[PPT] - Introduction to Data Mining Frequent Pattern Mining and Association PowerPoint Presentation

SLIDE 1

Introduction to Data Mining

Frequent Pattern Mining and Association Analysis

Li Xiong

Slide credits: Jiawei Han and Micheline Kamber George Kollios

1

SLIDE 2

Mining Frequent Patterns, Association and Correlations

 Basic concepts  Frequent itemset mining methods  Mining association rules  Association mining to correlation analysis  Constraint-based association mining

2

SLIDE 3

What Is Frequent Pattern Analysis?



Frequent pattern: a pattern (a set of items, subsequences, substructures, etc.) that occurs frequently in a data set

 Frequent sequential pattern  Frequent structured pattern



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?



Applications

 Basket data analysis, cross-marketing, catalog design, sale campaign

analysis, Web log (click stream) analysis, and DNA sequence analysis.

3

SLIDE 4

Frequent Itemset Mining

 Frequent itemset mining: frequent set of items in a

transaction data set

 Agrawal, Imielinski, and Swami, SIGMOD 1993

 SIGMOD Test of Time Award 2003

“This paper started a field of research. In addition to containing an innovative algorithm, its subject matter brought data mining to the attention of the database community … even led several years ago to an IBM commercial, featuring supermodels, that touted the importance of work such as that contained in this paper. ”

R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of

items in large databases. In SIGMOD ’93. Apriori: Rakesh Agrawal and Ramakrishnan Srikant. Fast Algorithms for Mining Association Rules. In VLDB '94.

4

SLIDE 5

Basic Concepts: Transaction dataset

5

Transaction-id Items bought 10 A, B, D 20 A, C, D 30 A, D, E 40 B, E, F 50 B, C, D, E, F

SLIDE 6

Record Data



Data that consists of a collection of records, each of which consists of a fixed set of attributes



Points in a multi-dimensional space, where each dimension represents a distinct attribute



Represented by an m by n matrix, where there are m rows, one for each object, and n columns, one for each attribute

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

10

SLIDE 7

Transaction Data

 A special type of record data, where

 each record (transaction) involves a set of items.  For example, the set of products purchased by a

customer during one shopping trip constitute a transaction, while the individual products that were purchased are the items.



Itemset: X = {x1, …, xk} (k- itemset)



Frequent itemset: X with minimum support count



Support count (absolute support): count of transactions containing X



Association rule: A  B with minimum support and confidence



Support: probability that a transaction contains A  B s = P(A  B)



Confidence: conditional probability that a transaction having A also contains B c = P(B | A)

12

Customer buys diaper Customer buys both Customer buys beer Transaction-id Items bought 10 A, B, D 20 A, C, D 30 A, D, E 40 B, E, F 50 B, C, D, E, F

SLIDE 13

Illustration of Frequent Itemsets and Association Rules

13

Transaction-id Items bought 10 A, B, D 20 A, C, D 30 A, D, E 40 B, E, F 50 B, C, D, E, F

 Frequent itemsets (minimum support count = 3) ?  Association rules (minimum support = 50%, minimum

confidence = 50%) ?

SLIDE 14

Illustration of Frequent Itemsets and Association Rules

14

Transaction-id Items bought 10 A, B, D 20 A, C, D 30 A, D, E 40 B, E, F 50 B, C, D, E, F

 Frequent itemsets (minimum support count = 3) ?  Association rules (minimum support = 50%, minimum

confidence = 50%) ? {A:3, B:3, D:4, E:3, AD:3} A  D (60%, 100%) D  A (60%, 75%)

SLIDE 15

Mining Frequent Patterns, Association and Correlations

 Basic concepts  Frequent itemset mining methods  Mining association rules  Association mining to correlation analysis  Constraint-based association mining

15

SLIDE 16

Scalable Methods for Mining Frequent Patterns

 Frequent itemset mining methods

 Apriori (Agrawal & Srikant@VLDB’94) and variations  Frequent pattern growth (FPgrowth—Han, Pei & Yin

@SIGMOD’00)

 Closed and maximal patterns and their mining methods  FIMI Workshop and implementation repository

