Computes the frequent itemsets in a transaction set using aggregation.

The type double function is imsls_d_aggr_apriori.

The function imsls_f_aggr_apriori performs the Apriori algorithm for association rule discovery. Association rules are statements of the form, "if X, then Y", given with some measure of confidence. The main application for association rule discovery is market basket analysis, where X and Y are products or groups of products, and the occurrences are individual transactions, or "market baskets." The results help sellers learn relationships between the different products they sell, supporting better marketing decisions. There are other applications for association rule discovery, such as the problem areas of text mining and bioinformatics. The Apriori algorithm (Agrawal and Srikant, 1994) is one of the most popular algorithms for association rule discovery in transactional datasets. For a full description of the Apriori algorithm, see imsls_f_apriori.

The interface to the function imsls_f_aggr_apriori is designed to complete the analysis over a series of steps, with each step requiring a call to the function. With this design, Apriori can be applied to separate blocks of transactions. For each dataset or block, call imsls_f_aggr_apriori with IMSLS_FREQUENT_ITEMSETS to obtain the frequent itemsets from each block. The same parameter settings, such as minimum support percentage, must be used in each separate call. Then, call imsls_f_aggr_apriori with the keyword IMSLS_UNION sequentially to obtain the union of all the frequent itemsets. The resulting set serves as the "candidate" itemsets for the global set of transactions.

An itemset which is frequent in one transaction set may or may not be frequent in the larger collection. To find the itemsets that are frequent over the entire set of transactions, imsls_f_aggr_apriori performs another pass through the individual blocks, this time counting the occurrences of each of the itemsets in each of the transaction sets. This step can be done in parallel, using keyword IMSLS_COUNT. The next step is then to sum up the individual counts before filtering for the frequent itemsets. This is achieved with the keyword IMSLS_SUM, applied successively to pairs of previous counts. After this step, the frequencies of each itemset over all of the transactions are known and it remains to be seen if any meet the threshold to be considered "frequent". The final step in determining the frequent itemsets is IMSLS_UPDATE_FREQ_ITEMSETS. Once the frequent itemsets are known, the strong association rules can be found using the step, IMSLS_ASSOCIATION_RULES , although this is not a special step in the aggregation. The method is due to Savasere, Omiecinski, and Navathe (1995) and is also summarized and compared with other approaches in Rajaraman and Ullman (2011).

Since imsls_f_aggr_apriori can operate on subsets of data, it can be used when physical memory cannot hold the entire data set. Additionally, this design may be useful in parallel computing environments where nodes can be programmed to calculate intermediate results in parallel.

The data structures used by imsls_f_aggr_apriori are described below. (For imsls_d_aggr_apriori, the structure names are Imsls_d_apriori_itemsets, Imsls_d_association_rules, and Imsls_d_rule_components where type float becomes double).

Structure definitions are provided for informational purposes and may be subject to change.

This example shows how to apply Apriori to separate blocks of data and combine results. The data are two separate blocks of 50 transactions involving five different product IDs. The minimum support percentage is set to 0.30, providing a minimum required support of 30 transactions overall.