Association rule: an implication
 A  B
 A ⊂I, B⊂I, A∩B=∅
Holds with some support s and confidence c
 Support (AB): the percentage of transactions
that contain A U B which is P(A U B)
 Confidence (AB): the conditional probability
that a transaction having A also contains B
which is P(B|A) = freq(AUB) / freq(A)
Minimum support and minimum confidence are
prespecified thresholds
8
Basic Concepts: Frequent Patterns and
Association Rules
Transaction-id
Items bought
1
A, B, D
2
A, C, D
3
A, D, E
4
B, E, F
5
B, C, D, E, F


Itemset I = {i1, …, ik}
Find all the rules X  Y with minimum
support and confidence


Customer
buys both
Customer
buys diaper
support, s, probability that a
transaction contains X  Y
confidence, c, conditional
probability that a transaction
having X also contains Y
Let supmin = 50%, confmin = 50%
Freq. itemset: {A:3, B:3, D:4, E:3,
AD:3}
Customer
buys beer
Association rules:
A  D (60%, 100%)
D  A (60%, 75%)
9
Association Rule mining



Goal: Find all rules that satisfy the user-specified
minimum support and minimum confidence
Association Rule mining can be viewed in two
steps
 Find all frequent itemsets: itemsets that occur
at least as frequently as prespecified minimum
support count min_sup
 Generate strong association rules: that satisfy
minimum support and minimum confidence
First part is more costly
10
Closed Patterns


Huge number of itemsets: if an itemset is frequent then
all its subsets are frequent
A long pattern contains a combinatorial number of subpatterns, e.g., {a1, …, a100} contains =

Too huge to compute or store

Solution: Mine closed patterns instead
11
Closed Patterns

An itemset X is closed if X is frequent and there exists no
super-pattern Y ‫ כ‬X, with the same support as X
(proposed by Pasquier, et al. @ ICDT’99)


i.e. use the biggest possible itemset for a support level
Closed pattern is a lossless compression of freq. patterns

Reducing the # of patterns and rules
12
Closed Patterns

Exercise. DB = {<a1, …, a100>, < a1, …, a50>}



Min_sup = 1.
What is the set of closed itemset?

<a1, …, a100>: 1

< a1, …, a50>: 2
What is the set of all patterns?

2100-1!!
13
Mining Frequent Patterns, Association
and Correlations
 Basic concepts and a road map
 Efficient and scalable frequent itemset mining
methods
 Mining various kinds of association rules
 From association mining to correlation
analysis
 Summary
14
Scalable Methods for Mining Frequent Patterns



The downward closure property of frequent patterns
 Any subset of a frequent itemset must be frequent
 If {beer, diaper, nuts} is frequent, so is {beer,
diaper}
 i.e., every transaction having {beer, diaper, nuts} also
contains {beer, diaper}
Scalable mining methods: Several approaches
 Apriori (Agrawal & Srikant@VLDB’94)
 Freq. pattern growth (FPgrowth—Han, Pei & Yin
@SIGMOD’00)
Any algorithm should find the same set of rules although
their computational efficiencies and memory requirements
may be different
15
Apriori: A Candidate Generation-and-Test Approach


Apriori pruning principle: If there is any itemset which is
infrequent, its superset should not be generated/tested!
(Agrawal & Srikant @VLDB’94, Mannila, et al. @ KDD’ 94)
Method:




Initially, scan DB once to get frequent 1-itemset
Generate length (k+1) candidate itemsets from length k
frequent itemsets
Test the candidates against DB
Terminate when no frequent or candidate set can be
generated
16
The Apriori Algorithm—An Example
Database TDB
Tid
Items
10
A, C, D
20
B, C, E
30
A, B, C, E
40
B, E
Supmin = 2
Itemset
{A, C}
{B, C}
{B, E}
{C, E}
sup
{A}
2
{B}
3
{C}
3
{D}
1
{E}
3
C1
1st scan
C2
L2
Itemset
sup
2
2
3
2
Itemset
{A, B}
{A, C}
{A, E}
{B, C}
{B, E}
{C, E}
sup
1
2
1
2
3
2
Itemset
sup
{A}
2
{B}
3
{C}
3
{E}
3
L1
C2
2nd scan
Itemset
{A, B}
{A, C}
{A, E}
{B, C}
{B, E}
{C, E}
C3
Itemset
{B, C, E}
3rd scan
L3
Itemset
sup
{B, C, E}
2
17
The Apriori Algorithm

Pseudo-code:
Ck: Candidate itemset of size k
Lk : frequent itemset of size k
L1 = {frequent items};
for (k = 1; Lk !=; k++) do begin
Ck+1 = candidates generated from Lk;
for each transaction t in database do
increment the count of all candidates in Ck+1
that are contained in t
Lk+1 = candidates in Ck+1 with min_support
end
return k Lk;
18
Important Details of Apriori

How to generate candidates?