16

SLIDE 17

Frequent itemset mining

 Brute force approach

Transaction- id Items bought 10 A, B, D 20 A, C, D 30 A, D, E 40 B, E, F 50 B, C, D, E, F

Itemset: X = {x1, …, xk} (k-itemset) Frequent itemset: X with minimum support count

SLIDE 18

Frequent itemset mining

 Brute force approach  Set enumeration tree for all possible itemsets  Tree search

Transaction- id Items bought 10 A, B, D 20 A, C, D 30 A, D, E 40 B, E, F 50 B, C, D, E, F

SLIDE 19

Apriori – Apriori Property

 The apriori property of frequent patterns

 Any nonempty subset of a frequent itemset must be

frequent

 If {beer, diaper, nuts} is frequent, so is {beer, diaper}

 Apriori pruning principle: If there is any itemset which is

infrequent, its superset should not be generated/tested!

19

SLIDE 20

Apriori: Level-Wise Search Method

 Level-wise search method (BFS):

 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

20

SLIDE 21

The Apriori Algorithm

 Pseudo-code:

Ck: Candidate k-itemset Lk : frequent k-itemset L1 = frequent 1-itemsets; for (k = 2; Lk-1 !=; k++) Ck = generate candidate set from Lk-1; for each transaction t in database find all candidates in Ck that are subset of t; increment their count; Lk = candidates in Ck with min_support return k Lk;

21

SLIDE 22

The Apriori Algorithm—An Example

22

Transaction DB

1st scan C1 L1 L2 C2 C2 2nd scan C3 L3 3rd scan

Tid Items 10 A, C, D 20 B, C, E 30 A, B, C, E 40 B, E Itemset sup {A} 2 {B} 3 {C} 3 {D} 1 {E} 3 Itemset sup {A} 2 {B} 3 {C} 3 {E} 3 Itemset {A, B} {A, C} {A, E} {B, C} {B, E} {C, E} Itemset sup {A, B} 1 {A, C} 2 {A, E} 1 {B, C} 2 {B, E} 3 {C, E} 2 Itemset sup {A, C} 2 {B, C} 2 {B, E} 3 {C, E} 2 Itemset {B, C, E} Itemset sup {B, C, E} 2

Supmin = 2

SLIDE 23

Important Details of Apriori

 How to generate candidate sets?  How to count supports for candidate sets?

23

SLIDE 24

Candidate Set Generation



Step 1: self-joining Lk-1: assuming items and itemsets are sorted in

rder, joinable only if the first k-2 items are in common



Step 2: pruning: prune if it has infrequent subset

Example: Generate C4 from L3={abc, abd, acd, ace, bcd}



Step 1: Self-joining: L3*L3

 abcd from abc and abd; acde from acd and ace 

Step 2: Pruning:

 acde is removed because ade is not in L3

C4={abcd}

24

Ck = generate candidate set from Lk-1;

SLIDE 25

How to Count Supports of Candidates?

for each transaction t in database

find all candidates in Ck that are subset of t; increment their count;

 Why counting supports of candidates a problem?

 The total number of candidates can be very huge  One transaction may contain many candidates

 For each subset s in t, check if s is in Ck

25

SLIDE 26

How to Count Supports of Candidates?

for each transaction t in database

find all candidates in Ck that are subset of t; increment their count;

 For each subset s in t, check if s is in Ck

 Linear search  Prefix tree  Hash-tree (prefix tree with hash function at interior

node)

 Hash-table

26

SLIDE 27

Example: Hash-tree

28

1,4,7 2,5,8 3,6,9 hash function 2 3 4 5 6 7 1 4 5 1 3 6 1 2 4 4 5 7 1 2 5 4 5 8 1 5 9 3 4 5 3 5 6 3 5 7 6 8 9 3 6 7 3 6 8 Transaction: 2 3 5 6 7

2 3 5 6 5

SLIDE 28

DHP: Direct Hashing and Pruning



DHP (Direct hashing and pruning): hash k-itemsets into buckets and a k-itemset whose bucket count is below the threshold cannot be frequent



Especially useful for 2-itemsets

 Generate a hash table of 2-itemsets during the scan for 1-itemset  If the count of a bucket is below minimum support count, the

itemsets in the bucket should not be included in candidate 2- itemsets

J. Park, M. Chen, and P. Yu. An effective hash-based algorithm for mining association
rules. In SIGMOD’95

29

SLIDE 29

DHP: Reducing number of candidates

30

SLIDE 30

DHP: Reducing number of candidates

31

SLIDE 31

Directly counting all 1-itemsets and 2-itemsets

32

SLIDE 32

Assignment 1

 Implementation and evaluation of Apriori  Performance competition with prizes!

