A priori algorithm
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Apriori is an efficient association rule mining algorithm, developed by Agrawal et al (Agrawal 93, Agrawal 94)
Apriori (Agrawal 94) employs breadth-first search and uses a hash tree structure to count candidate item sets efficiently. The algorithm generates candidate item sets (patterns) of length <math>k<math> from <math>k-1<math> length item sets. Then, the patterns which have an infrequent sub pattern are pruned. According to the downward closure lemma, the generated candidate set contains all frequent <math>k<math> length item sets. Following that, the whole transaction database is scanned to determine frequent item sets among the candidates. For determining frequent items in a fast manner, the algorithm uses a hash tree to store candidate itemsets. Note: A hash tree has item sets at the leaves and hash tables at internal nodes (Zaki, 99).
Apriori is designed to operate on databases containing transactions (eg: collection of items bought by customers or details of a website frequentation). Other algorithms are designed for finding association rules in data having no transactions (Winepi and Minepi), or having no timestamps (dna sequencing).
Algorithm
Apriori<math>(T,\varepsilon)<math>
<math>L_1 \gets \{ <math> large 1-itemsets <math> \} <math>
<math>k \gets 2<math>
while <math> L_{k-1} \neq \varnothing <math>
<math>C_k \gets <math>Generate<math>(L_k-1)<math>
for transactions <math>t \in T<math>
<math>C_t \gets <math>Subset<math>(C_k,t)<math>
for candidates <math>c \in C_t<math>
<math>\mathrm{count}[c] \gets \mathrm{count}[c]+1<math>
<math>L_k \gets \{ c \in C_k | ~ \mathrm{count}[c] \geq \varepsilon \}<math>
<math>k \gets k+1<math>
return <math>\bigcup_k L_k<math>
References
- Rakesh Agrawal and Tomasz Imielinski and Arun N. Swami, Mining Association Rules between Sets of Items in Large Databases, Proceedings of the 1993 ACM SIGMOD International Conference on Management of Data.
- Rakesh Agrawal and Ramakrishnan Srikant, Fast Algorithms for Mining Association Rules, Proc. 20th Int. Conf. Very Large Data Bases (VLDB), 1994.
- Heikki Mannila and Hannu Toivonen and A. Inkeri Verkamo, Efficient algorithms for discovering association rules, AAAI Workshop on Knowledge Discovery in Databases (KDD-94), 1994.
- Mohammed Javeed Zaki and Srinivasan Parthasarathy and Mitsunori Ogihara and Wei Li, Parallel Algorithms for Discovery of Association Rules, Data Mining and Knowledge Discovery, 1997.