Step 1: self-joining Lk

Step 2: pruning

How to count supports of candidates?

Example of Candidate-generation


L3={abc, abd, acd, ace, bcd}
Self-joining: L3*L3



Pruning:


abcd from abc and abd
acde from acd and ace
acde is removed because ade is not in L3
C4={abcd}
19
Step 2: Generating rules from
frequent itemsets



Frequent itemsets  association rules
One more step is needed to generate association
rules
For each frequent itemset X,
For each proper nonempty subset A of X,
 Let B = X - A
 A  B is an association rule if

Confidence(A  B) ≥ minconf,
support(A  B) = support(AB) = support(X)
confidence(A  B) = support(A  B) / support(A)
Generating rules: an example

Suppose {2,3,4} is frequent, with sup=50%


Proper nonempty subsets: {2,3}, {2,4}, {3,4}, {2}, {3}, {4},
with sup=50%, 50%, 75%, 75%, 75%, 75% respectively
These generate these association rules:







2,3  4, confidence=100%
2,4  3, confidence=100%
3,4  2, confidence=67%
2  3,4, confidence=67%
3  2,4, confidence=67%
4  2,3, confidence=67%
All rules have support = 50%
 support(A  B) = support(AB)
Generating rules: summary



To recap, in order to obtain A  B, we need to
have support(A  B) and support(A)
All the required information for confidence
computation has already been recorded in
itemset generation. No need to see the data T
any more.
This step is not as time-consuming as frequent
itemsets generation.
Bottleneck of Apriori Alg


Multiple database scans are costly
Mining long patterns needs many passes of
scanning and generates lots of candidates

To find frequent itemset i1i2…i100

# of scans: 100

Bottleneck: candidate-generation-and-test

Can we avoid candidate generation?
23
Mining Frequent Patterns Without
Candidate Generation

Grow long patterns from short ones using local
frequent items

“abc” is a frequent pattern

Get all transactions having “abc”: DB|abc

“d” is a local frequent item in DB|abc  abcd is
a frequent pattern
24
Construct FP-tree from a Transaction Database
TID
100
200
300
400
500
Items bought
(ordered) frequent items
{f, a, c, d, g, i, m, p}
{f, c, a, m, p}
{a, b, c, f, l, m, o}
{f, c, a, b, m}
{b, f, h, j, o, w}
{f, b}
{b, c, k, s, p}
{c, b, p}
{a, f, c, e, l, p, m, n}
{f, c, a, m, p}
Header Table
1. Scan DB once, find
frequent 1-itemset
(single item pattern)
2. Sort frequent items in
frequency descending
order, f-list
3. Scan DB again,
construct FP-tree
Item frequency head
f
4
c
4
a
3
b
3
m
3
p
3
min_support = 3
{}
f:1
c:1
a:1
m:1
p:1
25
Construct FP-tree from a Transaction Database
TID
100
200
300
400
500
Items bought
(ordered) frequent items
{f, a, c, d, g, i, m, p}
{f, c, a, m, p}
{a, b, c, f, l, m, o}
{f, c, a, b, m}
{b, f, h, j, o, w}
{f, b}
{b, c, k, s, p}
{c, b, p}
{a, f, c, e, l, p, m, n}
{f, c, a, m, p}
Header Table
1. Scan DB once, find
frequent 1-itemset
(single item pattern)
2. Sort frequent items in
frequency descending
order, f-list
3. Scan DB again,
construct FP-tree
Item frequency head
f
4
c
4
a
3
b
3
m
3
p
3
F-list=f-c-a-b-m-p
min_support = 3
{}
f:2
c:2
a:2
m:1
b:1
p:1
m:1
26
Construct FP-tree from a Transaction Database
TID
100
200
300
400
500
Items bought
(ordered) frequent items
{f, a, c, d, g, i, m, p}
{f, c, a, m, p}
{a, b, c, f, l, m, o}
{f, c, a, b, m}
{b, f, h, j, o, w}
{f, b}
{b, c, k, s, p}
{c, b, p}
{a, f, c, e, l, p, m, n}
{f, c, a, m, p}
Header Table
1. Scan DB once, find
frequent 1-itemset
(single item pattern)
2. Sort frequent items in
frequency descending
order, f-list
3. Scan DB again,
construct FP-tree
Item frequency head
f
4
c
4
a
3
b
3
m
3
p
3
F-list=f-c-a-b-m-p
min_support = 3
{}
f:4
c:3
c:1
b:1
a:3
b:1
p:1
m:2
b:1
p:2
m:1
27
Construct FP-tree from a Transaction Database
TID
100
200
300
400
500
Items bought
(ordered) frequent items
{f, a, c, d, g, i, m, p}
{f, c, a, m, p}
{a, b, c, f, l, m, o}
{f, c, a, b, m}
{b, f, h, j, o, w}
{f, b}
{b, c, k, s, p}
{c, b, p}
{a, f, c, e, l, p, m, n}
{f, c, a, m, p}
Header Table
1. Scan DB once, find
frequent 1-itemset
(single item pattern)
2. Sort frequent items in
frequency descending
order, f-list
3. Scan DB again,
construct FP-tree
Item frequency head
f
4
c
4
a
3
b
3
m
3
p
3
F-list=f-c-a-b-m-p
min_support = 3
{}
f:4
c:3
c:1
b:1
a:3
b:1
p:1
m:2
b:1
p:2
m:1
28
Find Patterns Having P From P-conditional Database