33

SLIDE 33

Improving Efficiency of Apriori

 Bottlenecks

 Huge number of candidates  Multiple scans of transaction database  Support counting for candidates

 Improving Apriori: general ideas

 Shrink number of candidates  Reduce passes of transaction database scans  Reduce number of transactions

34

SLIDE 34

DHP: Reducing size and number of transactions



Discard infrequent items



If an item occurs in a frequent (k+1)-itemset, it must occur in at least k candidate k-itemset (necessary not sufficient)



Discard an item from a transaction if it does not occur in at least k candidate k-itemset during support counting



Discard a transaction if all items are discarded

J. Park, M. Chen, and P. Yu. An effective hash-based algorithm for mining association rules. In SIGMOD’95

35

SLIDE 35

DIC: Reduce Number of Scans



DIC (Dynamic itemset counting): partition DB into blocks, add new candidate itemsets at partition points



Once both A and D are determined frequent, the counting of AD begins



Once all length-2 subsets of BCD are determined frequent, the counting of BCD begins

36

ABCD ABC ABD ACD BCD AB AC BC AD BD CD A B C D {} Itemset lattice Transactions 1-itemsets 2-itemsets … Apriori 1-itemsets 2-items 3-items DIC

S. Brin R. Motwani, J. Ullman, and S.
Tsur. Dynamic itemset counting and

implication rules for market basket

data. In SIGMOD’97

SLIDE 36

Partitioning: Reduce Number of Scans

 Any itemset that is potentially frequent in DB must be

frequent in at least one of the partitions of DB

 Scan 1: partition database in n partitions and find local

frequent patterns (minimum support count?)

 Scan 2: determine global frequent patterns from the

collection of all local frequent patterns

A. Savasere, E. Omiecinski, and S. Navathe. An efficient algorithm for mining

association in large databases. In VLDB’95

37

SLIDE 37

Sampling for Frequent Patterns

 Select a sample of original database, mine frequent

patterns within samples using Apriori

 Scan database once to verify frequent itemsets found in

sample

 Use a lower support threshold than minimum support  Tradeoff accuracy against efficiency

H. Toivonen. Sampling large databases for association rules. In VLDB’96

38

SLIDE 38

September 12, 2017 Data Mining: Concepts and Techniques 39

Scalable Methods for Mining Frequent Patterns

 Scalable mining methods for frequent patterns

 Apriori (Agrawal & Srikant@VLDB’94) and variations  Frequent pattern growth (FPgrowth—Han, Pei & Yin

@SIGMOD’00)

 Algorithms using vertical format

 Closed and maximal patterns and their mining methods  FIMI Workshop and implementation repository

39

SLIDE 39

Mining Frequent Patterns Without Candidate Generation

40

 Apriori: Breadth first search in set enumeration tree  FP-Growth: Depth first search in set enumeration tree  Basic idea: Find (grow) long patterns from short ones in

conditional DB recursively

 “abc” is a frequent pattern  All transactions having “abc”: DB|abc (conditional DB)  “d” is a local frequent item in DB|abc, then abcd is a

frequent pattern

 Details:  How to represent DB to find conditional DB quickly? - FP

tree (prefix tree)

 How to represent all patterns? – set enumeration tree

with ordering

SLIDE 40

Representing DB as FP-tree and Finding Conditional DB

41

{} f:4 c:1 b:1 p:1 b:1 c:3 a:3 b:1 m:2 p:2 m:1 Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3 min_support = 3 TID Items bought (ordered) frequent items 100 {f, a, c, d, g, i, m, p} {f, c, a, m, p} 200 {a, b, c, f, l, m, o} {f, c, a, b, m} 300 {b, f, h, j, o, w} {f, b} 400 {b, c, k, s, p} {c, b, p} 500 {a, f, c, e, l, p, m, n} {f, c, a, m, p}

