1. Ch5 Mining Frequent Patterns, Associations, and Correlations
Dr. Bernard Chen Ph.D.
University of Central Arkansas

2. Outline Association Rules Association Rules with FP tree
Misleading Rules
Multi-level Association Rules

3. 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

4. What Is Frequent Pattern Analysis?
Motivation: Finding inherent regularities in data
What products were often purchased together? bread and milk?
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?
Applications
Basket data analysis, cross-marketing, catalog design, sale campaign analysis, Web log (click stream) analysis, and DNA sequence analysis.

5. Association Rules

6. Association Rules
support, s, probability that a transaction contains X  Y
confidence, c, conditional probability that a transaction having X also contains Y

7. Association Rules Let’s have an example T100 1,2,5 T200 2,4 T300 2,3

8. Association Rules with Apriori Minimum support=2/9 Minimum confidence=60%

9. 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 that are contained in t
Lk+1 = candidates in Ck+1 with min_support
end
return k Lk;

10. Strong Association Rule
Strong association rules means the frequent rules that also pass the minimum confidence.
For example frequent rules: {I1, I2}
Confidence(I1->I2)= 4/6
(strong association rule!)
Confidence(I2->I1)= 4/7

11. Exercise
A dataset has five transactions, let min-support=60% and min_support=80%
Find all frequent itemsets using Apriori and all strong association rules
TID
Items_bought T1 T2 T3 T4 T5
M, O, N, K, E, Y
D, O, N, K , E, Y
M, A, K, E
M, U, C, K ,Y
C, O, O, K, I ,E

12. Association Rules with Apriori
K:5 KE:4 KE
E:4 KM:3 KM
M:3 KO:3 KO
O:3 => KY:3 => KY => KEO
Y:3 EM:2 EO
EO:3
EY:2
MO:1
MY:2
OY:2

13. Outline Association Rules Association Rules with FP tree
Misleading Rules
Multi-level Association Rules

14. Mining Frequent Itemsets without Candidate Generation
In many cases, the Apriori candidate generate-and-test method significantly reduces the size of candidate sets, leading to good performance gain.
However, it suffer from two nontrivial costs:
It may generate a huge number of candidates (for example, if we have 10^4 1-itemset, it may generate more than 10^7 candidata 2-itemset)
It may need to scan database many times

15. Association Rules with Apriori Minimum support=2/9 Minimum confidence=70%

16. Bottleneck of Frequent-pattern Mining
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
# of Candidates: (1001) + (1002) + … + (110000) = = 1.27*1030 !
Bottleneck: candidate-generation-and-test
Can we avoid candidate generation?

17. 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

18. Process of FP growth
Scan DB once, find frequent 1-itemset (single item pattern)
Sort frequent items in frequency descending order
Scan DB again, construct FP-tree

19. Association Rules Let’s have an example T100 1,2,5 T200 2,4 T300 2,3

20. FP Tree

21. Mining the FP tree

22. 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)
For Connect-4 DB, compression ratio could be over 100

23. Exercise
A dataset has five transactions, let min-support=60% and min_confidence=80%
Find all frequent itemsets using FP Tree
TID
Items_bought T1 T2 T3 T4 T5
M, O, N, K, E, Y
D, O, N, K , E, Y
M, A, K, E
M, U, C, K ,Y
C, O, O, K, I ,E

24. Association Rules with FP Tree
K:5
E:4
M:3
O:3
Y:3

25. Association Rules with FP Tree
Y: KEMO:1 KEO:1 KY:1
K:3 KY
O: KEM:1 KE:2
KE:3 KO EO KEO
M: KE:2 K:1
K:3 KM
E: K:4 KE

26. FP-Growth vs. Apriori: Scalability With the Support Threshold
Data set T25I20D10K

27. 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

28. Outline Association Rules Association Rules with FP tree
Misleading Rules
Multi-level Association Rules

29. Example 5.8 Misleading “Strong” Association Rule
Of the 10,000 transactions analyzed, the data show that
6,000 of the customer included computer games,
while 7,500 include videos,
And 4,000 included both computer games and videos

30. Misleading “Strong” Association Rule
For this example:
Support (Game & Video) =
4,000 / 10,000 =40%
Confidence (Game => Video) =
4,000 / 6,000 = 66%
Suppose it pass our minimum support and confidence (30% , 60%, respectively)

31. Misleading “Strong” Association Rule
However, the truth is : “computer games and videos are negatively associated”
Which means the purchase of one of these items actually decreases the likelihood of purchasing the other.
(How to get this conclusion??)

32. Misleading “Strong” Association Rule
Under the normal situation,
60% of customers buy the game
75% of customers buy the video
Therefore, it should have 60% * 75% = 45% of people buy both
That equals to 4,500 which is more than 4,000 (the actual value)

33. From Association Analysis to Correlation Analysis
Lift is a simple correlation measure that is given as follows
The occurrence of itemset A is independent of the occurrence of itemset B if
P(AUB) = P(A)P(B)
Otherwise, itemset A and B are dependent and correlated as events
Lift(A,B) = P(AUB) / P(A)P(B)
If the value is less than 1, the occurrence of A is negatively correlated with the occurrence of B
If the value is greater than 1, then A and B are positively correlated

34. Outline Association Rules Association Rules with FP tree
Misleading Rules
Multi-level Association Rules

35. Mining Multiple-Level Association Rules
Items often form hierarchies

36. Mining Multiple-Level Association Rules
Items often form hierarchies

37. Mining Multiple-Level Association Rules
Flexible support settings
Items at the lower level are expected to have lower support
uniform support
Milk
[support = 10%]
2% Milk
[support = 6%]
Skim Milk
[support = 4%]
Level 1
min_sup = 5%
Level 2
min_sup = 3%
reduced support

38. Multi-level Association: Redundancy Filtering
Some rules may be redundant due to “ancestor” relationships between items.
Example
milk  wheat bread [support = 8%, confidence = 70%]
2% milk  wheat bread [support = 2%, confidence = 72%]
We say the first rule is an ancestor of the second rule.