Apriori algorithm
- 1. DEFINITION OF APRIORI ALGORITHM • The Apriori Algorithm is an influential algorithm for mining frequent itemsets for boolean association rules. • Apriori uses a "bottom up" approach, where frequent subsets are extended one item at a time (a step known as candidate generation, and groups of candidates are tested against the data. • Apriori is designed to operate on database containing transactions (for example, collections of items bought by customers, or details of a website frequentation).
- 2. KEY CONCEPTS Frequent Itemsets: All the sets which contain the item with the minimum support (denoted by 𝐿𝑖 for 𝑖𝑡ℎ itemset). Apriori Property: Any subset of frequent itemset must be frequent. Join Operation: To find 𝐿𝑘 , a set of candidate k-itemsets is generated by joining 𝐿𝑘−1 with itself.
- 4. MARKET BASKET ANALYSIS Provides insight into which products tend to be purchased together and which are most amenable to promotion. Actionable rules Trivial rules • People who buy chalk-piece also buy duster Inexplicable • People who buy mobile also buy bag
- 6. The Apriori Algorithm : Pseudo Code • Join Step: 𝐶𝑘 is generated by joining 𝐿𝑘−1 with itself • Prune Step: Any (k-1)-itemset that is not frequent cannot be a subset of a frequent k-itemset • Pseudo-code :𝐶𝑘: Candidate itemset of size k 𝐿𝑘: frequent itemset of size k L1 = {frequent items}; for (k = 1; Lk !=null; k++) do begin Ck+1 = candidates generated from Lk; for each transaction t in database do increment the count of all candidates in Ck+1 that are contained in t Lk+1 = candidates in Ck+1 with min_support end return k Lk;
- 7. LIMITATIONS Apriori algorithm can be very slow and the bottleneck is candidate generation. For example, if the transaction DB has 104 frequent 1- itemsets, they will generate 107 candidate 2-itemsets even after employing the downward closure. To compute those with sup more than min sup, the database need to be scanned at every level. It needs (n +1 ) scans, where n is the length of the longest pattern.
- 8. METHODS TO IMPROVE APRIORI’S EFFICIENCY Hash-based itemset counting: A k-itemset whose corresponding hashing bucket count is below the threshold cannot be frequent Transaction reduction: A transaction that does not contain any frequent k- itemset is useless in subsequent scans Partitioning: Any itemset that is potentially frequent in DB must be frequent in at least one of the partitions of DB. Sampling: mining on a subset of given data, lower support threshold + a method to determine the completeness Dynamic itemset counting: add new candidate itemsets only when all of their subsets are estimated to be frequent
- 9. APRIORI ADVANTAGES/DISADVANTAGES Advantages • Uses large itemset property • Easily parallelized • Easy to implement Disadvantages • Assumes transaction database is memory resident. • Requires many database scans