Finding Frequent Itemsets and Association Rules with Apriori

Last updatedOctober 19, 2026

Problem Setup

Scenario:Identify the item combinations that occur frequently enough in the six transactions, then use the surviving combinations to form association rules.

Given:Six transactions containing items A, B, C, D, and E, with a minimum support of 50% and a minimum confidence of 70%.

Task:Apply Apriori to generate and filter candidate itemsets by support, continue until no larger frequent itemsets remain, and then evaluate the resulting association rules against the confidence threshold.

Need a quick refresher? Review Apriori theory

Transaction Dataset

Data Point	Items (Comma-Separated)✎
P1	a, b, c
P2	a, c, d
P3	b, c, e
P4	a, b, c, d
P5	a, c, e
P6	b, d, e

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Mining Solution

Total Transactions (N): 6

Required Support Count: 3(50% of 6)

Required Confidence: 70%

Iteration 1: Finding 1-Itemsets

1. Generate Candidates (

C_{1}

)Count

{a}	4
{b}	4
{c}	5
{d}	3
{e}	3

2. Filter by Min Support (

L_{1}

)≥ 3

{a}	4
{b}	4
{c}	5
{d}	3
{e}	3

Iteration 2: Finding 2-Itemsets

1. Generate Candidates (

C_{2}

)Count

{a, b}	2Drop
{a, c}	4
{a, d}	2Drop
{a, e}	1Drop
{b, c}	3
{b, d}	2Drop
{b, e}	2Drop
{c, d}	2Drop
{c, e}	2Drop
{d, e}	1Drop

2. Filter by Min Support (

L_{2}

)≥ 3

{a, c}	4
{b, c}	3

Stopping Condition

The only possible 3-itemset is {a, b, c}, but its subset {a, b} has support count 2, below the required 3. By the Apriori property, {a, b, c} is pruned without another transaction scan.

Final Association Rules

Rule ( $X \rightarrow Y$ )	Support Count ( $X \cup Y$ )	Support Count ( $X$ )	Confidence	Status
{a} → {c}	4	4	100 %	Keep
{c} → {a}	4	5	80 %	Keep
{b} → {c}	3	4	75 %	Keep
{c} → {b}	3	5	60 %	Drop

Final Answer

Frequent itemsets:The frequent itemsets are {a}, {b}, {c}, {d}, {e}, {a, c}, and {b, c}.

Accepted rules:{a} → {c} (100%), {c} → {a} (80%), and {b} → {c} (75%) meet the 70% confidence requirement.

The strongest accepted rule is {a} → {c}, with 100% confidence: every transaction containing a also contains c. The reverse rule has only 80% confidence because c also appears in a transaction without a. This shows why association rules must be evaluated in both directions.

Exam Takeaway

Convert minimum support into a count before filtering: For $N$ transactions and minimum support $s$ , use $\lceil sN \rceil$ as the minimum required count. An itemset meeting the threshold exactly must be retained.
Prune candidates using the Apriori property: A larger itemset cannot be frequent if any of its subsets are infrequent. Check the relevant subsets before counting a new candidate to avoid unnecessary scans.
Confidence depends on the rule's direction: For $X \rightarrow Y$ , divide the support count of $X \cup Y$ by the support count of $X$ . Reversing the rule changes the denominator, so calculate each direction separately.