Explain APRIORI PRINCIPLE.

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 APRIORI PRINCIPLE

  • The Apriori principle states that if an item set is frequent, then all of its subsets must also be frequent. For example, if (Rubber, Book, pencil) is frequent, so is [Rubber, Book), [Rubber. pencil], [Book, pencil], [Rubber), (Book), [(pencil). The Apriori principle holds due to the following property of the support measure:-
  • VX, Y: (XY)s(X) 2 s(Y) Where, X and Y are itemsets, that is, Support of an itemset never exceeds the support of its subsets. This property is also known as anti-monotone or property of support.
  • For example, consider the dataset D shown in table 5.1 above. Based on the given dataset in table 5.1 support of itemset (Pencil) 4 which is greater than the support of superset itemset (Pencil, Rubber) = 2. Similarly, support (Paper)> support (Pencil, Paper) and support (Book, Rubber) > support (Book, Rubber, Ruler) also holds. 
  • This property is used by the Apriori algorithm to reduce the complexity of the candidate generation as: "If there is any item set which is infrequent, its superset should not be generated or tested." For example, if item-set (a, b) is infrequent then we do not need to take into account all its super-sets (a, b, c). (a, b, d) and (a, b, c, d]. That these supersets of infrequent itemset (a, b) are pruned by the Apriori algorithm. Hence, this elimination helps to improve the itemset generation process.


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