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ACCTG 6910 Building Enterprise & Business Intelligence Systems (e.bis). Association Rule Mining. Olivia R. Liu Sheng, Ph.D. Emma Eccles Jones Presidential Chair of Business. Main Expectations. Knowledge pattern in focus Definitions and examples A basic method How to tune the method

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Acctg 6910 building enterprise business intelligence systems e bis

ACCTG 6910Building Enterprise & Business Intelligence Systems(e.bis)

Association Rule Mining

Olivia R. Liu Sheng, Ph.D.Emma Eccles Jones Presidential Chair of Business


Main expectations
Main Expectations

  • Knowledge pattern in focus

  • Definitions and examples

  • A basic method

  • How to tune the method

  • Decision support applications

  • When to use association rule mining

  • Reading – T2, pp. 225 - 236


Association
Association

  • Under a given condition,

    a set of objects  (implies) another set of objects

    Examples

  • Retail items purchased together

  • Services subscribed by the same customer

  • Web pages a user access in a session

  • Courses taken by the same student

  • Medications prescribed by a doctor for a patient visit

  • Genes that are expressed at the same level


Decision support applications
Decision Support Applications

  • Customer relationship management

  • Retail merchandise placement

  • Online retail catalog design

  • Website link re-organization

  • Fraud detection

  • Gene analysis for cancer prevention


Preliminary
Preliminary

  • Set Theory

    • A set is a collection of objects.

      E.g., set A = {3,5} and set B= {1,3,5}

    • Elements of a set are the objects belong to it.

      E.g., 3 {3,5}, 3 {1,3,5}, 3 A and 3 B

    • Set X is a subset of set Y if any element in X belongs to Y, denoted as X Y. E.g., A B or {3,5} {1,3,5}


Preliminary1
Preliminary

  • Two properties of set

    • An element in a set is counted only once

      E.g., {1,3,5} = {1,3,3,5}

    • There is no order of elements in a set

      E.g., {3,1,5} = {1,3,5}


Association rules
Association Rules

  • Given: A database of transactions

  • Example of transactions:

  • a customer’s visit to a grocery store

  • an online purchase at a virtual store such as ‘Amazon.com’

  • Format of transactions:

  • date transaction ID customer ID Item

  • 1/1/99 001 001 egg

  • 1/1/99 001 001 milk


Association rules1
Association Rules

Find: patterns in the form of association rules

Association rules : correlate the presence of one set of items (X)

with the presence of another set of items (Y), denoted as X  Y

Example : {purchase egg,milk}  {bread}

How to measure correlations in association rules?


Association rules2
Association Rules

Itemset: a set of items, ex. {egg, milk}

Size of Itemset: number of items in that itemset.

The ratio of the number of transactions that purchases all items in an itemset to the total number of transactions is called the support of the itemset.


Association rules3
Association Rules

Example:

TID CID Item Price Date

101 201 Computer 1500 1/4/99

101 201 MS Office 300 1/4/99

101 201 MCSE Book 100 1/4/99

102 201 Hard disk 500 1/8/99

102 201 MCSE Book 100 1/8/99

103 202 Computer 1500 1/21/99

103 202 Hard disk 500 1/2199

103 202 MCSE Book 100 1/2199


Association rules4
Association Rules

In this example:

The support of the 2-itemset {Computer,Hard disk}

is 1/3=33.3%.

What is the support of 1-itemset {Computer}?


Association rules5
Association Rules

Two important metrics for association rules:

If two itemsets X and Y co-exist in a transaction database,

the association rule XY holds with

supports s which is the ratio of

the # oftransactions purchasing both X and Y

to (÷) the total # of transactions

confidence c which is the ratio of

the # oftransactions purchasing both X and Y

to (÷) the # of transactions purchasing X only.


Association rules6
Association Rules

Association rule: {Computer} {Hard disk}

Support: 1/3=33.3%

Confidence: 1/2=50%

How about {Computer} {MCSE book}

{Computer, MCSE book}  {Hard disk}???