Starting at the frequent item header table in the FP-tree
Traverse the FP-tree by following the link of each frequent item p
Accumulate all of transformed prefix paths of item p to form p’s
conditional pattern base
{}
Header Table
Item frequency head
f
4
c
4
a
3
b
3
m
3
p
3
f:4
c:3
c:1
b:1
a:3
Conditional pattern bases
item
cond. pattern base
b:1
c
f:3
p:1
a
fc:3
b
fca:1, f:1, c:1
m:2
b:1
m
fca:2, fcab:1
p:2
m:1
p
fcam:2, cb:1
29
Example: conditional patterns having ‘p’





Start with the bottom of “header table”
Find all paths to ‘p’
Those are: (f:4, c:3, a:3, m:2, p:2) and (c:1, b:1,
p:1)
Paths that contain ‘p’
 (f:2, c:2, a:2, m:2, p:2) and (c:1, b:1, p:1)
Find prefix paths (remove ‘p’)
 (f:2, c:2, a:2, m:2) and (c:1, b:1)
30
From Conditional Pattern-bases to Conditional FP-trees

For each pattern-base
 Accumulate the count for each item in the base
 Construct the FP-tree for the frequent items of the
pattern base
min_support = 3
Header Table
Item frequency head
f
4
c
4
a
3
b
3
m
3
p
3
{}
f:4
c:3
c:1
b:1
a:3
b:1
p:1
m:2
b:1
p:2
m:1
m-conditional pattern base:
fca:2, fcab:1
All frequent
patterns relate to m
{}
m,

f:3  fm, cm, am,
fcm, fam, cam,
c:3
fcam
a:3
m-conditional FP-tree
31
Another example
Transaction
itemset
Sorted itemset
Freq items
T1
a,b,e
b,a,e
b:7
T2
b,d
b,d
a:6
T3
b,c
b,c
c:6
T4
a,b,d
b,a,d
d:2
T5
a,c
a,c
e:2
T6
b,c
b,c
T7
a,c
a,c
T8
a,b,c,e
b,a,c,e
T9
a,b,c
b,a,c
Min_sup = 2
32
Example –cont.
Item
Cond. pattern
Cond. FP-tree
Freq. patterns
e
{b,a:1}{b,a,c:1}
<b:2,a:2>
{b,e:2}{a,e:2}{a,b,e:2}
d
{b,a:1}{b:1}
<b:2>
{b,d:2}
c
{b,a:2}{b:2}{a:2} <b:4,a:2><a:2>
{b,c:4}{a,c:4}{a,b,c:2}
a
{b:4}
{b,a:4}
<b:4>
33
Benefits of the FP-tree Structure


Completeness
 Preserve complete information for frequent pattern
mining
 Never break a long pattern of any transaction
Compactness
 Reduce irrelevant info—infrequent items are gone
 Items in frequency descending order: the more
frequently occurring, the more likely to be shared
 Never be larger than the original database (not count
node-links and the count field)
34
Partition Patterns and Databases


Frequent patterns can be partitioned into subsets
according to f-list
 F-list=f-c-a-b-m-p
 Patterns containing p
 Patterns having m but no p
 …
 Patterns having c but no a nor b
 Pattern f
Completeness and non-redundency
35
Scaling FP-growth by DB Projection




FP-tree cannot fit in memory?—DB projection
First partition a database into a set of projected DBs
Then construct and mine FP-tree for each projected DB
Parallel projection vs. Partition projection techniques
 Parallel projection is space costly
36
Why Is FP-Growth the Winner?