1. Scan DB once, find

frequent 1-itemset (single item pattern)

2. Sort frequent items in

frequency descending

rder, f-list
3. Scan DB again,

construct FP-tree (prefix tree) F-list=f-c-a-b-m-p

SLIDE 41

Finding Conditional FP-Tree



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 DB (conditional pattern base)

42

Conditional pattern base item

cond. pattern base

c f:3 a fc:3 b fca:1, f:1, c:1 m fca:2, fcab:1 p fcam:2, cb:1 {} f:4 c:1 b:1 p:1 b:1 c:3 a:3 b:1 m:2 p:2 m:1 Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3

SLIDE 42

Representing Patterns



Frequent patterns can be partitioned into subsets according to f-list: f-c-a-b-m-p (assuming items are sorted) – essentially set enumeration tree

 Patterns containing p (patterns ending with p)  Patterns having m but no p (patterns ending with m)  …  Patterns having c but no a nor b, m, p (patterns ending with c)  Pattern having f but no c, a, b, m, p (patterns ending with f)



Completeness and non-redundancy



Question: how to order the items?

44

SLIDE 43

Representing Patterns



Frequent patterns can be partitioned into subsets according to f-list: f-c-a-b-m-p (assuming items are sorted) – essentially set enumeration tree

 Patterns containing p (patterns ending with p)  Patterns having m but no p (patterns ending with m)  …  Patterns having c but no a nor b, m, p (patterns ending with c)  Pattern having f but no c, a, b, m, p (patterns ending with f)



Completeness and non-redundancy



Question: how to order the items?



Intuition: start from least frequent items to frequent items, offers better selectivity and pruning

45

SLIDE 44

Mining Frequent Patterns With FP-trees



Idea: Frequent pattern growth

 Recursively grow frequent patterns by pattern and database

partition



Method

 For each frequent item, construct its conditional DB and FP-tree  Repeat the process recursively on the new conditional FP-tree  Until the resulting FP-tree is empty, or it contains only one path—

single path will generate all the combinations of its sub-paths, each of which is a frequent pattern

46

SLIDE 45

48 

Construct p-conditional DB



Construct the FP-tree for the frequent items of p-conditional DB



Repeat the process recursively on the new conditional FP-tree until the resulting FP-tree is empty, or only one path

Finding Patterns Ending with p

p-conditional DB: fcam:2, cb:1 p-conditional FP-tree (min-support =3) {} c:3 {} f:4 c:1 b:1 p:1 b:1 c:3 a:3 b:1 m:2 p:2 m:1 Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3 All frequent patterns containing p

p, cp

SLIDE 46

Finding Patterns Ending with m



Construct m-conditional DB, then its conditional FP-tree



Repeat the process recursively on the new conditional FP-tree

49

m-conditional pattern base: fca:2, fcab:1

m-conditional FP-tree (min-support =3):

{} f:3 c:3 a:3 {} f:4 c:1 b:1 p:1 b:1 c:3 a:3 b:1 m:2 p:2 m:1 Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3

All frequent patterns ending with m:

m, fm, cm, am, fcm, fam, cam, fcam

SLIDE 47

FP-Growth vs. Apriori

50

10 20 30 40 50 60 70 80 90 100 0.5 1 1.5 2 2.5 3 Support threshold(%) Run time(sec.)

D1 FP-grow th runtime D1 Apriori runtime

Data set T25I20D10K

SLIDE 48

Why Is FP-Growth the Winner?

 Divide-and-conquer:

 Decompose both mining task and DB and leads to

focused search of smaller databases

 Use least frequent items as suffix (offering good

selectivity) and find shorter patterns recursively and concatenate with suffix

 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

51

SLIDE 49

September 12, 2017 Data Mining: Concepts and Techniques 52

Scalable Methods for Mining Frequent Patterns

 Scalable mining methods for frequent patterns

 Apriori (Agrawal & Srikant@VLDB’94) and variations  Frequent pattern growth (FPgrowth—Han, Pei & Yin

@SIGMOD’00)

 Algorithms using vertical format (ECLAT)

 Closed and maximal patterns and their mining methods  FIMI Workshop and implementation repository

52

SLIDE 50

ECLAT

 M. J. Zaki. Scalable algorithms for association mining.

IEEE TKDE, 12, 2000.

