Apriori Algorithm

Definition

Apriori algorithm (Agrawal, Mannila, Srikant, Toivonen, & Verkamo, 1996) is a data mining method which outputs all frequent itemsets and association rules from given data.

Input: set $\mathcal I$ of items, multiset $\mathcal{D}$ of subsets of $\mathcal I$, frequency threshold min_ fr, and confidence threshold min_conf.

Output: all frequent itemsets and all valid association rules in $\mathcal{D}$.

Method:

1: level := 1; frequent_sets : = ∅;

2: candidate_sets : = {{i}∣i ∈ $\mathcal I$};

3: while candidate_sets ≠∅

3.1: scan data $\mathcal{D}$ to compute frequencies of all sets in candidate_sets;

3.2: frequent_sets : = frequent_sets ∪  {C  ∈   candi-date_sets ∣frequency(C) ≥ min_ fr};

3.3 level := level + 1;

3.4: candidate_sets := $\{A \subset \mathcal{I}\mid \vert A\vert = \mbox{ level and }B \in \mbox{ frequent\_sets for all }B \subset A,\vert B\vert = \mbox{ level} - 1\}$;

4: output frequent_sets;

5: for each F ∈ frequent_sets

5.1: for each E ⊂ F, E≠∅, E≠F...