Association Rule Mining Example

8/13/2019 Association Rule Mining Example

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1)

a) Define what is Apriori principle and briefly discuss why Apriori principle is

useful in association rule mining.

Apriori principle is,

If an item set is frequent, then all of its subsets must also frequent, or if an item set

is infrequent then all its supersets must also be infrequent.

Apriori principle reduce the number of candidate item sets in an association rule mining

process by eliminating the candidates that are infrequent and leaving only those that are

frequent. As a result the number of remaining candidate item sets ready for further support

checking becomes much smaller, which dramatically reduce the computation, I/O cost and

memory requirement. Also in Apriori principle support of an item set never exceeds thesupport of its subsets. This is known as the anti-monotone property of support. By using

Apriori principle it avoids the effort wastage of counting the item sets that are known to be

infrequent. Because of these reasons Apriori principle is very useful in association rule

mining.

b) Compare and contrast FP-Growth algorithm with Apriori algorithm.

Main difference between Apriori algorithm and FP-Growth algorithm is,

Apriori algorithm generates candidate item sets and test if they are frequent. But the

FP-Growth algorithm allows frequently item set discovery without candidate item set

generation.

Withal, there are more differences between Apriori algorithm and FB-Growth

algorithm as listed below.

Apriori algorithm FP-Growth algorithm

Use apriori property and join and pruneproperty

It construct conditional frequent patterntree and conditional pattern base from

database which satisfy minimum support

Due to large number of candidates are

generated require large memory space

Due to compact structure and no

candidate generation require less

memory

Multiple scans for generating candidate

sets

Database scanning happens twice only

Execution time is higher than FP-Growth

algorithm as time is wasted in producing

candidates every time

Execution time is less than apriori

algorithm


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2) Consider the market basket transactions given in the following table. Let

min_sup = 40% and min_conf = 40%.

Transaction ID Items Bought

T1 A,B,C

T2 A,B,C,D,E

T3 A,C,D

T4 A,C,D,E

T5 A,B,C,D

a) Find all the frequent item sets using Apriori algorithm.

Min_sup = 40% and min_conf = 40%

Minimum Support = 40% = 2/5


T1 A,B,C

T2 A,B,C,D,E

T3 A,C,DT4 A,C,D,E

T5 A,B,C,D

Item Number of Transactions

A 5

B 3

C 5

D 4

E 2


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Item Pairs Number of Transactions

A,B 3

A,C 5

A,D 4

A,E 2

B,C 3

B,D 2

B,E 1

C,D 4

C,E 2

D,E 2

Item Pairs Number of Transactions

A,B 3

A,C 5

A,D 4

A,E 2

B,C 3

B,D 2

C,D 4

C,E 2D,E 2

{A,B} & {A,C} A,B,C

{A,B} & {A,D} A,B,D

{A,B} & {A,E} A,B,E

{A,C} & {A,D} A,C,D

{A,C} & {A,E} A,C,E

{A,D} & {A,E} A,D,E

{B,C} & {B,D} B,C,D

{C,D} & {C,E} C,D,E


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Item Pairs Number of transactions

A,B,C 3

A,B,D 2

A,B,E 1

A,C,D 4

A,C,E 2

A,D,E 2

B,C,D 2

C,D,E 2

Item Pairs Number of transactionsA,B,C 3

A,B,D 2

A,C,D 4

A,C,E 2

A,D,E 2

B,C,D 2

C,D,E 2

{A,B,C} & {A,B,D} A,B,C,D

{A,C,D} & {A,C,E} A,C,D,E

Item Pairs Number of transactions

A,B,C,D 2

A,C,D,E 2

According to Apriori principle both {A,B,C,D} and {A,C,D,E} sets are bought together

frequently.


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b) Obtain significant decision rules.Subset of {A,B,C,D}

{A} , {B} , {C} , {D} , {A,B} , {A,C} , {A,D} , {B,C} , {B,D} , {C,D} , {A,B,C} , {A,B,D} , {A,C,D} , {B,C,D}

{A} {B,C,D}C = SUP {A,B,C,D} / SUP {A}

= 2/5

= 40%

{B} {A,C,D}C = SUP {A,B,C,D} / SUP {B}

= 2/3

= 66.6%

{C} {A,B,D}C = SUP {A,B,C,D} / SUP {C}

= 2/5

= 40%

{D} {A,B,C}C = SUP {A,B,C,D} / SUP {D}

= 2/4

= 50%

{A,B} {C,D}C = SUP {A,B,C,D} / SUP {A,B}

= 2/3

= 66.6%

{A,C} {B,D}C = SUP {A,B,C,D} / SUP {A,C}

= 2/5

= 40%

{A,D} {B,C}C = SUP {A,B,C,D} / SUP {A,D}

= 2/4

= 50%


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{B,C} {A,D}C = SUP {A,B,C,D} / SUP {B,C}