 For each item, store a list of transaction ids (tids)

53

10 B TID Items 1 A,B,E 2 B,C,D 3 C,E 4 A,C,D 5 A,B,C,D 6 A,E 7 A,B 8 A,B,C 9 A,C,D

Horizontal Data Layout

TID- list A B C D E 1 1 2 2 1 4 2 3 4 3 5 5 4 5 6 6 7 8 9 7 8 9 8 10 9

Vertical Data Layout

SLIDE 51

ECLAT

 Determine support of any k-itemset by intersecting tid-

lists of two of its (k-1) subsets.

 Advantage: very fast support counting  Disadvantage: intermediate tid-lists may become too large

for memory

54

A 1 4 5 6 7 8 9

B 1 2 5 7 8 10

 

AB 1 5 7 8

SLIDE 52

Scalable Methods for Mining Frequent Patterns

 Scalable mining methods for frequent patterns

 Apriori (Agrawal & Srikant@VLDB’94) and variations  Frequent pattern growth (FPgrowth—Han, Pei & Yin

@SIGMOD’00)

 Algorithms using vertical data format (ECLAT)

 Closed and maximal patterns and their mining methods

 Concepts  Max-patterns: MaxMiner, MAFIA  Closed patterns: CLOSET, CLOSET+, CARPENTER

 FIMI Workshop

55

SLIDE 53

Closed Patterns and Max-Patterns

 A long pattern contains a combinatorial number of sub-

patterns, e.g., {a1, …, a100} contains ____ sub-patterns!

 Solution: Mine “boundary” patterns

56

SLIDE 54

Closed Patterns and Max-Patterns

 An itemset X is closed if X is frequent and there exists no

super-pattern Y כ X, with the same support as X (Pasquier, et al. @ ICDT’99)

 An itemset X is a max-pattern if X is frequent and there

exists no frequent super-pattern Y כ X (Bayardo @ SIGMOD’98)

 Closed pattern is a lossless compression of freq. patterns

and support counts

57

SLIDE 55

Max-patterns

 Frequent patterns without frequent super patterns

 BCDE (2), ACD (2) are max-patterns  BCD (2) is not a max-pattern

58

Tid Items 10 A,B,C,D,E 20 B,C,D,E, 30 A,C,D,F

Min_sup=2

SLIDE 56

Max-Patterns Illustration

59

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 ABCD E

Border Infrequent Itemsets Maximal Itemsets

An itemset is maximal frequent if none of its immediate supersets is frequent

SLIDE 57

60

 An itemset is closed if none of its immediate supersets has

the same support as the itemset (min_sup = 2)

Itemset Support {A} 4 {B} 5 {C} 3 {D} 4 {A,B} 4 {A,C} 2 {A,D} 3 {B,C} 3 {B,D} 4 {C,D} 3

Itemset Support {A,B,C} 2 {A,B,D} 3 {A,C,D} 2 {B,C,D} 3 {A,B,C,D} 2

Closed Patterns

TID Items 1 {A,B} 2 {B,C,D} 3 {A,B,C,D} 4 {A,B,D} 5 {A,B,C,D}

SLIDE 58

Maximal vs Closed Itemsets

Frequent Itemsets Closed Frequent Itemsets Maximal Frequent Itemsets

61

SLIDE 59

Exercise: Closed Patterns and Max-Patterns

 DB = {<a1, …, a100>, < a1, …, a50>}

Min_sup = 1.

 What is the set of closed itemset?  What is the set of max-pattern?  What is the set of all patterns?

62

SLIDE 60

Exercise: Closed Patterns and Max-Patterns

 DB = {<a1, …, a100>, < a1, …, a50>}

Min_sup = 1.

 What is the set of closed itemset?  What is the set of max-pattern?  What is the set of all patterns?

 !!