Association rule mining
Association Rule Mining

  • Association rule mining: find all association rules with support

  • no less than user-specified minimum support and confidence no less than user-specified minimum confidence in a database

    • For small problems, the process

    • of mining association rules is not that complex.

    • How about a transaction database with 1billion transactions

    • and 1million different items?

    • An efficient algorithm is needed!


Association rules7
Association Rules

  • Two Steps in Association rule mining:

  • Find all large or frequent itemsets that have support above user-specified minimum support.

  • For each large itemset L, find all association rules in the form of a(L-a) where a and (L-a) are non-empty subsets of L.

  • Example: find all association rules in the example with minimum support 60% and minimum confidence 80%.


Association rule mining1
Association Rule Mining

  • Step 2 is trivial compared to step 1:

  • Exponential search space

  • Size of transaction database


Apriori algorithm
Apriori Algorithm

  • Apriori is an efficient algorithm to discover all large itemsets from a huge database with large number of items.

  • Apriori is developed by two researchers from IBM Almaden Research Lab.


Apriori algorithm1
Apriori Algorithm

  • Apriori algorithm is based on Apriori property.

  • Apriori property is that any subset of a large itemset must be large.


Apriori algorithm2
Apriori Algorithm

  • Step 1: Scan DB one time to find all large 1-itemsets.

  • Step 2: Generate candidate K-itemsets from large (k-1)-itemsets.

  • Step 3: Find all large k-itemsets from candidate k-itemsets by scanning DB once

  • Go back to step 2 and stop until no cadidate itemsets can be generated.


Apriori algorithm3
Apriori Algorithm

  • Step 2

    • Candidate k-itemsets are k-itemsets that could be large.

    • Why generate candidate k-itemsets only from large (k-1) itemsets?

    • How to generate?

      • Step 2-1: Join: Two large (k-1)-itemsets, L1 amd L2, that are joinable must satisfy the following conditions:

        • L1(1)=L2(1) and L1(2)=L2(2) and …. L1(K-2)=L2(K-2)

        • L1(K-1)<L2(K-1)

      • Step 2-2: Prune: prune itemsets generated in step 2-1 that have subset not large.


Apriori algorithm4
Apriori Algorithm

Minimum support =40%

Minimum confidence =70%


Association rule mining2
Association Rule Mining

Tid items

100 1, 3, 4, 6

200 2, 3, 5, 7

300 1, 2, 3, 5, 8

400 2, 5, 9, 10

500 1, 4

Minimum Support: 40%

Large 1-itemset:

{1} support=3/5=60%

{2} support=3/5=60%

{3} support=3/5=60%

{4} support=2/5=40%

{5} support=3/5=60%


Association rule mining3
Association Rule Mining

Large 1-itemset:

{1} support=3/5=60%

{2} support=3/5=60%

{3} support=3/5=60%

{4} support=2/5=40%

{5} support=3/5=60%

Candidate 2-itemset:

{1, 2} {1, 3} {1, 4} {1, 5}

{2, 3} {2, 4} {2, 5}

{3, 4} {3, 5}

{4, 5}


Association rule mining4
Association Rule Mining

Candidate 2-itemset:

{1, 2} {1, 3} {1, 4} {1, 5}

{2, 3} {2, 4} {2, 5}

{3, 4} {3, 5}

{4, 5}

Large 2-itemset:

{1, 3} support=2/5=40%

{1, 4} support=2/5=40%

{2, 3} support=2/5=40%

{2, 5} support=3/5=60%

{3, 5} support=2/5=40%


Association rule mining5
Association Rule Mining

Large 2-itemset:

{1, 3} support=2/5=40%

{1, 4} support=2/5=40%

{2, 3} support=2/5=40%

{2, 5} support=3/5=60%

{3, 5} support=2/5=40%

Candidate 3-itemset:

{1, 3, 4}

{2, 3, 5}


Association rule mining6
Association Rule Mining

Candidate 3-itemset:

{1, 3, 4}

{2, 3, 5}

Large 3-itemset:

{2, 3, 5} support=2/5=40%

Candidate 4-itemset:

No candidate 4-itemset. Stop.


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