= 2/3

= 66.6%

{B,D} {A,C}C = SUP {A,B,C,D} / SUP {B,D}

= 2/2

= 100%

{C,D} {A,B}C = SUP {A,B,C,D} / SUP {C,D}

= 2/4

= 50%

{A,B,C} {D}C = SUP {A,B,C,D} / SUP {A,B,C}

= 2/3

= 66.6%

{A,B,D} {C}C = SUP {A,B,C,D} / SUP {A,B,D}

= 2/2

= 100%

{A,C,D} {B}C = SUP {A,B,C,D} / SUP {A,C,D}

= 2/4

= 50%

{B,C,D} {A}C = SUP {A,B,C,D} / SUP {B,C,D}

= 2/2

= 100%


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Rule Confidence

{A} {B,C,D} 40%

{B} {A,C,D} 66.6%

{C} {A,B,D} 40%

{D} {A,B,C} 50%

{A,B} {C,D} 66.6%

{A,C} {B,D} 40%

{A,D} {B,C} 50%

{B,C} {A,D} 66.6%

{B,D} {A,C} 100%

{C,D} {A,B} 50%

{A,B,C} {D} 66.6%

{A,B,D} {C} 100%

{A,C,D} {B} 100%

{B,C,D} {A} 50%

Subset of {A,C,D,E}

{A} , {C} , {D} , {E} , {A,C} , {A,D} , {A,E} , {C,D} , {C,E} , {D,E} , {A,C,D} , {A,C,E} , {A,D,E} , {C,D,E}

{A} {C,D,E}C = SUP {A,C,D,E} / SUP {A}

= 2/5

= 40%

{C} {A,D,E}C = SUP {A,C,D,E} / SUP {C}

= 2/5

= 40%

{D} {A,C,E}C = SUP {A,C,D,E } / SUP {D}

= 2/4

= 50%

{E} {A,C,D}C = SUP { A,C,D,E } / SUP {E}

= 2/2

= 100%


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{A,C} {D,E}C = SUP { A,C,D,E } / SUP {A,C}

= 2/5

= 40%

{A,D} {C,E}C = SUP { A,C,D,E } / SUP {A,D}

= 2/4

= 50%

{A,E} {C,D}C = SUP { A,C,D,E } / SUP {A,E}

= 2/2

= 100%

{C,D} {A,E}C = SUP { A,C,D,E } / SUP {C,D}

= 2/4

= 50%

{C,E} {A,D}C = SUP { A,C,D,E } / SUP {C,E}

= 2/2

= 100%

{D,E} {A,C}C = SUP { A,C,D,E } / SUP {D,E}

= 2/2

= 100%

{A,C,D} {E}C = SUP { A,C,D,E } / SUP {A,C,D}

= 2/4

= 50%

{A,C,E} {D}C = SUP { A,C,D,E } / SUP {A,C,E}

= 2/2

= 100%


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{A,D,E} {C}C = SUP { A,C,D,E } / SUP {A,D,E}

= 2/2

= 100%

{C,D,E} {A}C = SUP { A,C,D,E } / SUP {C,D,E}

= 2/2

= 100%

Rule Confidence

{A} {C,D,E} 40%

{C} {A,D,E} 40%

{D} {A,C,E} 50%

{E} {A,C,D} 100%

{A,C} {D,E} 40%

{A,D} {C,E} 50%

{A,E} {C,D} 100%

{C,D} {A,E} 50%

{C,E} {A,D} 100%

{D,E} {A,C} 100%

{A,C,D} {E} 50%

{A,C,E} {D} 100%{A,D,E} {C} 100%

{C,D,E} {A} 100%


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c) Derive the FP-Tree for the above transaction table.


T1 A,B,CT2 A,B,C,D,E

T3 A,C,D

T4 A,C,D,E

T5 A,B,C,D

Support for each item sets

A = 5/5 = 100%

B = 3/5 = 60%

C = 5/5 = 100%

D = 4/5 = 80%

E = 2/5 = 40%

According to Support

A,C,D,B,E

Re-arrange the table


T1 A,C,B

T2 A,C,D.B,E

T3 A,C,DT4 A,C,D,E

T5 A,C,D,B


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FP-Tree

After TID T1

After TID T2

After TID T3

A1

Null

C1

B1

Null

B1

A2

C2

D1

B1

E1

Null

B1

A3

C3

D2

B1

E1


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After TID T4

After TID T5

E1

Null

B1

A4

C4

D3

B1

E1

E1

Null

B1

A5

C5

D4

B2

E1

Association Rule Mining Example

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