i) Find all frequent patterns using AprioriAlgorithm.
ii) List strong association rules.

1. $c_1$ = { {A} 6

{B} 7

{C} 6

{D} 7

{E} 6

{F} 3

{G} 1 X

{H} 3

{I} 1 X

{K} 3

{L} 4

Minimum support = 30%

$= \frac{30}{100} * 10$

$\therefore$ $L_1 $= { A } { B } { C } { D } { E } { F } { H } { K } { L } }

2.

$c_2 = L_1 x L_1$

= { { A B } 4 { C D} 5 { F H} 2 X

{ A C} 4 { C E } 2 X { F K } 0 X

{ A D } 4 { C F } 1 X { F L } 2 X

{ A E } 3 { C H } 1 X { H K } 1 X

{ A F } 1 X { C K } 2 X { H L } 2 X

{ A H } 2 X { C L } 1 X { K L } 1 X

{ A K } 2 X { D E } 4

{ A L } 2 X { D F } 2 X

{ B C } 5 { D H } 1 X

{ B D } 6 { D K } 2 X

{ B E } 4 { D L } 2 X

{ B F } 1 X { E F } 2 X

{ B H } 0 X { E H } 2 X

{ B K } 2 X { E K } 2 X

{ B L } 2 X { E L } 3

$\therefore$ $L_2$ = { { A B } { A C} { A D} { A E}

{ B C } { B D } { B E }

{ C D } { D E } { E L }

}

$L_3 = L_2 X L_2$ SC

= { { A B C } 3

{ A B D } 4

{ A B E} 2 X

{ A C D} 3

{ A C E } ---- Apriori

{ A D E } 2 X

{ B C D } 5

{ B C E } ---- X Apriori

{ B D E } 3

}

$\therefore$ $L_3$ { { A B C } { A B D} { A C D}

{ B C D } { B D E } }

4. $C_4 = L_3 X L_3$

= { { A B C D } 2 X

}

$\therefore$ $L_4 = \theta$

Confidence threshold = 70%

1. L = { A B C } $\rightarrow$ 3

{ A } { B } { C } { A B } { A C} { B C }

A = BC 3/6 > 70%

B = AC 3/7 > 70%

C = AB 3/6 > 70%

A B = C 3/4 > 70%

AC = B 3/4 > 70%

BC = A 3/5 > 70%

2. L = { A B D } $\therefore 4$

{A} {B} {D} {AB} {AD} {BD}

A = B D 4/6 > 70% X

B = A D 4/7 > 70% X

D = AB 4/7 > 70% X

AB = D 4/4 > 70% $\checkmark$

AD = B 4/4 > 70% $\checkmark$

BD = A 4/6 > 70% X

3. L = { A C D} $\rightarrow$ 3

{A} {C} {D} { A C } { A D} { C D }

A = CD 3/6 > 70% X

C = AD 3/6 > 70% X

D = AC 3/7 > 70% X

AC = D 3/4 > 70% $\checkmark$

AD = C 3/4 > 70% $\checkmark$

CD = A 3/5 > 70% $\checkmark$

4. L = {B C D} $\rightarrow$ 5

{B} {C} {D} {BC} {BD} {CD}

B = CD 5/7 > 70% $\checkmark$

C = BD 5/6 > 70% $\checkmark$

D = BC 5/7 > 70% $\checkmark$

B C = D 5/5 > 70% $\checkmark$

BD = C 5/6 > 70% $\checkmark$

CD = B 5/5 > 70% $\checkmark$

5. L = { B D E } $\rightarrow$ 3

{B} {D} {E} {E D} {B E} {D E}

B = DE 3/7 > 70% X

D = BE 3/7 > 70% X

E = BD 7/6 > 70% X

BD = E 3/6 > 70% X

BE = D 3/4 > 70% $\checkmark$

DE = 12 3/4 > 70% $\checkmark$