63

<a1, …, a100>: 1 < a1, …, a50>: 2 <a1, …, a100>: 1

SLIDE 61

September 12, 2017 Data Mining: Concepts and Techniques 64

Scalable Methods for Mining Frequent Patterns

 Scalable mining methods for frequent patterns

 Apriori (Agrawal & Srikant@VLDB’94) and variations  Frequent pattern growth (FPgrowth—Han, Pei & Yin

@SIGMOD’00)

 Algorithms using vertical data format (ECLAT)

 Closed and maximal patterns and their mining methods

 Concepts  Max-pattern mining: MaxMiner, MAFIA  Closed pattern mining: CLOSET, CLOSET+,

CARPENTER

64

SLIDE 62

MaxMiner: Mining Max-patterns

 R. Bayardo. Efficiently mining long patterns from

databases. In SIGMOD’98

 Idea: generate the complete set-enumeration tree one

level at a time, prune if possible

65

 (ABCD) A (BCD) B (CD) C (D) D () AB (CD) AC (D) AD () BC (D) BD () CD () ABC (C) ABCD () ABD () ACD () BCD ()

SLIDE 63

Algorithm MaxMiner

 Initially, generate one node N= , where h(N)=

and t(N)={A,B,C,D}.

 Recursively expanding N

 Local pruning

 If h(N)t(N) (the leaf node) is frequent, do not expand N

(prune entire subtree). (bottom-up pruning – not a max pattern)

 If for some it(N), h(N){i} (immediate child node) is NOT

frequent, remove i from t(N) before expanding N (prune subbranch i). (top-down pruning – same as Apriori)

 Global pruning

66

 (ABCD)

SLIDE 64

Local Pruning Techniques (e.g. at node A)

Check the frequency of ABCD and AB, AC, AD.



If ABCD is frequent, prune the whole sub-tree.



If AC is NOT frequent, prune C from the parenthesis before expanding (prune AC branch)

67

 (ABCD) A (BCD) B (CD) C (D) D () AB (CD) AC (D) AD () BC (D) BD () CD () ABC (C) ABCD () ABD () ACD () BCD ()

SLIDE 65

 Basic concepts and a road map  Frequent itemset mining methods  Frequent sequence mining and graph mining  Apriori based: GSP (EDBT 96)  FP-Growth based: prefixSpan (ICDE 01)  Mining various kinds of association rules  From association mining to correlation analysis  Summary

73

SLIDE 71

GSP Algorithm (Generalized Sequential Pattern)

ID 100 200 300 400 500 Record a→c→d b→c→d a→b→c→e→d d→b a→d→c→d Database D Sequence {a} {b} {c} {d} Sup. 3 3 4 4 {e} 1 C1: cand 1-seqs Sequence {a} {b} {c} {d} Sup. 3 3 4 4 F1: freq 1-seqs

Sequence {a→a} {a→b} {a→c} {a→d} Sup. 1 3 3 {b→a} {b→b} {b→c} {b→d} 2 2 1 {c→a} {c→b} {c→c} {c→d} 4 {d→a} {d→b} {d→c} {d→d} 1 1 C2: cand 2-seqs Sequence {a→c} {a→d} {c→d} Sup. 3 3 4 F3: freq 2-seqs

Scan D Scan D Scan D

Sequence {a→a} {a→b} {a→c} {a→d} {b→a} {b→b} {b→c} {b→d} {c→a} {c→b} {c→c} {c→d} {d→a} {d→b} {d→c} {d→d} C2: cand 2-seqs

Sequence {a→b→c} C3: cand 3-seqs Sequence {a→b→c} Sup. 3 F3: freq 3-seqs

SLIDE 72

Mining Frequent Patterns, Association and Correlations

 Basic concepts and a road map  Frequent itemset mining methods  Frequent sequence mining and graph mining  Mining various kinds of association rules  Summary

75

SLIDE 73

Basic Concepts: Frequent Patterns and Association Rules



Itemset: X = {x1, …, xk} (k-itemset)



Frequent itemset: X with minimum support count



Support count (absolute support): count of transactions containing X



Association rule: A  B with minimum support and confidence



Support: probability that a transaction contains A  B s = P(A  B)



Confidence: conditional probability that a transaction having A also contains B c = P(B | A)



Association rule mining process



Find all frequent patterns (more costly)



Generate strong association rules

76

Customer buys diaper Customer buys both Customer buys beer Transaction-id Items bought 10 A, B, D 20 A, C, D 30 A, D, E 40 B, E, F 50 B, C, D, E, F

SLIDE 74

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

81