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Apriori on t1-t5 with rules

Short answer

Apriori with min_sup=2 yields 15 frequent itemsets, largest {A,B,C,E}. 37 strong rules (conf≥60%) include A→C, B→E (100%), B→C (75%), A→B (66.7%), sorted by confidence.

Identify the candidate and large item sets of the following transaction table. Use Apriori algorithm with minimum support 2. Also, indicate association rules generated, underline the strong ones and sort them by confidence. (min_conf = 60%)

Transaction idItems
t1{A, C, D}
t2{B, C, E}
t3{A, B, C, E}
t4{B, E}
t5{A, B, C, E}

Minimum support count = 2, minimum confidence = 60%. Transactions: t1 {A, C, D}; t2 {B, C, E}; t3 {A, B, C, E}; t4 {B, E}; t5 {A, B, C, E}.

Frequent itemsets by Apriori

C₁: A 3, B 4, C 4, D 1, E 4 → D is removed. L₁ = {A, B, C, E}.

C₂ and L₂

ItemsetCountFrequent?
A, B2Yes
A, C3Yes
A, E2Yes
B, C3Yes
B, E4Yes
C, E3Yes

C₃ and L₃ (all subsets frequent, no pruning)

ItemsetCountFrequent?
A, B, C2Yes
A, B, E2Yes
A, C, E2Yes
B, C, E3Yes

C₄ and L₄: {A, B, C, E} count 2 → frequent. No C₅.

Total frequent itemsets: 4 + 6 + 4 + 1 = 15.

Association rules

Every non-empty proper subset X of each frequent itemset L (size ≥ 2) gives X → L − X with confidence = count(L)/count(X). Rules are sorted by confidence; the strong rules (≥ 60%) are in bold.

RuleSupport countConfidenceStrong?
A → C33/3 = 100.0%Yes
B → E44/4 = 100.0%Yes
E → B44/4 = 100.0%Yes
A, B → C22/2 = 100.0%Yes
A, B → C, E22/2 = 100.0%Yes
A, B → E22/2 = 100.0%Yes
A, E → B22/2 = 100.0%Yes
A, E → B, C22/2 = 100.0%Yes
A, E → C22/2 = 100.0%Yes
B, C → E33/3 = 100.0%Yes
C, E → B33/3 = 100.0%Yes
A, B, C → E22/2 = 100.0%Yes
A, B, E → C22/2 = 100.0%Yes
A, C, E → B22/2 = 100.0%Yes
B → C33/4 = 75.0%Yes
B → C, E33/4 = 75.0%Yes
C → A33/4 = 75.0%Yes
C → B33/4 = 75.0%Yes
C → B, E33/4 = 75.0%Yes
C → E33/4 = 75.0%Yes
E → B, C33/4 = 75.0%Yes
E → C33/4 = 75.0%Yes
B, E → C33/4 = 75.0%Yes
A → B22/3 = 66.7%Yes
A → B, C22/3 = 66.7%Yes
A → B, C, E22/3 = 66.7%Yes
A → B, E22/3 = 66.7%Yes
A → C, E22/3 = 66.7%Yes
A → E22/3 = 66.7%Yes
A, C → B22/3 = 66.7%Yes
A, C → B, E22/3 = 66.7%Yes
A, C → E22/3 = 66.7%Yes
B, C → A22/3 = 66.7%Yes
B, C → A, E22/3 = 66.7%Yes
C, E → A22/3 = 66.7%Yes
C, E → A, B22/3 = 66.7%Yes
B, C, E → A22/3 = 66.7%Yes
B → A22/4 = 50.0%No
B → A, C22/4 = 50.0%No
B → A, C, E22/4 = 50.0%No
B → A, E22/4 = 50.0%No
C → A, B22/4 = 50.0%No
C → A, B, E22/4 = 50.0%No
C → A, E22/4 = 50.0%No
E → A22/4 = 50.0%No
E → A, B22/4 = 50.0%No
E → A, B, C22/4 = 50.0%No
E → A, C22/4 = 50.0%No
B, E → A22/4 = 50.0%No
B, E → A, C22/4 = 50.0%No

Answer: 15 frequent itemsets (largest {A, B, C, E}). 50 rules are generated (12 from the 2-itemsets, 24 from the 3-itemsets and 14 from the 4-itemset). Of these, 37 are strong (14 at 100%, 9 at 75% and 14 at 66.7%), and the other 13 have confidence 50%.

✓ Answer checked by Claude Opus 5.5 (high effort)

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