Divide-and-conquer:



decompose both the mining task and DB according to
the frequent patterns obtained so far
leads to focused search of smaller databases
Other factors

no candidate generation, no candidate test

compressed database: FP-tree structure

no repeated scan of entire database

basic ops—counting local freq items and building sub
FP-tree, no pattern search and matching
37
Mining Frequent Patterns, Association
and Correlations
 Basic concepts and a road map
 Efficient and scalable frequent itemset mining
methods
 Mining various kinds of association rules
 From association mining to correlation
analysis
 Summary
38
Mining Various Kinds of Association Rules

Mining multilevel association

Miming multidimensional association

Mining quantitative association

Mining interesting correlation patterns
39
Mining Multiple-Level Association Rules


Items often form hierarchies
Flexible support settings
 Items at the lower level are expected to have lower
support


Logitech wireless laser mouse M505 & Norton antivirus 2015
Difficult to find strong associations

use multiple min_sup
reduced support
uniform support
Level 1
min_sup = 5%
Level 2
min_sup = 5%
Milk
[support = 10%]
2% Milk
[support = 6%]
Skim Milk
[support = 4%]
Level 1
min_sup = 5%
Level 2
min_sup = 3%
40
Problem for uniform support

If the frequencies of items vary a great deal, we
will encounter two problems


If min_sup is set too high, those rules that
involve rare items will not be found.
To find rules that involve both frequent and
rare items, min_sup has to be set very low.
This causes combinatorial explosion because
those frequent items will be associated with
one another in all possible ways.
CS583, Bing Liu, UIC
41
Mining Multi-Dimensional Association

Single-dimensional rules:
buys(X, “milk”)  buys(X, “bread”)

Multi-dimensional rules:  2 dimensions or predicates

Inter-dimension assoc. rules (no repeated predicates)
age(X,”19-25”)  occupation(X,“student”)  buys(X, “coke”)

hybrid-dimension assoc. rules (repeated predicates)
age(X,”19-25”)  buys(X, “popcorn”)  buys(X, “coke”)


Categorical Attributes: finite number of possible values, no
ordering among values—(occupation, brand, color)
Quantitative Attributes: numeric, implicit ordering among
values—discretization, clustering, and gradient approaches
42
Mining Quantitative Associations
Techniques can be categorized by how numerical
attributes, such as age or salary are treated
1. Static discretization based on predefined concept
hierarchies (data cube methods)

2. Dynamic discretization based on data distribution
(quantitative rules)

Intervals dynamically determined
3. Clustering: Distance-based association

one dimensional clustering then association
43
Mining Other Interesting Patterns

Flexible support constraints



Some items (e.g., diamond) may occur rarely but are
valuable
Customized supmin specification and application
Top-K closed frequent patterns

Hard to specify supmin
44
Mining Frequent Patterns, Association
and Correlations
 Basic concepts and a road map
 Efficient and scalable frequent itemset mining
methods
 Mining various kinds of association rules
 From association mining to correlation analysis
 Summary
45
Interesting Measure - Lift


Strong rules are not necessarily important
 Only an estimate, not measure real strength of
correlation
Not basketball
Sum (row)
Cereal
2000
1750
3750
Not cereal
1000
250
1250
Sum(col.)
3000
2000
5000
play basketball  eat cereal [40%, 66.7%] is misleading


Basketball
The overall % of students eating cereal is 75% > 66.7%.
play basketball  not eat cereal [20%, 33.3%] is more accurate,
although with lower support and confidence
46
Interestingness Measure: Correlations (Lift)

Measure of dependent/correlated events: lift
P( A B)
lift 
P( A) P( B)
lift ( B, C ) 
Basketball
Not basketball
Sum (row)
Cereal
2000
1750
3750
Not cereal
1000
250
1250
Sum(col.)
3000
2000
5000
2000 / 5000
 0.89
3000 / 5000 * 3750 / 5000
lift ( B, C ) 

If lift > 1 positively correlated

If lift < 1 negatively correlated

If lift = 0 independent
1000 / 5000
 1.33
3000 / 5000 *1250 / 5000
47
Mining Frequent Patterns, Association
and Correlations
 Basic concepts and a road map
 Efficient and scalable frequent itemset mining
methods
 Mining various kinds of association rules
 From association mining to correlation analysis
 Summary
48
Summary

Frequent pattern mining—an important task in data mining

Support & confidence

Scalable frequent pattern mining methods

Apriori (Candidate generation & test)

FPgrowth (Projection-based)

Mining a variety of rules and interesting patterns

Correlation analysis

lift
49